JPRS ID: 10641 TRANSLATION PHOSPHATE LASER GLASS BY N.Y. ALEKSEYEV ET AL.

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7 July 1982
Translation
PHOSPHATE LASER GLASS
By N. Y. Atekveyev st al.
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JPRS L/10641
7 July 1982
PHOS.PHATE IASER GI.ASS
Moscow LAZERNYYE FOSFATNYXE STEKLA in Russia 1980 (siqned to press
28 Nov 80) pp 1-352 -
IBook "Phosphate Lassr Glasa" by Nikolay Yefimovich Alekseyev,
Valentin Pavlovich GapantseNi, Mark Yefremovich Zhabotinskiy, Valeriy
- Borisovich Rravchenko and Yu.riy Petrovich Rudnitskiy, edited by
M. Ye. Zhabotinskiy, "Nauka", 2600 copies, 352 pages]
CONTENTS
- Anno ta t i.on
Foreword
Introduction
CHAPTER 1. GENERAL REQUIREMENTS ON PHYSICAL PAItAMETERS OF LASER G:ASS
�1.1. Spectral Luminescence Parameters Determining the Energy
Characteristics of Glass
�1.2. Nonlinearity of the Index of Refraction of Glass
�1.3. Resistance of %3lass to Laser Emisaion
�1.4. Thermooptical Distortions in Active Laser Elements
�1.5. Thermophysical Properties and Thermal Strength of Laser Glass
�1.6. General Description of Laser Glasa
CHAPTER 2. STRUCTURE OF PHOSPHATE GLASS
CHAPTER 3. NONRADIATING ELECTRON EXCITATION ENERGY TRANSFER IN LASER GLASS
�3.1. Cl.assification or Nonradiating Tranafer Processes
�3.2. Ion-Ion Excitation Transfer--Theoretical Concepts
�3.3. Ion-Ion Transfer--Experimental Results
�3.4. Ion.-Vibrational Excitation Transfer
CHAPTER 4. NEODYMIUM-I30PED PHOSPHATE GLASS
�4.1. General Description of Neodymium Laser Glass
�4.2. Spectral Lumineacent Charactaristics of Neodymium
Phosphate Glass
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20
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29
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FUR UM'NICIAI. UbE ()NI.Y
�4.3. Spectroscopic Methods of Measuring Some Lurainescence aad
Lasing CharRCteriatics of Neodymium Glass 140
�4.4. C;:oss Section of Induced Emission of Nd9+ Ions in Glass 144
�4.5. Laaer Methode of Determining the Induced Emission Cross Section 151
�4.6. Value of the Effective Cross Sectian of the Induced Emission
_ of Nd9+ in Phosphate GZass 155
64.7. Amplification of Laser Pulses in Phosphate Glass Doped with
Nd9+ Ions 159
�4.8. Lasing Characteristica of Neodymium-Doped Phosphate Glass 164
�4.9. Free-Running Phosphate Glasa Lasers . 170
�4.10. Use of Phosphate Glass to Obtain Short and Ultrashort
- Pulses 173
- CHAPTER 5. THERMOOFTICAL PROPERTIES OF PHOSPHATE GLASS AND SELECTION OF
NEODYMIUM GLASS :'OR LASERS OF VARIOUS TYPES 175
�5.1. Thermooptical Characteristica of Phosphate Glase 175 ,
�5.2. Phosphate Glass for Pulse-Periodic Lasers 190
�5.3. Glass for High-Energy Laser Systema 204
CHAPTER 6. ERBIUM-AOPED LASER GLASS
208
�6.1. Specific Nature of Erbium Lasers and Requirements on the
Active Medium 208
�6.2. Spectral Luminescent Properties of Erbium Glass 217
�6.3.. Tube-Pumped Erbium Lasers 230
�6.4. Erbium Laser Reemitters. Free Lasing Mode 234
�6.5. Possibilities of the ELP Under Lasing and Amplification
Conditions of KI [Short Pulaes] and SKI [Supershort Pulses] 240
Bibliography
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j
ANNOTATION
A detailed description is presented of the physical properties of new efficient
laser materials--phosphate glass activated by rare earth ions. The possibilities
and prospects for their application in various types of lasers are demonstrated.
Information is presented the structure of phosphate glass, the spectral lumines-
cence, lasing, thermooptical, nonlinear optical characteristics of laser phosphate
glass activated by Nd3} ions. The processes of energy transport and quenching of
luminescence in phosphate glass, and sensitizacion of luminescence in glass co-
activated by Nd9+ and Ybg+, Yb9+ and Er9+ ions were investigated.
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FOREWORD
Phosphate glass, which is now beeoming more and more widespread in the basic
industrially developed countries, first appeared in the Soviet Union. Phos-
phate laser glass has especially great significance in creating powerful and
superpowerful lasers and lasers that operate in the periodically repeating
pulse mode.
At the present time it is possible to talk about the completion of a
defined phase of research and development of phasphate laser glass, recogni-
tion of its advantages and the beginning of industrial output and applica-
tion in series laser systems. This determines the urgency o� the pro;..)sed
monograph. It must be noted that the last exhausicive survey of laser glass was published
about 10 years ago and, jusr as the preceding ones, contained almost no
iriormation on phosphate laser glass.
The authors of this book are participants in the development and investigation
of many types of phosphate laser glass, including the firet, so that a sig-
nificant part oi its content is based on their work, and the book itself does
not pretend to encompass the mult;faceted problem of laser glass completely.
A dincussion is pxesented of the results of physical and spectral luminescence
studies of phosphate laser glasa, the etudy of the processes of excitation
of rare earth ions, transmission of excitation and relaxation procesaes in
laser glass. The obLained data indicate both the advantages of phosphate
laser glass over other glass and the potential possibilities inherent in these
types of glass. Phyaicochemical and lasing characteristics of thja glass is
also presented, and phosphate laser glass is compared with silicate laser
glass.
The book is designed for pY~ysicists interested in studying laser materials
and processes occurring in lasers, for technologists involved with imprcving
laser materials and the active elements made from them, and for laser
designers in need of apecific characteristics of active elements without
which it is impossible to design and builci lasers.
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The book is written in six chapters.
- Chapter 1 investigates the requirements on the physical parameters of laser
glass arising from the problea[of optimizing the cha.racteristics of lasers
of various types for various purposes. These parameters include, for
examp7_e, the spectral luminscence parameters which determine the energy
_ characteristics of lasers, including their efficiency. The corresponding
parameters for lasers operating in the free lasing mode differ significantly
from those required for the short and supershort pulse modes.
Special attention is given to the parameters determining the applicability of
glass in powerful and superpowerful lasers, for which the nonlinear character-
istics, optical and thermal stability, and thsrmooptical distortior.s become
no less important than the efficiency.
Chaptei- 2 is devoted to the structure of phosphate glass. The structure of
phosphate glass differs significanfly from the structure of silicate glass,
in the final analysis, insuring the advantages of phosphate glass over sili-
cate glass. The physicochemical processes occurring when making phosphate
glass determine its structure, having features characteristic of inorganic
polymers. This, in turn, determines Che nearest vicinity of the ion activators
and the structure of subsequent coordination spheres, and at the same time
insures exceptionally good spectral luminescence and lasing characteristics
of phosphate laser glass and also the possibility of controlling its thermo-
optical characteristics.
~ The modern concepts of the mechanisms and laws of occurrence of the processes
of nonradiating electron excitation energy transfer in laser glass. An
analysis is made of var'Lous versions of ion-ion transfer, including the
' excitation energy migration process and also the processes of multiphonon
nonradiating relaxation of the excited states of rare earth ions caused by
interaction with the vibrations of admixed hydr.oxyl groups and structural
elements of the glass itself. The discussion is primarily based on original
results of the authors, the greater part of which are published for the first
time. For exhaustive substantiation of the uniqueness of the properties of
phosphate glass, the authora considered it neceasary to expand the class of
analyzed objects by using other activators and glass-like systems, which
lends the obtained results a fundamental nature. The ideas and the results
of this chapter played an important role in the development of laser phos-
phate glass.
Chapter 4 is devoted exclusively to neodymium-doped phosphate laser glass and
the possibility of its application in various types of lasers.
The primary content of Chapter 5 3s data on the thermooptical properties of
phosphate laser glass, the study of whirh permitted purposeful synthesis of
compositions with properties optimized as applied to specific problems. In
- particular, in this chapter a study is made of the problems arising when
making glass for pulsed-periodic lasers and high-energy laser sygtems. In
both cases the advantages of phosphate glass over ailicate laser glass are
especially clearly manifested.
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Ch.zpter 6 analyzes the spectral luminescence and lasing characteriatics of
erbium-doped phosphate laser glass, and the specific nature of the construc-
tion of lasers based on this gIa$s is investigated. Special attention is
given to neodymium laser pumped erbium lasers, inasmuch as the combined systems of this type permit the creation of radiation sources in the
range of 1.5 microns which are similar with respect to lasing characteristics
to neodytnium lasers, and in certain respects even superior to them in the
short aad supershort pulse amplification mode.
The limited size of the book makes it impossible to consider the properties
of phosphate laser glass coactivated by neodymium and ytterbium, which is
prospective for application in powerful amplifiers. Those'who are interested
in this subject can refer to the background material [48, 82, 85, 101].
A bibliography containing 545 references was collected up to the end of 1979.
It includes the most significant publications, but does not pretend to com-
pleteness.
The collective of authors expresses sincere appreciation to all researchers
permitting use of figures from their publications: The corresponding foot-
notes are included in the text or in the captions to the figures.
The authors acknowledge the assistance of coworkers of the IRE [Institute of
Radio Engineering and Electronics], and the IONKh [Institute of General and
Inorganic Chemistry] of the USSR Academy of Sciences, and the "Rubin" PTO
[Production and Technical Asaociation], together with which they studied and
made phosphate laser glass. They also acknowledge coworkers of the FIAN
[Physics Institure of the USSR Acadsmy of Sciences] and the C,OI [State
Insti;:ute of Optics] imeni S. I. Vavilov for useful discussion.
The materials of this book were distributed among the authors as follaws:
N. Ye. Alekseyev, �94.1 to 4.3, 4.8 to 4.10; V. P. Gapontsev, Chapters 3 and 6;
M. Ye. Zhabotinskiy, the introduction; V. B. Kravchenko, H1.4 to 1.6,
Chapter 2, �95.1 and 5.2; Yu. P. Rudnitskiy, 991.1 to 1.3, ��4.4 to 4.6,
4.7 and 5.3.
M. Ye. Zhabotinskiy
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INTRODUCTION
The 20-year mark of the laser age was reached in 1980. Industrial laser
production is being engaged in on a large scale and has acquired great sig-
nificance in the economies of the developed countries. Lasers are widely used
in industry, construction, medicine and ecientific work. Therefore the lit-
erature on lasers initially devoted primarily to investigation of such
physical problems as the problems of lasing and amplification, including
various operating modes of the laser, such physical characteristica as co-
herence and fluctuations of laser emission, its divergence and spectral com-
position, has gradually come to include the analysis of problems arising in
the design, development, production and application of lasers.
As is known, the first laser was a ruby laser. It was pumped by a pumping
tube. Soon a report came out on the first gas laser using a mixture of helium
and neon pumped by electric discharge. Thus, fram the very beginning two
competing and mutually complementary areas were distinguished--the develop-
ment of solid-state and gas lasers. Subsequently, semiconductor lasers and
liquid lasers using organic (dyes) and inorganic liquids were distinguished
- as separate areas.
The cevelopment of quantum electronics based on studying the physical pro-
cesses lea-ding to realization of the laser effect had a clearly expressed
applied nature. Researchers set the goal of increasing the pawer of lasers,
their efficiencies, assimilation of a broader and broader range of wavelengths,
inclcding the possibility of continuous wavelength adjustment, the assimila-
tion of various operating modes from conCinuous lasing to supershort pulse
lasing, and an increase in frequency stability of laser emission, and so on.
This, in turn, stimulated the search for and the investigation of new active
media suitable for use in lasers. At the present time hundreds of different
gas mixtures are known (including pure gases and metal vapor), which are
capable of lasing at different points of the optical band--from the ultra-
violet region to submillimeter. A number of crystals, liquids and glass of
different composition and an entire series of semiconductor compounds are
known, the number of which is grawing constantly.
However, the majority- of materials for which the laser effect has been
studied have not found practical application, for the set of characteristics
providing for real:Lzation of certain specific goals is encountered relatively
rarely.
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Thus, the achievement of high pulse energy and maximum high power in the
short and supershort pulse mode requires high density of the active particles
which is characteristic of solid-state active elements. In,spite of per-
sistent research and improvement of the methods of growing artificial single
crystals, until recently only two types of active crystals have found appli-
cation in industrially produced lasers. These are rubies and neodymium-doped
yttrium-aluminum garnet. The latter has found especially broad application,
for it successfully combines the mechanical and thermooptical properties of
yttrium-aluminum garnet with the laser characteristics of the neodymium ions
in this crystal. Recently neodymium-doped yttrium aluminate crystals have
been added to this list.
Continuous and pulsed-periodic neodymiinn-doped YAG and yttrium aluminate
lasers are being used successfully. They provide an average power on the
order of tens and even hundreds of watts, and in unique models, when using
special circuits and structures, they provide a power on the order of several
kilowatts. However, the cost of large monocrystalline laser elements increases
much more rapidly than the obtained power, which is explained by the diffi-
culties of growing large optically homogeneous samples.
Neodymium-doped glass was one of the first materials in which the laser ef�ect
was obtained. The superior optical chara--teristics of the glass, the high
technological level of founding and working it, availability and relat3.ve
cheapness of the raw material insured rapid progress in the creation of laser
glass and lasers based on them.
The application of lasers in industrial production processes has required
mass output of laser glass, and the problems of laser thermonuclear research
have stimulated the manufacture of large active elements with dimensions
entirely unattainable by the existing methods of grawing crystals.
Thus, glass has become the most important active element for solid-state
lasers. For a long time, only silicate glass was used, the, manufacturing
technology of which was developed to the highest degree in the optical industry.
- The efforts of physicists and process engineers were aimed at improving the
laser characteristics of silicate glass, its physicochemical and optical
parameters, such as optical homogeneity, radiation strength (body and surface),
and also chemical strength, theXmooptical and thermomechanical characteristics,
adaptability to manufacture, and so on.
Efforts to create nonsilicate laser glass, for example borate and germanate
glass, did not lead to hopeful results.
The presented book has the goal of investigating phosphate laser glass, which
has recently become one of the most important materials for making the
active elements of solid-state lasers for various purposes.
Phosphate glass was lrnown to specialists as nontechnological, it had a very
narrow range of application and was industrially produced in small quantities.
For this reason, for a number of years there was no effort made to create
phosphate laser glass.
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It was only in 1966 that the collective of researchers working at the Institute
of Radio Engineering and Electronics of the USSR Academy of Sciences, which
included the authors of this book, arrived at the con clusion of the potential
:ldvantages of phosphate laser glass if such could be created. The conclusion
followed from the results obtained by this collective while studying the
luminescence of ions of rare earth elements in polyphosphoric acids and from
known concepts regarding the structure of phoaphate glass. A collective of
coworkers of the Institute of General and Inorganic Chemistry of the UBSR
Acadetuy of Sciences, among whom V. V. Tsapkin and the late G. V. Ellert
played a leading role, became involved in this research.
As a result of purposeful research, a method of synthesizing phosphate laser
glass based on alkali and alkali earth element metaphosphates was developed.
_ In the following year neodymium-doped phosphate glass laser elements were made
which had satisfactory physicochemical properties and were superior to sili-
cate glass with respect to the primary laser characteristics. Thus, tbe
width of the lasing spectrum of the new glass was 4 angstroms as oppased to
80 to 120 angstroms for silicate glass, and the efficiency was 1.5 to 'L times
as high under identical excitation conditions. Soon this glass, under the
, name of LGS-40, became the first industrial phosphate laser glass. The dis-
advantage of this glass was relatively low chemical stability.
It must be noted that studies of the possibili.ty of creating phosphate laser
glass were performed independently at the same time by Deutschbein and his
coworkers in France. They published comprehensive results of spectral
luminescence studies of a number of compositions for neodymium-doped phosphate
glass, and they reported that lasing had been obtained.
The phosphate laser glass of the IRE Institute of the USSR Academy of Sciences
developed jointly with the LZOS and called LGS-40 M, LGS-41 and LGS-42,
has improved physicochemical characteristics.
The second generation of phosphate laser glass of the IRE Institute of the
USSR Academy of Sciences waa intended specially for application in large
industrial and research devices in which rigid rzquirements arise both with
respect to thermooptical characteristics of the glass and its efficiency.
The athermal characteristics of phosphate laser glass LGS-I were subsequently
reproduced also in the corresponding silicate glass.
A number of compositions of neodymium glass developed by the State Institute
of. Optics imeni S. I. Vavilov and the LZOS and manufactured by industry under
tile names GLS-21, GLS-22, GLS-23, GT.S-24, LGS-55 and LGS-56 must be included
in the second generation phosphate laser glass.
The next step in the development of phosphate glass was the creation of
"athermal" phosphate glass with reduced temperature dependence of the thermo-
optical characteristics (type LGS-M), with diminished concentration quench-
ing of lj.miinescence and, correspondingly, with high activator concentration
(glass of the LGS-K type developed by the IRE Institute of the USSR Academy
of Sciences, lithium neodymium phosphate glass developed by the Physics
Institute of the USSR Academy of Sciences). Recently work on highly concen-
trated glass has been started abroa3.
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Tn spite of the progress in improving the characteristics of phosphate laser
glass, one area has lagged behind, in w%ich phosphate laser glr_ss cannot
compete with yttrium-aluminimm garnet. This area involves operation in the
rapidly repeated pulse mode. In this mode the thermomechanical characteris-
tics of the material, especially its thermal conductivity and mechanical
= 5trength, acqu3re primary significance. YAG crystals have significant
advantages over glass with respect to both of these characteristics.
The known methods of strengthening glass, for example, quenching, have sig-
nificant disadvantages, among which long buildup to the operating mode and
negative effects on the thermooptical characteristics are the most undesir-
able.
The IRE Institute of the USSR Academy of Sciences developed original methods
of strengthening the active elements made of phosphate laser glass. As a
result, elements operating at a pulse repetition frequency of 10 hertz
develop almost the same average pawer as YAG active elements of the same
dimensions, under identical pumping conditions, but at appreciably less cost
- and greater availability.
- Two more advantages of phosphate laser glass must be noted.
One of these advantages is manifested in large devices designed to obtain high
power short and supershort pulses with high emission density. Nonlinear
processes leading to the appearance of internal deteriorarion as a result of
_ self-focusing turn out to be limiting factors in this case. Correspondingly,
the limiting energy flux densities in phosphate glass are approadmately twice
those in silicate glass.
A second advantage is connected with more efficient energy transfer between
rare earth ions in phosphate glass campared to silicate glass. The use of
this advantage made it possible to develop high quality erbium laser glass
sensitized by ytterbium ions. The authors of the monograph obtained lasing
in the 1.54 micron range for the first time in this glass in 1969, using
free-running neodymium-doped glass lasers as the excitation 3ource. Later,
the indicated erbium glass was brought up to industrial standards (type LGS-E),
for which, in particular, it was necessary to solve the technologically
- complicated problem of deep dehydration of it. Systematic studies were also
made of the spectral luminescence characteristics of erbium glass and the
class of problems connected with optimizing the lasing characteristics of
both laser-pumped and tube-punped erbium lasers. In 1973, one of the authors
presented convincing substantiation of the expediency of using erbium rP-
emitters of neodymium lasers as amplifying stages of powerful laser systems
designed for various applications.
Another sensitized phosphate laser glass developed and systematically studied
in those years at the IRE Institute of the USSR Academy of Sciences was
neodymium (sensitizer) and ytterbium (activator) doped glass which was pros-
pective for use in the terminal stages of pawer amplifiers for pulses of
medium duration, fram 10'6 to 10'4 seconds.
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Recently, Soviet industry has developed and is manufacturing a number of types
of phosphate laser glass, and active elements for various purposes are being
made from it.
The orientation toward silicate glass prevailed for a Iong time abroad,
ahd there was no ser3.ous concern with the develupment of phosphate glass.
However, in reccnt years the situation has changed. Industrial phospnate glass
was nroduced in ;iapan, an3 later in the United States. This glass is used in
large production units and devices for thermonuclear plasma heating in the
United States, Japan and France. The developers of laser systems for other
applications are also becoming reoriented to phosphate glass.
The possibilities of phosphate laser glass have been far from exhausted. Many
laboratories are continuing basic research in order to improve the characteris-
tics of phosphate glass and glass with several glass formers, including
phosphorus. A significant increase in the average pulse energy and power of
lasers using glass of these types, possibilities of obtaining lasing on new
wavelengths, further shortening of the duration of supershort pulses, the
application of active fibers, and so on should be expected.
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- CHAPTER l. GENERAL REQUIREMENTS ON PHYSICAL PARAMETERS OF LASER GLASS
�1.1. Spectral Luminescence Parameters Determining the Energy Characteristics
of Glass
The phenomenon of forced (induced) emission, which forms the basis of the
operation of a11 lasers is observed on interaction of the emission with a
set of exnited atoms or ions in which the population of one of the excited
states with energy Em is greater than on the lawer-lying level with an energy
of Ek. The radiation is amplified on frequencies equal to the transition
frequencies between the indicated states, as a result of emission of light
quanta coherent to the incident radiation by the excited atous. The prob-
ability of forced emission, according to the theory of interaction of radia-
tion with matter is determined by the dipole moment (the oscillator force)
of the transition and intensity of radiation. Broadening the energy levels
of the atoms as a result of their interaction with the environment decreases
the density of states in the given energy range and correspondingly decreases
the efficiency of the induced processes. The probability of the torced
transition wind �n interaction of an atom with a light beam of intensity I(v)
is easy to find using the induced emission cross section v(v):
(l(v) _ a (v) I (v).
Key: 1. ind
(1. i)
On interaction with not strictly monochromatic radiation distributed in the
frequency range comparable to the width of the spectral transition band
Avind, the total probability of the induced tra�isition is
u,N (v) dy = (t (v) I (v) dv. (l. la)
ev,I
Key: l. ind (1) (1)
If we consider that at the limits of this band
i(v) = 1 = const,
then
I ~Q (v) dv = Ivo,
(l. lb)
where vo is the integral radiation cross section.
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It is possible to show that on normalization of the function r(v) describing
the form of the spectral band, by 1, we obtain
aM = aol'(-r).
(l.lc)
In accordance with the theory of interaction of radiation with matter [1], we
have
v~, oa I ''".ti P J,
(1.2)
where rmk is the dipole moment of the transition, J=hvI is the radiation
energy f lux with frequency v= (F,m-Ek)h'1.
From expressions (1.1), (1.2), it follows that a0tijrmkj2, and the induced
emission cross section on a frequency corresponding to the maximum luminescence
band vo is inversely proportional to the halfwidth Ovp o f the b and, that is,

R (vb) C., .
:1%"i
(1.3)
varies
Let us consider how the intensity of the light beam with frequency vm,
on propagatj.on through a laser active medium. Let the populations of the m-th
and k-th levels, that is, the number of particles in th e indicated states in
1 cm3 be Nm and Nk, respectively. The variation of the intensity in the layer
of matter dx thick is determined by the difference in probabilities of emission
and absorption of photons:
dI -~QmhNm - QkmNN) I dx - armt (Nvn ok~ N"vmax'~ , where "max is the boundary frequency of
the spectrum of basic vibrations o~ the matrix, the function WDA(Z) again
becomes decreasing close to the exponential curve. Thus, the microtheory of
BPV has made it possible more precise'Ly to define the limits of applicability
of the Foerster theory and has proposed several mechanisms, for the
phenomenological approach obviously not considered. Unfortunately, on the
basis of indeterminacy of the approximations made in different models and
also as a result of the presence of parameters not subject to direct expex-
imental determination, the microtheory of BPV does not permit calculation of
absolute and relative, efficiencies of the interactions caused by these
mechanisms, which complicates the selection between the transfer models in
specific experimental situations. Nevertheless, the conclusions of the
theory of the nature of the functional dependencies WDA(e), WDA(RDA) and
WDA(T) put the "keys" in the hands of the experimenter for checking its
principles and discovering the predominating mechanisms of the ion-ion trans-
fer between RZI.
- Interrelation of the Macrocharacteristics of BPV with the Pa;rameters of the
Elementary Acts. With respect to nature of occurrence of the energy transfer
processes in the D*+A system, usually two situations are distinguished:
static and dynamic. The sign of the static nature of the BPV is absence of
spatial wandering of the excitation with respect to the donor subsystem,
which is typical of small donor concentrations. Zhe procedure of averaging
the probabilities of elementary acts with respect to configurations of the
set of statistically uniformly d{stributed particles of the donor with respect
to the acceptor was first proposed by Foerster 1256]. Later, it was developed
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in references 1274-279] and a nwnber of other etudies. In the case of multiple
approximatiora of the donor-acceptor interaction the luminescence damping
kinetics D* are described by the expression
Np( (t) = Y (t) exP ~3 ..MeP (1- 13 ) CRA tSlm} (3.4)
and, in particular, for dipole-dipole interaction by the relation
Nu (t) = Y (t) exp (-1'Yt I, (3.4a)
where ND(t) is the population of the radiating state D*; the function Y(t)
expresses the luminescence damping law D* in the absence of A(in the general
case, nonexponential); r(x) is the gamma function; CDA is the microparameter
of the interaction D*-A related to WDA by the expression WDA(R)=CDARDA'
y is the parameter determined from the expression
. y =4 3 CAAXA� (3.5)
The formulas (3.4), (3.4a; are valid for the following restrictions:
1) the inverse transfer A*->D is absent; 2) ,~'~���,/I~ ; 3) .MA/.M,,,ax < 1, where Y'm:
is the total nimber of plaees wh3ch could be occupied by acceptors per unit
volume. The last restriction provides that the averaging be carried out with-
in the limits of the statistically uniform distribution of D* with respect to A
without considering afinite number of places which can be occupied by the
accepton, 'n the nearest coordination spherea near D*; this is admiasib le
only for small A concentrations. The case NA/NMaX+1 was investigated in
[274, 2791. It was demonstrated that here the luminescence decay kinetics
approach exponential with characteristic time determined by the total sum of
the probabilities of the interaction with respect to all nodes of the acceptor
sublattice. The exponential kinetics are manifested first of all in the
initial phase of the process of luminescence decay. In [280], consideration
is given to the influence of the minimtmi distance of approach of the donor
and the acceptor Rmin. It is demonstrated that in the initial stage of decay
(for t� 6inIC DA) there ia a relatively short exponential section which can
be noted6�or NA-~N~X or for very small interactions, that is, for
c DAT ZD~min'
The formulas (3.4), (3.4a) are derived for the case of excitation by a
d-pulse.. The damping law for any other type of excitation can be written
in the form of a convolution in time:
t _
N~ (t) f NR (c) % (t - ti) dT, (3.6)
0
where a(t) is the shape of the
switching off the steady-atate
are significantly closer to ex
with an exchange nature of the
sharply from that described by
of the indicated restrictions,
optical excitation pulse. For example, after
excitation, the luminescence damping kinetics
3onential than (3.4) 12751. The decay law
interactions in the pairs D*-A also differs
formula (3.4) 1278]o Nevertheless, in spite
the 1axr (3.4) is r,uite universal and applicable
81
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according to [286], also to fhe media with nonuniform broadening if instead
of WDA we use the probability WDA averaged with respect to the transition
energies.
'kith in creased concentrations of D, the process of quenching by the acceptor
is stimulated by migration of the excitations with respect to the donor sub-
system and when finding the function ND(t) it is necessary to consider the
dynamics of the spatizl distribution of D* with respect to A. This situation
is more complicated for interpretation and it is describ ed within the frame-
work of various models of quenching [274, 278-2881. Qualitatively, the energy
migration with respect to D leads in all models to an increase in the rate
of the luminescence decay process and its exponentialization in the final
phase. The parameter of the exponential curve W defining the rate of migra-
tions controlled quenching of luminescence of D* depends not only on N.A and CDAS
but also on the concentration of the donors NA and probability of the ele-
mentary act of donor-donor interactions WDD=CDDR'DW. However, the form of this
function is essentially different in different theoretical models. Analysis
of the conditions of applicability of one model or another, their approxima-
tions and limitations can be found in references [281, 284]. The results of
s uch an analysis reduce to the follawing.
First, it is necessary to distinguish the migration controlled phase of
q uenching from the kinetics phase.l The condition o~ realizing migr~tion
controlled quenching has the form WDA�~, where C=WDAn(TA)-1/(wDA~(TA)_1)
defines the rate of irreversible energy runoff to the acceptor subsystem;
WDAn is thelprobability of the elementary act of BPV at a minimum distance
Rmdn; (TA)- is the average energy relaxation rate in the acceptors. Thus,
the bottleneck in the given case is the migration rates of the energy with
respect to the donor subsystem. In the kinetic� stage of quenching (WDD"~)
the limiting factor is the excitation energy discharged through the acceptors.
Here the luminescence quenching rate can be limited by the transport D*-A
(WDAn� (TA)'1) or the excitation- relaxation in the accep tors WDAn� (TA)-1).
Secondly, in the migration controlled phase the quenching kinetics are
described within the framework of the diffusion or jump limits. The former
is applicable for a ratio of CDA� CDD' The solution of the diffusion equations
is found in different approximations in references [274, 279, 280, 283, 284,
2 87-289, 291, 2921. The asymptotics obtained by different authors do not
agree with each other. For resonance dipole-dipole interactions in the
pairs D*-D and D*-A for uniformly broadened transition b ands, the process can
b e approximated by the following analytical function [281, 293]:
n'; (1) M 1,~--Tt --~+)'l (3.7)
1
The latter is sometimes called "supermigration" [281).
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c(-Jk:,)" -X' c(';m)`,
(3.8)
different authors use different values of the coefficient A, and the value
of x varies from 5/6 to 3/4.
For CD>C DA the application of a 3ump limit is more substantiated. In this
case ~he results of references [273, 274, 279, 282-286, 289, 291, 292] are
much closer to each other:
1Y B.Mn,MACunCAU� (3.9)
However, the values of the coefficient B do not coincide here, varying as a
function of the simplifying assumptions made within the limits of 16 to 27.
Uniformity of expressions (3.8) to (3.9) was also confirmed by numerical
simulation [287], but here the coeffici ent B turned out to be smaller:
B was equal to approximately 14 for ordered arrangement of D and 3.5 for
random arrangement. Finally, the calculations performed in [289] demon-
s trated that the function (3.9) is main tained with an error to 10y in the
region CDD>0.5CDA'
Thirdly, the kinetic stage of quenching_is realized in a broad range of
concentrationa ND>NDr, where PIDr= (2n l-l.a(CAA)�.a ' except in
\ 3 / CT�IA ~Rmin)-e,
the jump model. Here
W = 3 nR.MACAA (Rraln)-e
(3.10)
and does not depend on ND and CDD [284, 2851. At the diffusion limit the
kinetic phase is attainable only in the region ND/Nmax+1.
The above discussed results are obtained under the assumption of resonance
- dipole-dipole nature of the interaction of the donors with uniformly broadened
b ands. The equation for ND(t) consider ing nonuniform broadening was obtained
- at the jump limit in reference [290]. Its approximate solutian when replac-
ing real probability distribution of the elementary acts of energy migration
in the donor subsystem by d-distribution with some average probabtlj.ty
8n3
WAA = 27 CAAA"u has the f orm [ 5161
~ _ - -
wnA (R) g' (1r) ait , (3.11)
W-f
0 1 d wAA (R)IwAJi~
where g'(R) is the distribution density of the acceptor around D*. Fo nnula
(3.11) is quite conanon, for it is valid both in the case of multipole and
for exchange nature of D-D and D-A int eractions, and it describes the
migration controlled and kinetic atages of luminescence quenching. In the
limiting cases WDD� E and WDD �E with dipole-dipole nature of the inter-
actions 3ts asymptotics coincide with (3.9) an,d (3.10), respectively.
83
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Thus, at the present time theory presupposes quite simple relations between
the relation of the integral kinetics of luminescence decay D* and the micro...
parameters of the elementary act of D-D and D-A-interactions,and certain
stipulations used also in the case of.activated glass. They provide the
basis for the method of precision investigation of the integral kinetics of
lwninescence or the method of microparameters most comprehensively developed
in [281, 283, 2931. This method permits certain definition of the micro-
parameters averaged naith respect to energies of the D-A interactions CDA and
m and in the case of realization of the kinetic phase of quenching,
estimation of the distance Rmin. At the same time, the eetimates of the
parameter CDD are less exact and possible only in the presence of preliminary
information about the multipole nature of the interactions D-D. In real
experimental situations, the choice between models of migration controlled
quenching of luminescence is also complicated.
More complete information about the microparameters and mechanisms of donor-
donor interactions is permitted to be obtained by the methods of investigating
spectral migration in the donor subsystem. This migration is specifically
characteristic of inedia with NUP, and it is manifested for the corresponding
setup of the experiment, for example, for low temperatures or selected excita-
tion, in the time evolution of the spectral composition of luminescence.
Efforts at theoretical description of the spectral migration were undertaken
in references 1252, 266, 290, 294-301]. The most successful of them obviously
is reference [290], in which it was possible to obtain;. in particular, rela-
tions generalizing formula (3.4) to the case of the luminescence quenching
law of spectrally isolated centere in various sections of the resonance NUP
curve : .
Nu (F', t) = g(L') Y(E, c) orp~- 3 i,~1- ~3 ).e,011F (E)J, (3.12a)
E
where F (E) _ S [CI[A (e)131"` g (E - e) de,
o (3.12b)
For known ND(E, t) and Y(E, t) expressions (3.12) permit determination of the
parameter m and the functional dependence CDDW which sheds light on the
mechanism of the interactions D-D, which was used as the basis for the method
of selECtive observation of the kinetics of the quenching of lumines cence
on the shortwave branches of the resonance lines (SNKL) [254]. Additional
information about the mechanisms of interactions and relative contrib ution of
transitions between different Stark components can be given by the temperature
functions CDA(T) and W(T) [290].
Thus, the results of investigating the integral and selective kinetics of the
damping of the D* luminescence carry sufficient information to determine the
microparameters and mechanisms of donor-donor and donor-acceptor interactions
and their interrelation to the structure of las er glass. Let us emphasize
that the study of the concentration and temperature dependence of other
characteristics of BPV, for example, the quanttun yield q or the average
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duration of the lwninescence T D does not have analogous informativeness, and
it is necessary to take a crit~cal position with respect to the conclusions
drawn on the basis of it regarding the mechanisms of pair interactions.
_ � 3.3. Ion-Ion Transfer--Experimental Results
.Analysis of the Published Data. At the present time a numb er of exoerimental
papers have been concluded, in which certain characteristics of the BPV pro-
cesses are presented for different pairs of rare earth ions in glass. The
known reviews of these papers becare obsolete long ago 182- 85, 302]. An
effort is made below to classify the published data and to some degree analyze
their quality and reliability.
The greater part of the experimental papers are devoted to studies of such
macroscopic characteristics of the BPV as depenclence of the density of
lumines cence, quantum yield and some "effective duration of luminescence" of
the donors on the concentration of the acceptors and in a number of cases on
the composition of the glass and temperature. The data presented in Table 3.2,
not pretending to�completeness, pernit an idea to be formed of the volume and
the accents in the performed research. As we shall see, primary attention is
given to silicate systems and then phosphate systems, and among the investi-
ga~ed p~rs, the pairs important for laser applications Nd~-Nd~, Nd~"-Yb~',
~3+ Er andcertain others predominate. The series of indicated papers is
characterized by an arbitrary choice of compositions of glass, imperfection
of procedures and experimental equipment and absence of clarity in defining
the concept of "effective ltmiinescen ce duration." In many cases when analyzing
the quenching processes, consideration is not given to possible competition
on the psrt of the accompanying impurities which are not taken into accoun.t,
for example, the OH-groups. The conclusions of these papers regarding the
mechanisms of pair interactions, as hAs already been noted above, must be
approached with caution. Neverth zless, the research has made it possible to
obtain primary information about the efficiency and specific nature of the
BPV pro cesses in one pair or another, and it has created defined prerequisites
for deeper research.
In another group of papers laser methods of studying transport processes are
developed. This group must include the cycles of works iri which investiga-
tions are made of the dynamics of the reproduction of the eq uilibrium curve
of the luminescence band of rare earth ions after clearing of the latter
by passage of a single band laser pulse through the sample [346, 348, 380-382],
the dynamics of development of the generation spectra [202, 3841, 1asing
kinetics 1202, 335, 353] and other processes. The limited . natti.re of the
laser methods consists in the fact that for imp2ementation of them it is
necessary to have a powerful pulse source of coherent radiation with lasing
frequencv cninciding with the freq.uency of the luminescence band of the in-vesti-
gated transitiq7 of the rare earth ions; in some cases the las ing mode must be
implem;:nted in the investigated sample itself. Therefore at the present time
the ci::r_�le of BPV processes investigated by such methods is limited to
migration of the excitation energy with respect to the Nd-3+ ions in silicate
and phospha,te glass. In addition, the abtained results reduce only to
estimating the phenomenological charactieristics of energy migration defir.ed
in one way or another, the unique rela*ion of which to the parameters of the
elementary acts cannot be traced.
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In recent years various versions of the chronospectroscopic or spectroscopic
method with time selection for investigation of resonanEe luminescence of
rare earth ions in glass combined with the methods of selective excitation of
individual types of luminescing centera have developed quickly [389, 3941.
Selective excitation of rare earth ions in glass was used for the first time
1n reference [415] to investigate Fu3+ ians, and the presence of spectral
migration was discovered, which insures astablishment of equilibrium in the
set of luminescence centers. The method of selective excitation supplemented
by the chronospectroscopic method of recordir.g was later used many times to
study the parameters of the spectral and spatial migration of energy with
respect to the ions Nd3+ [370, 379, 383, 387, 3881, Yb 3+ [301, 351, 3771,
Eu-34- [251-253, 349, 371, 375, 377, 379, 389, 3901 in phosphate, silicate,
borosilicate, fluoberyllate and germanate glass.. In the majority of indicated
papers, only qualitative estimates were obtained for the phenomenalogical
migration parameters. In some cases conclusions were drawn regarding the
mechanism of elementary acts of the iCnteractions. However, the procedures for
processing the results of such studies have atill been inEUfficiently developed,
and they do not permit reliable identit.ication of the mechanism of inter-
action or the obtaining of quantitative data on the microparameters of
migration. In this sense, r_he sttuation with investigation of migration in
Eu3+ doped glass is characteristic. In reference [252], the mechanism of the
elementary act is defined as . dipole-dipole nonresonance single-phonun,
in [253], as .4uadrupolar-qua,drupolar resonance, in [375], as dipole-
dipole two-phonon nonresonance, and, finally, in [390], as dipole-dipole
resonance.
More reliable and complete results can be obtained on combinatior_ of the
chronospectroscopic method of recording, selective excitation and low tempera-
tures (kBT�A"vH) where the processes of phonon absorption are "frozen" and
BPV within the limits of the NUP curve proceeds only in the direci:ion of
lower energies. Obviously, this fact was first indicated in [372], where for
4.2 K in silicate glass, a long wave shift of the luminescence band of the
Yb3+ ions is noted (the transition 2F5/2(1)-*2F7/2(1)) on excitation of them
by quasimonochromatic emission with frequency vH=10330 cm 1 to the short wave
edge of the resonance absorption band, and a valid interpretation of it ie
given qualitatively. Later, long wave conceiitration shift of the lumines-
cence band of Yb3+ ions, and then Nd3+ was investigated in cietail during wide-
band excitatior; in silicate, phosphate and fluophosphate glass in the cycle
of papers [294, 356, 357, 369, 373, 384, 392]. The authors of these pauexs,
confirming the conclusion of [372] regarding the single phonon nonresonance
mechanism of BPV between the Yb3+ ions in glass of kBT�p"vH, tried many timPs
to calculate the relation from the experimental data for the phenomenologieal
value introduced in a defined way which characterizes the effective spectral
migration rate of the exr-itation as a funetion of the difference in energies
of the interacting transition E. How�ever, such efforts do ng give any unique
result. Only recently when using selective excitation of Yb ions, were
qualitatively valid data obtained [301]. In Figure 3.5, for phosph4te g~l.ass
with NYb=7�1020 cm 3, the form of the resonance luminescence band of Yb
ions is presented for narrow band excitation by kryPton..tube emission
with ;DB=10254 cm71 (1) and absorption (2) corresponding to the transition
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Table 3.2
D*
IIepexpA~ I
A
IlepexoA I
THu I
Iicrovusic naHei14x
Nds+
#Fs/sis/s:ia/z
Nd'+
4jelz-'!Iisl2, 15/2
1a
[74(ck), ~(c,~), 85(c), 2~(c,
6/c), 223 (c, (p), 225 @), 226 229
�
236 (c, 303 (c, 6), 304 (c, (D),
305 (c), 306 (c, 6, r, 6/c), 307 (x),
308 (c), 309 3!0 (c, r), 311 (c),
' 4I
4F
+
368 (c), 470 (c)]
is/z
5/2
Nd9
4F3/2-'2G7/2
SR
1249 (c)]
4F9/2 ~ 4I9I~

.'F~~2--~'F5~2
16
.
(82 (c), 101 304 (c), 315 (c), 318
(6), 320 (6), 331(c), 339 (c), 336 (~/6),
'
�
347 (4), c), 358 (6/c), 3E0.(6); 369
'
385 (c) ] '
UO a
9~ou-''j ou
1A
1246 (c, 6/~r), 359 (c, c~, 6/(p) ]
Er'*
-`If$/2-'`Itf/z '
16
[2ri8 (c, 4)), 338 (c~, 4)7~), 361 c)l
~Fsl2 ii/z
Pr"
aH&-.IG; -
16
1248 (c, (p) J
.
Sme+
aHS/Z-*�F9/2
1a
TOT ~te (4)
AF �I 9/2 11/2;9/2
DY9+
6H15/2-+BF5/Z' � �N5/2
1a
TOT xce
4F3/2 alis/~
Tm9+ .
�Ife-.aHb
16
TOT ixc
4F3/2 4l ia./z
Hoa*
OIg-.'Ia
16
TOT Me �
4F3/s 41 15/9
Tb�+
7e-.7a; ~ ,
1a
TOT xce
Eu3"
7F0-7F6
1aj
TOT n:o
4 Fs/s ~I o/aci1M
Cut+ '
`1a ,
Tor mo
V!+
9a
ToT ;r,f�
]Nii*
9a
TOT ;sW
Fep+
1a I
TOT ;rc
yb'+
�F 5/2'2F7/2
Er'*
V15/2-'4Its12
16
148 @, c?, 85 (c, 101 312 (c).
326 (c), 332 (c), 338 ((D/~, r), 339 (c),
360 (6). :;(;l (c, 4)), 386 (c)1
Er3*
~I131 2o,4F912
I!l
1343 (r)J .
Ho'*
6I8-+6I6
16
1317 (c). :132 (c), 366 (c, c~)1
Tm3''
3lfa-''Ilb
16
1317 (a/c;j]
Tm'*
3N4-+3F3i 3Fl-1C4
1R
1343(r))
Nd3+
4I9/2-'+I15/2
1a
[374 (0)]
�
UQz+
3nou-`t~ ou
1A
[359 (c, d)1
Yb3+-f-Yb9+
I 9F5/2-'2F7/2
I Tbl+
~
i
I 'Fa-�SDa
I 1e
I1363 r)1
Er9+
!1f3/2-'V15/2
Tm3+
alfs.~:~~,�~
76
1317 (auc), 344 6)1
Ho3+
16
1332 (c). 345 (~/fl, 366 (c, c~)]
Nd'+
~I91'~-'4I 15/2
la
[33;) (c), 361 (c, 4))1
Er3+
4I012-''.4I9/2
1u l
1338 (a), (DT, 7')1
Eu3+
~DQ,-.7I;o 1
YL9+
2Fi/2-'`I'5/3
16
1241 (c, r, G,c))
aDo_ 7F0,'1: z; 3
U02+
anouou
1R
1246 359 c)~
Key: 1--Transition; 2--Type of BPV; 3--Data source; 4--the same
87
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jTable 3.2, continued]
I
D*
I IIepezoR
A
I IIePe=o1[ (1` Tert
!
I (3) HC709flH1f j[8HRL12
Tb"
*D,-�7F0
Yb'* C
�F7/2'-'2F5/2 16
1241 (c, r, 6/c)]
.
�
Nd3+ &A.,
fI9/2-4(''9/2 ' 16
[363
.
sDg_'sDa
iPr'*
3lyi_''3F2; s. � ia
1352 @)l
'
Tb'+
.'Fe-+7FO; 1; 2 1e
ToT Hce' (4) �
TM3*
3E$-.'H4 16
ToT sxe .
Dy'+
�Nf5/2'-'Ggif/2 : !a.
ToT xce
Nda*
615/2 ia
ToT me
Sma+
'R5/2-'''F1/2; 3/2 1a
Tor xte .
Sm3'
I4G5/2'6A5/2; 7/2
I Eu'+
I7Fo; i-�6Do I 16
I1313 314;@, 6)1
Tm~+
1Dg--o-3Ha
I Er'+
( 16
~Is
'-'G
I1313
364 @
6)
6)I
,
sia
7J2: 9/2
,
.
,
,
I
Gdl+
SP7/2-`�&97/2
I
Tb'+
7Fe- ~ I 16
I[313 (c~, 6), 321 (c)]
Cu;
-
I Tb3*
16
I1328 (c)l
Ce'+
Nd3+
16
[315 (e/c), 3i8 (a/c), 3i9 (c), 327 (c)j
Yb'*
16.
[3l6 (a/c)] .
Tb3+
~ . . . 16
1328 (c)J _ ' �
-
TM'*
- � . ' 16
[367 (6) ]

Cr
-
3+
N
4'r 9/2'4F3/2; 5/2; 7/2 16
1327 (c), 329 (c)1
- . '
Yb'+
'F7/2-'sFs/2 16
1330 (c), 333 (c), 361 (c, ~)1
Afu''
-
Nd'*�
16
1295 (c), 325 (c), 327 (c), 337 (~)l
-
Ers*
�16
(337 (c)]
-
H�'*
16
1337 (c) ]
Dlu=+ I
I
Ers*
I
. 16
I
1330 (c)] .
U01+
9TIou --.128 '
1Nd3+
~I9/z-'2Co/2: 7/2; ~S5/2 16
1246 W 6/4), c), 315 (c), 3?/1 (c), 325 (c),
354 (c), 359 (4;, c, 6/4)), 365 (c) ]
-
Eu'*
7Fo; .115Do . 16
1246 c, 6/~). 3:~3 (G/c), 354
359 6 c~) J
-
E +
~j1512-`~S312; 'H, f/z 16
1323 (c)] '
The letter in parentheses indicates which glass is investigated in the given
paper: c--silicate, ~--phosphate, b--borate, b/c--boroscilicate, b/~--boro-
phosphate,. r,--germanate, 0/~--fluophosphate, ~/b--fluoberyllate, OT--fluoride,
a/c--alumosilicate, k--quart z.
Key: 1--Transition; 2--Type of BPV; 3--Data source; 4--the same
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2F5/2(1)* 2F7/2(1), and in Figure 3.6, the spectral dependence of the macro-
scopic characteristic of��the energy migration proceas w using the expression
w,h(e =v.-v) ~ I,;(v)/g(v) � Th3s relation confi~s on tht phenomenological
/mtio AMyo mazu 102M /o.1no v, C,.,-,
Figure 3.5. Form of the resonance band corresponding to the
transition =Fd2 (l~ of Yb3+ ions in phosphate glass
[301].
1--luminescence with selective excitation, 2--absorption.
JWyb = 7�1020 cr''J�
level the theoretically important results previously established j2541 using
the SNKL 'method: a sharp increase in probgbility of the elementary BPV act
- within the limits of the NUP with an increase in 9 which.is valid at least
for K$T;0"vg and refutes the widespread opposite opinion based on preference
given to the resonance mechanisms of BPV.1 Let us r.ote that the function
YO does not have a aimple relation to the probability of the elementary
act so that it is at least difficult to use it to determine the micro-
parameters of the.D-D interaction and the functional .form o� the relation
CDD(e).
0
'f
t
~a` o
C ,
~1) ~s
o :n 4/7 so aa '
e; ca �r
Figure 3.6. Spectral dependencE of the proba ility of transmission
w~(Z) for phosphate glass with N~=7�1020 c~ri ~[301]
Key :
1. wo, arbitrary units
1The results obtained using the SNKL method are discuased in more detail on
PP 103-105.
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In Table 3.3 data are presented from experiments in which the method of
investigating the integral kinetias of luminescence was used successively.
There are very few of these papers, and in the majority they are devoted to
determining the microparaneters of BPV in neodymium--doped glass. Their
authors unanimously come to the conclusion of dipole-dipole nature of the
interactions in the investigated papers, but for the interactions D-D, this
conclusion is not confirmed by eonvincing experimental proofs. The conclu-
sion that the migration quenching of luminescence in neodymiimm-doped glass
must be considered within the framework of the jump model appears to be
reliable. Quantitative estimatee-are made of the microparameters CDD &nd
CDA fot a number of pairs. However, in sone cases they are questionable
(see the remarks to Table 3.3) and for 4.2 K for CDD using formula (3.9), they
are in general not incorrect. The temperature dependence of C and C,
in particular, the relatirms obtained for the pair Eu~-Cr~ inA[350] DD
giving information about the BPV mechanisms, are of interest. In [205] an
effort was made to trace the dependence of the parametersCDD and CDA for
Nd3+ ions on the type of glass former, but it was not possible to obtain
complete, sufficiently reliable data. In 12381 an effort was made to
explain the reduced concentration quenching in Li-La-Nd-phosphate glass:
namely, the combination of a sma11 value of the parameter CD characterizing
the process of cross relaxation of the ions Nd3+ (about 3�10A41 cm6-sec 1),
and the relatively large value of Rmin (about 4.7 angstroms). However, the
causes of significant developments in the degree of concentration quenching
in the series of phosphata systems, in our opinion, remain still unclear and
require additional study.
In the papers mentioned in Table 3.3, it was proposed in accordance with the
theoretical concepts discussed in �3.2, that the functions W=f(ND) and
W=f(NA) in the migration controlled phase of quenching are linear. Experi-
mental testing of this proposition (with the exception of the case of con-
centration quenching in neodymium glass which is complicated for interpreta-
tion [2381) was not carried out. Moreover, in references [340, 341, 3951, in
- which the BPV was investi ated in 12 pairs of rare earth ions (Nd~ Yb
Yb~-Er~', Nd~-Sm~, Dy~ Dy3+, Dy3+-Eu3'}', Sm3+-Eu3+, and so on) in phosphate
glass it is'poirited out that in the latter, in contrast to the silicate glass,
the functions W=f(ND) are nonlinear, and W increases appreciably faster than
the concentration ND. It is demonstrated there that the experimental values
of the excitation energy diffusion coefficients with respect to the investi-
gated donors in phosphate glass exceed by an order or more the ones calculated
for dipole-dipole interaction6using the overlap integrals of the spectra with
respect to the formula (3.3), at the same time as the indicated values are
close in silicate and germanate glass.
On the basis of these results, the conclusion is drawn of exchange nature
at least the donor-donor interaction phosphate glass. However, the set
of results obtained recently on a large number of objects using the precision
methods of investigating BPV, in particular, the SIv'IM method, does not confirm
this conclusion (see belaw). In addition, it is necessary to recognize the use
of the diffusion model for descrigtion of the migration controlled stage of
quenc.hing in the majority of investigated pairs as unconvincing, inasmuch as
the efficiency of the D-D interactions, as was indicated in these papers, exceeds
the eff iciency of the D-A interactions (see � 3.2). At the same time, the indi-
cations of nonlinearity of the concentration functions W- f(' V D) require fixed
attention.
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Table 3. 3
W
I
N0+
� Nda+
Gu'+ eDo-OF u. 1� 2
~
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[Table 3.3, continued]
Matrix ~ T; x~o A ~ye, m _Other"' ~
sec- -results A a�, . a
8� 7. 8 9 10 !f 12
13a-K-SiOs .300 7,8. G Gri; Y(T), F .[283] (1)
500
?00 0,25-0;9
NU r; � (1)
,Aa--SiO. 41, ~ 0,13
sto o,s s I2051(1)
450 o,/,
uuu, u,a
Na-GeOs 300 1,6 \a-13:U, ;ilt~) 11 li (4)
u � l'iCl s i _ 11,5 ~ -
:{UU ,i~.~ ~
Nu-SiOz 4,2 3,9 C1f; F (1,5)
300 /,,0 {
450 4,4 G ' (1)
600 4,4 ~1)
Nn-GeO2 300 17 G CD1
Nu-P=4. 4,' 2,2 G CM;'r (2,5)
1-Du-Sb-- 3iU
- SiU~ 'I~lU l$'t 6 (355) ~1)
I 70)
~
1:-Ba-SL- 300 24 G~h[; r [355j (1, 3)
SiO2
300 ;15
_ 3uU 8,5 (1,3)
300 20 G J(1I (1, 3)
d,i-l.u-I'103 4,2 0,3 G Rnlin-/,,7 :1 [238] .
300 0 3

:.n r:~[
;1f~lJ 1(n)
~
~
- _ i

L~i~l 77 ,~:;i;r',i~i;; i: i
iuu 11l( l l; ~~I : i
B
,
z,;,~.,uo u Ilat
;
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[Table 3.3]. Notes. (1) The dispersion T0D with respect to the NUP curve
is not taken into account; (2) the competition on the part of quenching on
the OH-groups is not considerec:; (3) the uae of tlie diffusion model is
queszionable; (4) the quenching on the matrix vibrations is nat considered;
, (5) the use of formula (3.9) to determine CDll~ ~at 4.2K is invalid.
The following abbreviations are used: ~M -jump model of migration
quenching; DN--diffusion model; F--effective macroscopic energy migration
rate with respect to donors; y(T)---dependence of the ma.croparameter of BPV y
(3.5) on temperature; D(T)--diffusion coefficient as a function of tempera-
ture.
On the whole it can be stated that there are insufficient data presented in
the above investiga;ted papers to put together a clear representation of the
mechanisms and relations of the BPV process parameters in glass or their
dependence on the type of glass former, modifier or glass structure.
, The original experimental data are presented below (the greater part of them
are published for th;e first timel) fi11 the indicated gaps to some degree.
The described results are obtained by analyzing the luminesceiice decay
kinetics, includiiig with spectral selection with respect to the excitation
channel and with respect to the recording channel, in a wide temperature
range on a large numb er of samples with specially selected relations of the.
activator concentr.ations. Here use was made of the precision experimental
setup (Figure 3.7) providing for recording the luminescence decay kinetics
in the multichannel photon counting mode in the dynamic range to 80 decibels
with sensitivity to 10 photons pe-, excitation pulse, spectral resolution to
0.5 angstrom and time resolution to 10 microseconds, with automated process-
ing of the experimental results. The recording of the luminescence decay
kinetics in the infrared range was insured in an analogous mode in the
45 decibel range using the cooled germanium photoresistance, signal: from
which after preamplification was normalized with respect to in*_ensity and
averaged in the two-channel gate integrator with time resolution to 100 nano-
seconds, and then input through a ma_r.ching device to the minicomputer memory.
The latter was used to approximate the curves obtained by calculation with
output of the results on the display screen for visual comparison.
- Donor-Acceptor Interaction of Rare Earth Ions. Measurements of the D-A
interacrion parameters were performed on samples with very small donor conc:en-
tration (on the order of 1�1019 crr3) which excluded tnigration of excitation
energy with respect to them. The acceptor concentration varied within broad
limits, from 1�1020 to 2�1021 em 3. The program for processing the experi-
mental results on a computer car.sidered the presence of dispersion of the
radiative probability with respect to the set of donor centers manifested in
the nonexponential nature of the cv.rves for the radiation luminescence decay
[250]. In Figure 3.8a, in the example of the Yb3+-Er3+ pairs in phosphate
1Some studies were performed jointly with Yu. Ye. Sverchkov and S. M. Matytsin
on samples fixed by A. A. Izyneyev, A. K. Gromov, V. B. Kravchenko,
V. M. Kozyukov, and U. Ya. Sedmalis.
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1 2
~ Figure 3.7. Functional diagram- of� a modern experimental setup
for kinetic studies of-.BPV processes.,>
1--nitrogen laser (X=0.337 micron, TpulB =10 nanoseconds,
Frepeat�0 to 500 hertz); 2--YAG las~er: I~d3'~' (a=1.064, 0.532,
0.355 micron; T ulse=l5 nanoseconds; Fregeat�0-100 hertz);
3--the tunable ~dye laser (a-0..4 to 0.75 micron) or LiF
crystal laser: F+' (0.85- to 1.1 microna); 4--sample; 5--helium
cryostat (2-300 K~; 6--double-monochromator (dispersion
5 angatroms/mm); 7--cooled photomultiplier; 8--photomultiplier
' coaling system; 9--preamplifier; 10--module for eampling single
photon eventa; 11--multichannel statistical pulse analyzer
(1024 memory channels; scanning rate with.reapect to channels
10 microaecaads/channel); 12--minicomputer; 13--storage element
based on flexible ma.gnetic diecs;14--terminal; 15--digital
plotter; 16--avalanche photodiode; 17--delayed pulse generator
in the synchron ization channel
glass with the camposition Ba~A1La(P03)1~, into which the activators were
introduced by replacement of a, standar experimental luminescence decay
curves of D* are presented which were measured with high precision in the
dynamic range of intensities occupying more than three orders. On approxi-
mation of these curves by the expression (3.4) with variation of the intro-
duced values of the parameters m and C the best matching in the entire
investigatQd time interval was achieveR Afor m-6+0.1, that is, the process of
static quetrching was described well within the framework of the concept of
the dipole-dipole interaction. An increase in concentration of A was not
accompanied by aignificant changes'in the nature of the functional dependence
ND(t) or the value of the parameter CDA, but in the initial section (t->0) a
trend was traced to an e onentialitation of the decay. In glass *aith high
A concentration (to 2.10~ cm 3), this trend was expressed quite clearly,
indicating upper bounding of the lumineacence quenching rate as a result of
minimum distance between rare earth i ons Rmi (see �3.2) and, on the other
hand, absence of a noticeable contribution o? other, shorter acting types of
interactions even in the cloaest pairsa
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The pair YO+-Er3'}' ia characterized by almost complete overlap of the
luminescence spectrum Of D* and absorption spectrum of A(Figure 3.9a).
Analogous studies of samples with different acceptor co centration were per-
formed for etandard nonresonance paira-YO=Tm3+ and Yb-Ho3+ and also for
the pair of ions Nd34'-Yb3+r the epectra of which partially overlap in
their wings (Figure 3.9b). For-example, in Figure 3.8b, the experimental
curve is shown for the -luminescence-decay of Yb3+ in 'glass with high H03+ ion
concentration (about 2.1�1021 cm 3). A calculated relation pr sented
there which was obtained ueing ~~mula (3.4) for CDA=1.3�10 cm~-sec 1
meagured on samp les with 1ow Ho concentration. As is obvious, the experi-
mental curve differs fr.om the calculated curve by the initial, more gently
sloping and exponential section�in the dynamic range of intensities of more
than one order. Using the relation of 12381
1/8 (3.13)
Rmin =1 YZ W
it is possible to estimate RminZ5.0 angstroms by the luminescence decay rate
in this section We. This value is close to the known data for crystal phos-
~ n=5.~.9 angstroms) or LiNdP4012 (R~ =5.64
phates, for example, NdPSP (
angstroms) [238], and it iniieates the isolated location of the RZI ~rare
earth ions] in pho sphate glass,._._
' Ybfi
a)
v
~
� Yh"
r,
Nd" ~I
I~
~
i
~aooo nqov' ~onao v ~H-,
Figure 3.9. Position and shape of the luminescence and
absorption bands of rare earth ion.s connected with excitation
energy transfer in the pairs Yb3+-Er3'f', Yb3+-Pr3+, Yb3+-Ho3+,
Yb3+-Tm3+ (a) and Nd3+-Yb3+ (b); T=300 K.
For Er3+ and Ho3+, the scale on the y-axis has been doubled,
and for Pr3+, it has 'ueen multiplied by five.
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For the Nd3+-Yi:3+ pair studiea were also made of the lawi3 of burning of
lwninescence of the acceptor, and their; corr�espondence or, the whole to the
nature of the damping curves wes discovered.
Thus, the obtained results indicate that the Foerster theory is applicable for
measuring the averagedparameters of the elementary acte of donor-acceptor
interactions of m and CDp in glaes in a wide range of acceptor concentrations.
The measurements for high A concentrations permit additional estimation of
Rmin�
Experimental values are presented in'Table.3.4 ~or the parameters of the pair
interactions m, CDA and R0, where Ro=(CBA�TQD)1 b is the critical Foereter
radius for a large nwnber of pairs of rare earth ions in phosphate glass calc
the compoaition Ba3A1La(P03)12 . The calculated values of the parameter CDA
obtained from the integrals of overlap of the spectra under the assumption
of dipole-dipole resonance nature of the BPV using (3.3) are given for a number
of pairs in the same table.l For nonresonance pairs the upper bounde of
Zcalc are presented considering the resonance overlap of the electron apectra
oz'D* and A with the electron vibrational satellites of the partners, the
intensities of which could not always be determined because of their smallness.
As was obvious from Table 3.4, in all cases, dipole-dipole interactions (m=6)
predominate, and, therefore, the conclusions of the authors of certain papers
regarding effective manifestation in the BPV between the rare earth ions in
glass of other types of interactions--dipole-quadrupole 1352, 3631, exch nge
13401, and so on--are not confirmed. For resonance paire (Yb3+-Er3+, Yb-Pr3+,
and so on), quite good correspondence of the values of CD and CDA1c is
observed, and for nonresonance pairs, the experimental va~ues are systematically
an order (or more) larger than the calculated values. The divergencea�
increase sharply w3.th an increase in energy deficit during the transfer act
Emin, where Emin is the minimum eaergy difference of the transitions between
the Stark componenta of the interacting multiplethe D* and A. It is remarkable
that the experimental values of CDeA and, the more so, R0 for variation of Zmin
in broad limits (someti~aes to 1000 cm 1) differ relatively little for tranaitions
with close integral cross sections. This is easilq traced in the example of
quenching of the luminescence by Yb3+ ions from the series Er3+, Pr3+, Ho3+,
Tm3+ (Bee Figure 3.9 and Table 3.4). The differences in values of CDA for
these >>airs do not exceed one order, and the values of RQ differ by one and
a half timea and correlate with the differences in the transverse cross sec-
tions of the absorption bands of the acceptors. Only for emin>l00G to 1200 cm 1
(emaX>2000 cm 1, where emax is the energy miamatch between the moat intenae
components of the transitions D* and A) a sharp decrease in the value of CDA
is observed of which it is easy to e convinced in the exemple of the pairs
Eu~-Yb~' (E~ Z1300 cin 1), Yb'~+-Eu RminZ3000 cm 1), Yb3+-Tla3+
(eminZ3500 cd-1), and so on. Attention is attracted by the fact that the
admissible ineteraction energy deficit corresponds to the maximum frequenciea
of the vibrational spectrum of phosphate glass ("vmaxZ-1200 cm 1). Thus, the
13'he valuea of CDalc obtained in this way are somewhat high, for the corrections
for N1JP are not taken into account.
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Tab le 3. 4
'
U
m
.
q.
o
cx,
I^
�
e
CgA'
C~A'
D*
Tra~nsition
A
Transition
~
C
;
m
~
-40
-40
R~~ A
C
r � C1
cr 8 c1
Nda+
!F 3/2'!j9/2
yb'*
=p7/., ,,....sp
5/2
16
0
I 1200
6
0 37
~
16
8 5
,
9 2
~
Ho3+
11Ie-�616
16
250
800
G
0,37
7
c0,1
8,0
phs/2-'4lif/z:o/a
SMe+
6N5/2-''6F5/2;7/?.;e/2;11/2
la
0
250
6
0,37
90
18
12,2
dF9/2"Jf3/2
Na,"
~If9/2-'~Ifs/2
1s
800
1400
6
0,37
0,45
O,Ofi
5,!
4F3/2-'1I15/2
Eu'*
IFo-IFa
fa
0
800
.6
0,37
y
1,2
7,3
,
Tme+
aJfcoafJ4
16
350
1200
6
0,37
12
1 is
partially permitted as a resu_lt of anharmonism af the vibrations. Thus, the
elementary act of BPV in the given case is of a local nature, that is, a
- quantum of electron energy is replaced by vibrational quanta of a specific
molecular group and not by ouanta of collective vibrations of the surroundings
as a whole. As was pointed out above, in the single-frequency model the
nature and degree of localization of active vibrations in the MFR are not
specified.
With this approach far calculation of the probability Wiv of interaction of
an electron oscillator with the i-th vibration, it is possible to use the
formulalanalogous to (3.3):
YVo~; 2,3�10-4x21?-� (ioA)-1 f Q,c ~v) b' ~v) ~t-~ ~y) v-Qdv (3.17)
~1)
Key: 1. ev
1The factor n 4("v) was introduced in (3.17) under the sign of the integral,
for in the inv6sttgated region it is impossible to neglect the dispersion of
the index of refraction.
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where Ri is- the distance from the RZI to the center of the i-th oscillator,
rrk("v) is the absorption cross section of the quenching vibrational groups,
g0) ie the form factor of the luminescence band correaponding to the
electron tranaition (1000=1).
The probability of the MFR act
result of staamation of Wi with
in thQ vicinity of the REY:
Wt� ~W`
for the 3-th electron center is defined as the
respect to all the que'nching oscillators
Key: 1. ev
(3.18)
and the averaging procedure with respect to these centers in order to determine
the effective macroscopic probability of WB= depends on the nature of the
spatial distrib ution of the vibrational oscillltors with respect to the
RZI-centex. With regular arrangement of them in the nearest coordination
sphere W=iWev� For statistically uniform dist~.ibution of the impurity
vibrational oscillatora in the metrix, the kinetics of the MFR process become
not exponential, but close to Foerster, and for its description it is possible
to use formula (3.4a). In this case it becomes possible to determine' the
average parameters of the elementary act WeV or Cey=We R6 directly experi-
mentally by the kinetics of the decay of the excited eYectron statej
The first version is realized during quenching on ttue vibratfons of tlie ~
structural elements of the matrix, the second on the vibrations of the
impurity oecillators, for example, the OH-groups.
Direct application of the formulas (3.17), (3.18) for interpretation of the
- experimental data w3th respect to MFR in the case of regular arrangement of
the vibrational oscillatore ususlly is complicated by the absence of reliable
data on the coordination numbsrs of the first, and especially the sedond
coordination spheres of the RZI. In addition, the vibrations themselves fre-
quently are not completely localized. Therefore it is possible with good
approximation to replace the summation in (3.18) by integration with respect
to volume and then we obtain [239]
yyq g (w)'k. ~v) n ~ (v)v-~dv~ (3.19)
~ - 46rc4RxsoA
where kM("v) 3s the linear absorption coefficient of the matrix in the multi-
phonon region, Rk is the radius of the sphere around the RZI not containing
high-frequency oscillators.
Thus, the inductive rescmance model of MFR permita determination of the prob-
ability of MFR in terms of the experimentally measured spectroscopic char-
acteristica of the electron transition (TOD, G(G)) and the matrix (kM(u)).
Here the function WS(AE) is defined by the dependence of ~ on ;0, in which
automatic consideration is given to the contribution of all of the types of
the vibrations active in the infrared apectra (which means in the MFR)
determined by their anharmonism, both mechanical and electrooptical,
connected with nonlinear dependence of the dipole moment on the vibrational
coordinates. As is known from the theory of infrared spectra of amorphous
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bodies (see, for example, [402]), in the multiphonon region basically these
spectra are determined by ttie overtones and the component vibrations (among
the highest frequencies of the given matrix), which also explains the appli-
cability of the single-frequency approximation. Mareover, the spectrum
kM(~D) in the multiphonon region in many cases can be calculated veginning
with the structure of the matrices both for the crystals aud for amorphous
- bodies [402]. The calculations ehaw that for s� 1 where in the given case
s has the meaning of the overtone number, the spectral function kM("v)
approaches the asymptotic E~(~)=exp(-bD), where b=const. Substituting it in
(3.19), we obtain W=exp(-aA. Thus, within the framework of the inductive
resonance model of MFR, the exponential dependence of W6 on AE is easily
explained by ttie analogous function kM(0. At the same time, this model
explains tiwnerous deviations from the exponential function, especially in
the region of small s. Here the spectral function kM('0) is less monotonic
and Wg must follow its peculiarities. The inductive resonance model does
not exclude consideration of the individual characteristics of the electron
transition, explaining the differences in values of WS for AE=const by the
differences in the radiating probabilities of the tranGitions.
It must be emphasized that the effective value of the energy of the gap
AE ff which must be usEd in the framework of the applied model far from always
coincides with AEmin. According to (3.17) AEe f corresponds to the maximum
of the expression Qkn-4gv-4. Therefore AEeff~'~Emin in the region of large
steepness 1cMO), and where dkM(~U) /d"v->0, the value of AEeff>t1Emin, and it
corresponds to the Center of gravity g(;D). Considering that the Stark splitting
of the electron states of the rare earth ions reaches 400 to 800 cm 1,
neglecting the indicated correction can significantly distort the results.
The temperature function WS(T) within the framework of the inductive-resonance
model corresponds to the temperature function kM("v). In the region
kgT>hwmaX, the latter is described by an expression similar to (3.16). In the
low temperature range anamalies are possible which are connected with trans-
formation of the spectra g("v) and variation of the radiative probabilities
for thermal combination of populations of the upger Stark components. Within
the framework of the given model, the term "electron-phonon bond strength"
acquires specific physical meaning, and for other equal factors, it is deter-
min ed by the distances from the RZI to the center of gravity of the vibra-
tional oscillators (-R76), the nature of the distribution in the matrix and
the degree of anharnwnism of the vibrations. It is natural that in the
matrices with less dense paclcing or for the OH-group, tke bond strength is
_ 1ess, that is, for the eame kM(,~), lower probabilities of MFR are observed.
Finally, the inductive-resonance model presupposes the possibility of dis-
persion of the probabilities MFR even for regular arrangement of the vibra-
tional acceptors the sources of which can be: 1) variation of the frequencies
- and degrees of anharmonism of the high-frequency vibrations as a result of
local lattice deformation; 2) dispereion of the distances from the rare earth
ions in the high-frequency groups; 3) dispersion of the radiating probabili-
ties of the electron transitions; 4) dispersion with respect to the RZI-
centers of the transition energies and, consequently AEeff� The degr`e of
the contribution of any of them a priori is not clear and requires experi-
mental determination in each specific case. Let us only note that the
firat three factors in the single-frequency model are not taken into account,
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so that the expetimental isolation of their contribution will serve as one of
the proofs in favor of the applicability of the inductive-resonance model.
The vulnerable part of this model is the possible strong deformations of the
given components in the vicinity of the RZI, whereas 1cM(3)) is determined
; integrally for the matrix as a whole. The degree of the influence of this
factor requires experimental study.
Thus, the inductive-resonance model opens up new possibilities in the studies
of the mechanisms of parameters of the MFR, and it has explicit advantages
- over the single-frequency model under the condition of obtaining weighty
proofs of its applicability to vitreous matrices, theoretically permitting
solution of the above-formulated basic problems. In [239], quite convincing,
although indirect proofs of its suitability in the case of liquid solutions
and rydrated crystals are presented. Beginning with the general principles,
it can be stated th$t the situation in amorphous glass (in contrast to crys-
tals with significantly different dynamic vibrational movements) does not
differ in theoretical respects from the situation in liquid solutions, with
the exception, perhaps, of significantly smaller frequencies of the high-
frequency vibrations of the glass forming elements by comparison with
uniquely high frequencies of hydrogea bonds. According to modern theoretical
models of oxide glass I1111, the high-frequency part of their vibrational
spectrum is determined by the vibrations of the bonds of the glass-forming
ions Si4+I B3+, p5+, Ge4+ or Te4+ with oxygen. The frequencies of the vibra-
tions connected with the modifier ions are to 3 times less. The high-
frequency vibrations are weakly bound to the lattice as a whole and are
sufficiently we11 approximated by independent local oscillatora. The nwnber
of oscillators in the first coordination sphere of the rare earth ions is
equal to the product of the number of nearest glass-forming polyhedra (6 to 8
for oxide glass) times the number of high-frequency modes in each of them.
The indicated oxygen bonds are sufficiently elastic, and their frequencies
are close to the frequencies of the free elastic bonds of the oxygen and the
glass former. Therefore the inhomogeneity of the crystal field in the vicin-
ity of the rare earth ions is primarily obviously connected not with deforma-
tion of the polyhedron, but with variation of their mutual orientation. For
this reason, it is not necessary to expect strong distortion of the phonon
spectrwn in the vicinity of the introduction of the rare earth ions by com-
parison with the lattice spectrum as a whole. However, in order to obtain
' reliable information, it ia neceaeary to study the electron vibrational
excitation apectra of rare earth ions in glass during selective excitation.
Let us also note that in multiphase glass or aystems with several glase-
formers the rare earth ions can be introduced in diffsxent sublattices with
essentially different vibrational structure. This fat;t must be considered
when analyzing the processes of MFR in such systems.
The discussed arguments regarding the vibrational structure of glass favor
the application of the inductive resonance model to the glass-forming matrices.
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A description is presented below of the set of experimentnl data obtained by
usl permitting reliable confirmation of its advantage and effectiveness for
studying the processes of MFR for rare earth ions in glass.
Experimental Studies of the MFR Processes on Vibrations of the OH-Groups in
Glass. As has already been noted, the admixture origin of the OH-groups and
their statistically uniform distribution connected with this in glass create
the prerequisites for quantitative testing of the applicability c,f the
inductive-resonance model of MFR to the glass, and i.n the case of a positive
result, for direct calculation of the integral parameters of the elementary
act CeV W v R6 and m according to the data on the decay kinetics of the'
residual luminescence of the set of rare earth ions after photoexcitation by
a 6-pulse. Actually, the decay kinetics will be similar to Foerster kinetics
(3.4) only in the case of multipole and local nature of the interaction.
If the elementary act of MFR is the result of coherent interactions of the
electron excitation with the collective of the vibrational oscillators or
(and) the interactions of other types, for example exchange interactions)
predominate, the kinetics will be significantly closer to exponential. In
the literature devoted to studies of the quenching of the luminescence of the
rare earth ions by OH-group'sthere were no data on the precision kinetic
measurPments. Moreover, the linear nature of the concentration functions
TD1=f(NOH) noted in 1101, 183, 185, 1931 was not in favor of the multipole
nature of the interaction. We measured the luminescence decay kinetics on
10 transitions in different RZI (Tab1e 3.9) in phosphate glass with the composi-
tion Ba3A1La(P03)1 . The selective transitions correspond to energy gaps in
the range of 5000 10 10000 cm 1, where the quenching of the luminescence by
_ the lattice is already quitP weak, and it is possible to isolate the contribu-
tion of the quenching by the OH-groups which is more effective on the basis
of the lower order of the MFR process. The concentration cf the OH-groups
in the investigated samples varied as a function of the technological pro-
cedures of founding and preparing the charge by almost 3 orders of magnitude,
for 1.1018 to 6-1020 cm 3. It was determined by the absorption level in the
range of 3000 cui-1 with respect to the standard sample calibrated with an
error of +20% by remelting in a vacuum with trapping of the water vapor in a
nitrogen trap. The RZI concentration was 1�1019 cm 3, which almost excluded
the possibility of migration of the excitation enelrgy with respect to them.
The luminescence kinetics were measured on the device described above. The
experiment demonstrated that for all activators with an increase in NOH
the ltuninescence decay kinetics of the RZI vary fram almost exponential for
NpI.-~O to sharply nonexponential for Np~>1020 cm 3. The standard experimental
decay curves are presented in Figure 3.19 in the form of a photograph from
the screen of a multichannel analyzer. The result of the theoretical
approximation of the luminescence decay kinetics is illustrated by expression
(3.4). Complete coincidence of the theoretical and experimental curves was
detected in a wide range of intensities. An analogous procedure performed
for a large set of differeiit samples demonstrated that for each activator
1The experiments were perfo nned by the author 3ointly with Yu. Ye. Sverchkov
and M. R. Syrtlanov. The samples were fixed bY A. A. Izyneyev, A. K. Gromov
and V. B. Kravchenko.
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Table 3.9
11
f- ,
Dn
Traresl st
v
r,,,4
w
d
o
It~
� y
q'
m
~v
~
V
~ .N
1 u ~
CD
i
rV o
I103+
6I7-+6Is
4800
0,37
57
6t0,3
23f2
26
Nd1+
4N3/2-'!1 15/2
53004'
0,37
21
1
4.3
~Fa/2-'`Ifa/2
7~
0,37
300
~6t01J }
4,Gt0,51
{
0,98
Tm"'
'/!#-+3Ile
5250
0,21
130
Gt0~3
25:0
27 ,
7'lia +
'''Da-.bDO
570U
1,1
63
GfO,t
4,7-1-0,5
-
Er''
111312"115/2
6500
8,2
100
6f0,i
1,3i0,3
1,6
Pra`
1Dj-r1GO
68U0
0,25
2000
, 61:0,2
18f2
-
Sul'+
5/2-�F11/2
6950
3,1
19
8f0,2
0,1i0,05
-
DY"
!F9/2-
7250
1,0
90
6f0,2
. 0,1 �0,05
-
-'`Fa/2; i/2
Yb3+
2F5/2-1-3F7/2
9900
1,15
870
6f0,2
0,055f0,2
0,035
at thergiven temperature there is a constant set of values of the parameters
m and CeV which does not depend on NOH (Table 3.9), permitting description of
the experimental luminescence decay curves by the expression (3.4). Here
the parameter m was in all cases close to six. This result permits the con-
clusion to be drawn that the investigated MFR process.is caused by the dipole-
dipole interaction of local impurity cen*_ers 14141.1 The applicability of
the inductive-resonance model of MFR is traced further if we calculate the
value of the parameter Ccalc, using formula (3.17). As is obvious from
Table 3.9, quantitative correspondence of these values with the experimentally
measured values is detected. Figure 3.20 shows the standard function 1cOH("v)
for the imvestigated glass (curve 2). The absorption spectrian of the matrix
itself (curve 1) and the experimental values of the product CeV(AE)T1D"v4 are
illustrated there for comparison. It is clesrly obvious that the spECtral
dependencQ of this value sCrictly follaws the function kOH(N)). Nevertheless,
if ws simply construct the graph of CeV(AE), quite strong deviations from the
curve lcOg(40) are observed, which are connected with differences in the
radiative probabilities of the transitions. Their difference is manifested
especially clearly when comparing the tra sitions wiLth close values of AEeff�
for example, for the pair Sm~ Pr~ or Nd Tm'-"}'-Ho"".
The obtained resulta are of a fundamental nature, more precisely defining the
mechanism of MFR in amorphous media and indicating the applicabiltty of the
dipole-dipole resonance model to the description of the ion-vibrational BPV
1Recently reference [238] also appeared, in which clos e values of the
parameter CeV were obtained for the Nd3+ ions in Li-La-Nd-phosphate glass.
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1[r
k,40
!U
~n
i
i�
!u
1l~
T
ca
9
~p
F)

~
~U
(b)
j
~o�

i. ~
~
- 1/ }IUS` IC
1 Tm�',, 3~ T,,;: ~~j~,y)
~ , .
~ . i . ,
~ � -
~ T-'''i
~Fi..t r
~ n~3 r
-Dy" /U'
- ~ .
yb3+
.t I
;YJO 4UJU S~~vJ G;.^C',: :7)U 90U41 9i/VU /[/'li
dE,Q,~�v, ' (a)
Figure 3.20. Spectral relations for the linear coefficients
of absorption of the matrix (1) and OH-group (2) in glass
with the camposition Ba3A1La(P03)12-end normalized experi-
mental values of the microparameter C v for difrerent
transitions of rare earth ions (aster~sks).
Key:
a. AEeff, v, c~n 1
b. CeVA 1~4, 2.3�10-26 ~m2
and its corollary--multiphonon relaxation of excited states of the RZI in
glass. On the other hand, the possibility of calculating the probabilities
of quenching luminescence of rare earth ions by OH-groups with respect to the
absorption spectra and the known radiating probabilities without performing
comple.x experiments and also the solution of the inverse problem--calculation
of the radiating probabilities of the transitions with respect to the measured
values of Cev and kolr-facilitate the development of new compositions of laser
glass and determination of the rec#uired degree of their dehydration, and
they also permit direct measurement of the radiating probabilities of the
transitions between the high excited states, which is difficult or impossible
in general by other methods.
Finally, let us note that the process of quenching of the lumincscence of RZI
by OH-groupa is subordinate to all the laws of the theory of BPV discussed
in 93.2 as applied to ion-ion interactions. In particular, a compar"on of
the data presented in Table 3.7 and 3.9 permits the conclusion that at least
for the Nd3+, Yb3+ and Er3+ ions, the migration contralled phase of quenching
by OH-group must be considered within the framework of the jump model.
The studies of the functions W=f(NOH) indicates that, in accordance with
(3.9), they are linear in a wide range of concentrations of No. As examples,
in Figures 3.21a, the relations are presented 1/T=W+1/Tk=f(Np~~ for ultra-
phosphate glass of the camposition Lal_XNdXP5014 [229], and in Figure 3.21b,
for erbium glass with the composition BA3AlLa(Pb3)12�
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(A)
3U
~ fl
!0
a)
(B) ^4c
M 5U0
.
(A)
b) ko",
C) , cN 'Iin, 101u [ -Ai J
Figu"re 3.21. The probabilities 1/T(a,b) and 1/Te 1/TR (c)
of quenching of the ltaninescence of rare earth'ions in
phosphate glass as a function of the OH-group concentration.
a) Glass with the composition Lal-xNdxp5014, exPeriment;
x=1 (1), 0.28 (2), 0.12 (3); b) glass with the composition
Ba3A1La~P03)~2 with Er3"F', experiment; NEr 3.5Y10�o cm 3(1),
l. 3� 102 cn~ (2) ; c) lass with the composition Ba3A1La(P03)12
with Er~'; NEr=1.5�101~ cm 3; solid line--calculation.
Key:
A. 1/t, 103 sec 1
B. 1/Te 1/TR, sec 1
The linear behavior of these relations permits easy estimation of the maximum
admissible values of T. and q in the dehyrated glass without realizing the
technologically difficult operation of removal of the OH-groups from the
glass. This is especially convenient for erbium and highly concentrated
neodymium-doped glass, where the degree of dehydration must be very high.
For examp le, f~r neodymiunrdoped glass when x=7, it is required that
PJ 0, that is, the oscillator strength in-
creases, and its frequency decreases under the effect of uniaxial stress. The
values of Da and AF vary monotonically with B, which is connected with almost
identical parameter kn varying from -0.89 to -0.96 for these types of glass.
For glass based on the metaphosphates of alka.line metals (Table 5.3), the val-
ues of kn ara small, that is, the oscillator strength varies little, and its
energy varies approximately identically for all of the investigated alkaline
glass. As a result, the values of B vary little--approximately from 1.5 �
10-7 to 2- 10-7 cm2/kg.
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Table 5.6
_
Basic
io-4e~1�cJ�
u
iu-7em~ikg
Glass No
Cation
�kg-1)
,
t
nig
--11.57
2,02
('a
--ll,.t,l
-0.91
1,78
3
Sr
-0,82
1,;47
4
13u
-U,t'l
--U,96
u,:,:l
5
zn
-0 ;821
'
-o,! 1�
.i,ur;
a
ed
-6,i-.:
-o,s()
2,52
7
Pb
-U,uS:i
eF, ~
Basic o-4eV2. kT h~x T,.C
Glass No Cation c"`�kg-~
1
11Ig
21,5
-4,1
-0,94
44
124
'L
Ca
12,7
3,4
-1,02
-11
126
3
Sr
7,4
4,5
-1,2
-42
94
i
lia
G,:)
5,3
-1,19
-82
132
' 5
%n
:5,7
0,8
-1,9
54
81
(i
(:d
10,3
-4,7
-0,9
37
125
7
1'b
1,7
5,5
-1,1
-72
148
The sign of the patameter z for the majority of types of glass (except glass
with Zn) does not coincide with the aign of the derivative dn/dT; their values
_ vary symbatically. Here the proportionality is violated as a result of the
variable value of kT which varies by more than twofold in the metaphosphate
glass series. When z> 0, the temperature increase leads to an increase in
energy of the equivalent oscillator Eo, n decreases with temperature; for
Z< 0 the picture is the reverse.
Although the model of the single-frequency oscillator is also phenomenological,
the parameters in it have an obvious physical meaning, and the formulas ob-
tained with its help describe not only the variation of the optical properties
with temperature and pressure well, but also the dispersion of these proper-
ties (formulas (5.4)). This approach supplements the one used earlier in the
Ramachandran model [465, 466], and it also permits standardization of the de-
scription of thermooptical properties of crystals and glass.
95.2. Phosphate Glass for Pulse-Periodic Lasers
Pulse-periodic lasers based on glass, primarily activated by Nd3+ ions, are
finding broad application in various areas of technology. The parameters of
these lasers vary within broad limits: the lasing energy varies from hun-
dredths of ajoule to tens of joules, the periodicity of the effect varies
from fractions of a hertz to approximately 100 hertz, the emission power in
the Q-switching.mode varies from hundreds of kilowatts to hundreda of inega-
watts. The survey information about industrial periodic glass lasers can be
found in [48, 119, 488], and information about the laser glass for them, in
[47, 48, 119, 489, 4901. As a reault of the wide range of variation of the
spectral-luminescent and thermooptical properties of phosphate glass, they
- offer the possibility of detailed investigation of various lasing modes and
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establishment of the physical principlea of the optimal selection of the glass
for application in various pulse-pericdic laser systems.
In the given section, using the general concepts discussed in ��1.1, 1.4 and
1.5, let us specify the rec~uirements for the active elements of pulse-periodic
lasers using glass with Nd Inasmuch usually an effort is made to increase
the average power of such lasers with given size of the active elements, the
lasers operate in the mode with large heat release and, correspondingly, with
hi.gh temperature gradient in the active element, which leads to powerful ther-
mooptical distortions. We shall discuss these distortions in more detail on
the basis of the results presented in �1.4. Let us consider the dependence of
the energy characteristics of the lasers on the properties of the material of
the active elements, and let us compare the parameters of the pulse-periodic
lasers based on phosphate and silicaCe glass. Here we sha11 not consider the
technical peculiarities of the structural design of such lasers, for we are
interested primarily in the requirements on the material.
In �1.5 it was demonstrated that in order to improve the thermal conditions in
pulse-periodic lasers it is expedient to use long and thin active elements
made of glass having high thermal conductivity ah. Increasing the length of
the active elements also leads to an increase in the gain and a decrease in
the threshold pumping energy [491, 492]. The thermal conductivity of laser
glass is approximately 0.4-2 watts/(meter-K) [47, 48, 490, 493, 494]. Among
the silicate glass, lithiumcalciumsilicate ID-2 glass has the greatest thermal
conductivity (about 1.2 watts/(meter-K)). The data on the thermal conductiv-
ity of phosphate glass are limited. Glass similar in composition to aluminum
metaphosphate (Figure 5.10) has the largest values of ah (about 1.2 watts/(me-
ter-K)), and potassium glass [111, 494, 495] has the least values (z0.3
watts/(meter-K)). Figure 5,11 shows the thermal conductivity of vitreous
metaphosphates as a function of the ion potential Ze/R of the cation mudifier
[495]. The thermal conductivity increases with an increase in the ion poten-
- tial of the cation. However, as was demonstrated in the preceding item, the
values of the thermooptical characteristics of P and W increase simultane-
ously, and the luminescence and lasing bands are broadened. The induced emis-
sion cross section of Nd3+ decreases (Chapter 4), and consequently the thresh-
old pumping energy increases. Therefore when selecting the glass composition
for active elements it is necessary to s.onsider immediately the set of proper-
ties of the glass and the solution depq*!3s on the requirements on the output
parameters, overall dimensions and pumping energy of the laser. In particu-
]_ar, the requirement of low energy threshold of lasing and high efficiency of
the Iaser is usually the most important. For small threshold energy of pump-
ing 0'thresholdp the efficiency increases with the same values of the pumping
energy "Wpump in the pulse as a result of growth of the ratio
Y'rpump/ ~`~threshold �
'I'he value of 7f`threshold decreases wi:.h an increase in the induced emission
cross section and with an increase in the Nd3+ ion concentration; the laser
eiFiciency also increases aimultaneously. In Figure 5.12, we have the values
of 7i"threshold (normalized for YPthreshold at .Mrra2o3 = 2 percent by weight)
and the output ener~y ~lase (normalized for )1''lase at Y'rra.:o., = 6 percent by
weigttt) as a iunction of the Nd203 concentraCion in silicate glass [496] for
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cylindrical actfve elementa 5 mm in diameter by 80 mm. The analogous picture
occurs alsa for phosphate glase. With a diameter of the active elements of
6 to 8 mm, the optimal concentration of the Nd3+ ions is (3-4) � 1020 cm 3;
for a diameter of 3 to 5 mm it is (5-8) � 1020 cm 3. In [497], for example,
lasing on a frequency to 100 hertz was obtained using Li-Nd-La-phosphate glass
with a concentration of Nd3 5.8 � 1020 cm 3. Here a lasing power of 6.5
watts was obtained on an active element 5 mm in diameter by 50 mm with a pump-
ing power of 1 kilowatt and pulse repetition frequency of 10 hertz. In this
case the energy efficiency is low inasmuch as the dimeneions of the active
element, the illuminator and pumping tube do not match. For a laser with ac-
tive e.lement made of silicate glass 8mm in diameter by 80 mm at a concentra-
tion of Nd203 of 6 percent by weight, an average free running power of 7 to 8
*aatts is obtained at a frequency of 7 hertz, a pumping power of 420 watts and
efficiency of 1.8 percent and 7.5 watts at a frequency of 37 hertz and effi-
ciency of 2.5 percent [492]. However, silicate glass providing such charac-
teristics ia not "athermal," and the divergence of the emission reaches 40-50'.
;,;a
i 4-
~ � 5
Q2 0,4 Ub'
x, mole fraction
Figure 5.10. Thermal conductivity ah as a function of x for phosphate glass
- with the compoaition xMemOn x(1 - x)P205 (where x is the mole
~ fraction of the metal oxide) [495]. Me: 1--A1, 2--Mg, 3--Ca,
4--Ba, S--Li, 6--K.
~
i
\
3
~
, 0, 5
i
aL3`
My2'o
Ca~'
8~2,
NaY
oLi` .
K*
7. 4 6 B 2,
, 6
Figure 5.11. Thermal conductivity Xh of vitreous metaphosphates as a function
- of the ion potential of the cation Ze/R [495].
- The presence of a positive thermal lens in the active element of pulse-
periodic lasers with moderate pumping powers improves the energy
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characteris*ics of the laser. In a resonator of length 1 with lens introduced
inside it with a focal lengt:i f, the diffraction losses are proportional to
0 - 1/20 [492]. For small pumping powers f is large and the losses are sig-
nificant. With a decrease in f with an increase in pumping power for glass
with P> Q, the diffraction lossea decrease, 7Nthreahold decreases, and the
efficiency increases. For example, for the above-mentioned active elements
8 mm in diameter by 80 mm made of ailicate glass with Nd203 content of 6 per-
cent by weight )rthreshold decreases from 25 joules per pulse for the single
pulse mode to 9-10 joulea approximately every 8 seconds af ter the beginning of
operation in the pulse-periodic mode with a frequency of 10 hertz (the thermal
relaxation time of the active element in this case is less than 15 seconds).
Therefore if the requirements on the radiation divergence are not very signifi-
cant, it is preferable to use such glass.
(l, B
~
~
~
~
Q4
0 0 4 6'
"N'Ndzo31 %-W t
Figure 5.12. T'nreshold lasing energy (1) and lasing output power (2) as a
function of the Nd203 concentration in ailicate glass for an ac-
_ t,ive element 5 mm in diameter by 80 mm [496].
Laser phosphate glasa with large values of Q and optimal Nd203 concentration
permit us to obtain low thresholda and high laeing efficiency. In Figures
5.13, 5.14, relations are presented for the lasing energy for single and re-
peated pulaes in the free lasing mode and for Q-switching by a rotating prism
(16,000 rpm) [81]. (The size of the active elements ia 6.3 mm in diameter by
- 76 mm, the glass is Q-88* (atrengthened version), 4.3 percent by weight Nd203,
resonator length 20 cm for free lasing and 30 cmfor giant pulse mode, silvered
illuminator, water cooling.)
In the fre~ running mode with single pulses and small repetition frequency
(smal.l average pumping power) the output energy of lasing, as shown by Figure
5.13, a and b, depends linearly on the pumping ensxgy. The efficiency calcu-
lated by the slope of the curve is 4.5 percent for single pulses, 3 percent
for a f requency of 1 hertz; the energy efficiency is equal to 3.5 and 2 per-
cent, respectively. The lasing threshold for the periodic mode in the given
case is almost half that for the single pulses. With Q-switching in the sin-
gle pulse mode, the efficiency is 1.43 percent (mirror with 65-percent reflec-
tion, pumping energy 15.8 joules, emission energy 0.22 joules, Figure 5.13c).
Q-88* glass is not "athermal," the magnitude of W which we calculated accord-
ing to the data of [493] is approximately 50 � 10-7 K-1 f or it. Therefore
with an increase in the average pumping power, the divergence of the emission
193
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A increases, the output power decreases (when the diffraction losees become
lesa than [he losaes to inactive absorp�tion, and the effeets of birefringence
become important [50, 498]),for the Q-switching mode, the lasing pulse dura-
tion t188e increases. The lasing energy drop per pulse is also obaerved for
the above-mentioned active elementa made of "athermal" Li-Nd=La-phoephrate
glass, where the average pumping power exceeds 0.3 kilowatt for the active
elements and illuminatora used in [497, 499] (Figure 5.15).
n--, i, 2
w
~Ud
0,4
12 ?0' ZB ,'76
8
.
~0,24
~
~ 0,16
QOB
~n
~
~
~
4 6 B 10 12
' b j
/
2
B lp. lo /4 16
c ?vp. i
Figure 5.13. Lasi-!zg energy as a function of the pumping energy for an active
element 6.3 ma in diameter by 76 mm made of Q-88* glass [81].
a) Single pulse mode; b) frequency 1 hertz, free lasing mode;
c) single pulse mode, Q-ewitching, reflection coefficient of the
output mlrror 75 percent (1) and 65 percent (2).
cW
�n
421) ~
..a
U' 2 B 10 4 18
v. H Z
Figure 5.14. Lasing energy as a function of the pulse repetition frequency
for an active element 6.3 mm in diameter by 76 nnn made of Q-88*
glass at a pumping power of 11 joules per pulse in the free las-
ing mode (1) and in the Q-switching mode (2) [81].
The values af tlase and 9 for active elementa made of Q-88* glass with a pump-
ing power of 11 joules per pulse and an increa8e in the pulse repetition fre-
quency are as follows, reapectively [811: 25 nanoseconds and 8' (single
pulses), 30 nanosecands and 11' (1 hertz), 45 -io^Loseconds and 15' (5 hertz),
55 nanoseconds and 18' (10 hertz), 70 nanoseconda and 21' (15 hertz). The
194
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lasing energy per pulse at v= 15 hertz is about 0.07 joule (Figure 5.14).
Thus, with an increase in the average pumping power as a result of growth of
the pulse repetitian frequency the lasing power in the giant,pulse mode in-
creases from 0.07 to 1.05 watts, the divergence increases by twofold, and ttne
pulse duration by almost 2.5 times. The radiation energy flux density in each
pulse decreases correspondingly by several times. The maximum efficiency for
a laser with active element of the indicated size made of Q-88* glass with Q-
switching is achieved for a frequency of 5 hertz, and it amounts to about 0.9
percent. The lasing energy in ona pulse in the free Iasing mode also passes
through a peak at 5 hertz, the efficiency reaches 2.2 percent, the output
power is 1.2 watts. For 15 hertz the free running power is about 2.9 watts at
an efficiency of about 1.6 percent. Let us note that it is not the absolute
values of the efficiency that depend on the optical quality and the machining
of the active elements, the values of the inactive power in the glass and in
the resonator or the pumping conditions and other factors that are signifi-
cant, bur the variation of the efficiency, energy and diver_gence of the emis-
sion with an increase in the average pumping power and lasing power (�1.5).
0
~
0,5
- U 5 1, (l 1,5 Ep, (C{q
Figure 5.15. Output laser power (per pulse of emiasion) as a function of the
average pumping power ePump [497]. Normalization by the lasing
power 1i'o in the air.gle pulse mode.
When using "athermal" phosphate glass with low values of P� Q/2 (for a cylin-
- drical active element) in pulse-peziodic lasers, the divergence of the emission
decreases, and an increase in the a-qerage lasing power, especially in the
giant pulse mode becomes posaible. For "athermal" glasa, some data were pre-
sented in �1.4, and shown in Figures 1.3-1.8. Let us consider in more detail
the optical strength of the thermal lenses and lasing parametera for such
glass under the conditions of a large temperature gradient between the axie of
the active element and its edge [60]. Here the initial expression is expres-
siou (1.41). The thermal lens formed for large temperature gradients A't' is
nonideal, in contr3st to the lensas with small gradients ((1.37), (1.38)).
Actually, from expresaion (1.41) and the formula for the focal power
I - (5.5)
/
w}iere Qp is the difference in optical paths between the axis and the edge of
- ttie lens, it follows that the thermal lens in an active element with focal
puwer of 1/f can be represented as the sum of two lenses with focal powere of
1/fl and 1/f2, where
j
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~ 2A7' ?z (Pot (')o -1 (IT(5.6)
i
(A / 0 (5.7)
� Rs
The lens defined by expression (5.6) is a spherical lens, its sign and focal
power depend on the thermooptical characteristics of the glass, the tempera-
ture gradient in the active element and emisaion polarization, and they do not
, vary with respect to croas section of the active elements. The lene defined
by (5.7) is aspherical, always poeitive, its power does not depend oa polar-
ization and varies with variation of E; therefore the compensation of the dis-
tortions (closeness to zero of the focal power of the total thermal lans) is
possible only for negative spherical leneea (5.6) and only in a sufficiently
narrow ring zone with respect to the croes section of the active element. Tne
temperatures T1 and T2 for which the focal power of the total thermal lens
vantshes at the edge and on the axis of the active elements, are equal respe,c-
tively [60] to
T~(rw) - AT - (Po t Qo/' 2)/0, (5.8)
-2e r-(no t 4oi 2)ie.
The resonator with negative lens introduced into it is unstabley and therefore
it is expedient that the total thermal lens be poeitive with respect to the
entire crosa section of the active element, at least for r-polarization. Theu
T1 defines the minimum temperature, for which the given glasa can operate ef-
ficiently for the given value of AT determined by the pumping power. As fol-
lows from formula (5.8), T1 is in the room temperature range only for (Po �
Qo/2) < 0. Expression (5.8) differs from the one used earlier in [52] (for-
mula (1.44)) by considering the temperature gradient in the active element,
which turns out to be highly significant for high average lasing power, when
it can exceed 80 to 100 K[57-59].
As is obvious from formulas (5.5), (5.6), the focal power of a thermal lens in
the active element depends on the temperature. Figure 5.16 ahows tl:a tempera-
ture dependence of the focal power of the thermal lens formed nesr the axis of
a cylindrical active element for "athermal" phosphate glasa GLS-22, LGS-I and
LGS-M (r- and �-polarizationa) [60]; in Figure 5.17 we see the average free-
running output power as a function of the pulse repetitlon frequency for a
pumping energy per pulse of 100 joules.
The temperature gradienta between the edge and the axis of the active elements
are about 40 and 80 K for LGS-I and LGS-M glass with a pumping power of 250
and 500 watta, respectively. The measurement conditions were discussed in
994.9 and 4.10, the surface temperature of the active elementa was varied by
means of the cooling liquid. With an increase in the pumping power 7h1ase
increases linearly. In the free lasing mode the laeing power reached 10 watts
with a pumping power of 700 watta. During Q-awitching of the resonator using
nn opticomechanic.al shutter (rotation rate 21,500 to 43,000 rpm), the lasing
energy on the active elements made of LGS-I glass obtained under optimal con-
ditions was 0.6 Jou?e with a pumping power of 40 joules and pulse repetition
frequency of 10 hertz. 'The magnitude of the angular divergence with respect
196
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to the 0.8 level of total power is 22' [59]. The "athermal" glaes thue en-
surea higher radiation brightneas than glsss with large thernwoptical con-
stanCa.
. ,
� ~
i
- 1 46 �
i~ ~ � 1 i ,~y � ~ / .
~
i
~
0,4
~ � ~

n,,, , ~ . ~
- -20 , z ~.4o r, �c
~ zo ~o so r, �c
~
~
al ti
Figure 5.16. Temperature dependence of the focal power of thermal lenses tor
a temperature gradient of 30� C in active elemente 8 mm in 4i-
ameter and 200 mm long on a wavelength of the sounding pulse uf
0.63 micron. a) r-polarization; b) ~-polarization. (r/R) - 0.5
(dotted lines). (r/R) - 0.82 (solid lines). The glass LGS-I
(1), GI,S-22 (2). LGS-M (3) [60].
 The variation of the laeing energy with temperature dependa on the temperature
behavior of the focal power of the thermal lens that ia formed. Since P de-
, creases with temperature, the thermal lens with low focal power for "athermal"
glasa at room temperature can become negative at low tenperatures, especially
for ~-polarizRtion (Figure 5.16). Here the magnitude of the temperature de-
- rivative of 9- dP/dT is significant: the smaller it is, the more slowl~ the
a focal power of the thermal lens varies. Fox LGS-M glaes (9 = 0.09 � 10' K'2)
the laeing power at negative temperaturee decreaees (by comparison with the
lasing power at room temperature) appreciably more elowly than for GLS-22
glass (9 a 0.14 � 10'7 K-2) (Figure 5.18). Thie agrees with the temperature
behavior o� the focal power of thermal lenaes in active elements (Figure 5.16).
For negative lenses part of the beams leave the active element, the Q-factor
- of the reeonator becomes worse, the reeonator becomes unstable, the lasing ef-
ficiency decreases, and with high power of the negative lens the lasinp, stops.
Accordingly, "athermal" glass, as hga already been noted in 91.4, cannot oper-
ate efficiently in the pulse-periodic mode at temperatures appreciabYy below
optimal [52], for which the combinatione of Ehermooptical characteriatics de-
fining the optical difference in path for the ~-polarization vaniah.
The above-presented arguments pertain to a fixed temperature gradient in the
active elements. However, the focal power of the negative lens as a function
of the temperature gradient in the active element is not monotonic under cer-
tain conditione. This is easily established from formula (1.41) for a cylin-
drical active element. Differentiating it with reepect to AT and equating the
obtained derivative to zero, let us define the value of the temperature grudi-
ent ATcr for two polarizationa of light:
197
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- r4/l+y7'
E) '
�l0 (2 ~
(5.9)
on exceeding of which instead of a further increase in focal power of the nega-
tive lens with an increase in AT# it begins to decrease, and then the lens be-
comes poaitive. Thus, the value cf aTcr corresponda to the minimum as a func-
tion of the focal power induced in the active element of the thermal lene as a
- function of the temperature gradient. Aere expreseion (5.9) ie meaningful
- only when the numerator is negative (or equal to zero), for the values of 6
and ATcr are positive, and C S 1(5 1.4).
b'
3
w
.Wy
- 0
ID
w
2
F i g u r e 5.17. k,vera ge out put power of free lasing as a function of pulse repe-
tition frequency for a pumping power per pulse o f 100 jou les for
_ LGS-I glass with active element 8 mm in diameter by 100 mm [59].
r, c�
Figure 5.18. Lasing power as a function of the coolant.temperature [60].
Pulse repetition frequency 10 herCz, active element 8 mm in
diameter by 100 mm; LGS-M glass (1), GLS-22 glass (22). The
ratio 7P1ase/ Y'lase, room is plotted on ~he y-axis.
For the given glass the temperature gra3ient in the active; elements is propor-
tional to the pumping energy power. For example, for cylindrical active ele-
ments 8 mm in diameter by 10 mm made of T.GS-I-3 glass in a highly efficient
illuminator the temperature gradient increases by 16� C with an increase in
pumping power by 100 watts [58, 59]. The focal power of tine thermal lens
changee correeppndingly.
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Let us conaider an example of phoaphate glass LGS-I and LGS-M, the thernwopti-
cal parameters of which were presented in Table 1.3. Table 5.7 shows the val-
_ ues af the combinations of thermooptical characteristica entering into formula
(5.9) and the values of ATcr for the temperatures of the side surface of the
active el.ement of 20 and -60� C, and Figure 5.19 shows the dependence an OT
of the focal power of the total thermal lens in the active elements made of
this glass for two polarizations and two values of C at T= 0� C. As we
shall see, the smaller the initial values of the swns (Po � Qo/2 + AT), the
greater the temperature gradient in the active element needed for variation of
- the course of the dependence of the focal power of the thei-mal lens on AT.
Here the active element operates etably under two conditions--at AT z 0(rare
pulse conditions) and at AT exceeding ATo corresponding to the intersection
point with the x-axls of the curve 1/f(AT), for r-polarfzation and 4 = 0
(curve 1 in Figure 5.19). In the region between AT = 0 and AT = ATo, whexe
the negative lens under steady-state ccmditions occupies the entire croas sec-
tion of the active element, the lasing power decrea9es, and the divergence in-
creases [56]. In real active eletnents under transition conditions and on de-
viations from parabolic dependence of the temperatLre on the radius of the ac-
tive slement (the data in Table 5.7 and in Figure 5.19 are calculated under
the assumption of parabolic dependence), the pattern of the variation of the
thermooptical distortions with Cemperature gradient differs somewhat from
idealized, but the general diagram of the variations is mainCained. These
arguments muat be considered when aelecting glass for pulse-periodic lasers
with high average power, where phosphate glass turns out to be optimal. Under
such conditions the active elements made of glaes with a value of (Po +
Qa/2 + AT) which for the given temperature gradient enaures a sma.ll positive
lena for r-polarization near the axis of the active elemente, give the leaet
angular divergence of the emission, and in the Q-switching mode, the op-
ticomechanical ehutters ensure the shortest duration and high Stability of the
lasing pulae.
Table 5.7 , LGS-I I LGS-M
I T=20 �C IT-00 �C T-20 ' C IT'=--fSO 'C
(1'�+Qj2-{-0T), 1.0-7 H-1 1,15 -10,05 -1,3, -8,/t
(~'u-~n/2'"0T) 10'7 K-1 -3,55 -1/i,75 -i,1 -14,3
'
t=0
-2,0
-18,0
-3,5
23
'pol�
t=1
-4,0
36
?
/tti
ATcr
t_ 0
6,3
26,3
20
b0
q"Pat .
E=1
12,6
52,5
40
80
Note: Negative values of ATcr indicate that the thermal lens is always posi-
tive.
An important factor limiting the output power of such lasers is the limiting
- temperature gradient sustained by the active element without rupture.
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Therefore the methods o� improving the therroal strength inveatigated in 91.5
and used recently for "athermal" laser phosphate glass [58, 59, 70] have im-
portant pract3cal significance. For certain types of technological lasers,
the choice of phosphate glass with small values of the coefficient of thexmal
expansion (less than 100 � 10-7 K-1) and increased thermal conductivity makes
it possible to increase the maximum temperature gradient in the active element
[497, 4991 and it ensures an increase in the output lasing power (with simul-
taneous increase in radiation divergence).
~
y
\
~
/,G
ar, -L'
a)
hl
Figure 5.19. Focal power of a thermal lens as a function of the temperature
gradient AT between the edge and the axis of the active element
made of LGS-I glass (a) and LGSM glass (b) for T a 0� C.
1, 3--r-polarization; 2, 4--~-polarization; 1, 2--~ 6 0; 3, 4--
~ = 1.
Tables 5.8 and 5.9 show the parameters of pulse-periodic lasers using ailicate
and phosphate glase. The table data are not exhauetive and serve only to in-
_ dicate the possf.bilities of active elements made of glass and approximate com-
parison of glass of varioua types, for the laser parametera depend on an en-
tire series of factors. At the same time, from the tables it is obvious that
- phoaphate glass eneures higher lasing power and efficiency and less angular
divergence of the emisaion for active elements of similar size. According to
the estimates of [500], the use of active elemeats made of phosphate glass in pro-
duction lasers germits-achievement of lasing efficiency which is 1.5 times
greater than for silicate glass, 1.5 times lees radiation divergence and twice
the pulse repetition frequency. In reality, for "athermal" phoephate glass
tha gain in energy and divergence is even more. Here the lasing efficiency
for "athermal" glass (type LGS-I, LGS-M. GLS-22, and so on) remains high for
high average pwaping pawer.
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Table 5.8
A
(12)
(12)
]1~A~~I~A i17111
T)til CTrK~a .
-
pcm1M rcitPpnuu~~
�
2
Tan A8
3
�
Paarep A2
xN
(4
Y8C70T6
IIOD70PP-
HNA NM-
G}'71bC08,
ru
r'iHPnTAA
H8N84KH
A1 A~1-
AyJIbCC,
)IM
C *
p
IS (o
p

yr,lOHBq
PBCXOAN-
bfOC7b.~,
A1NH.
]ICT04fiNN
',18HHdY
T38 - T3-Cil-
CNO6OxU+ll!
UHJINIIJ(p.
02X50
. 30
4
0,001
0,025
1501)
JIIIKilTH00
J'.~IC-!
(lrj)
f~16Xl30
. 25
100
0,15
0,15
(18)
1501
5
l00
0,3
0,3
150j
~:I1{IRaTD(1B
f
nJIflCTH89.
2x6x76
85
19
0,07
O,~i
DCPT. T,
171~
r
Moalnu~ixr-Nlab-
crawH (16)
(11)
~
8x20x175
i
490
1,0
0.2
rop. `LS
-
1502)
}:I)-�rS
I
URnuaAp.,
06,3X77
i0
23
0;!
0,4
34
~ M.
Ci,murawoe
Ceo6oprj4
0(17)
08X80
7
60

1,8
60
~ .
r (1SY
01OX80
3
100
2,5
2,5
-
~
~
s
Moaot~Mnynb-

s
fT16Xi2
05X80
20
10
125
100
0,5
0,1
0,4
0,1
14921
caum (16)
.
y
0i0X80
3
125
1,0
0,8
,
hrcc-7(13)
Cuu6oAa~i~ (15
0
*
06x120
f~8X~1
10
1
200
600
1,0
'~,5
0,5
0,45
!2
157
J1fC-28-2 ~1
) �
i
07Xf30 �
!
980
6,3
0,65
-
1503
JlI'C-24
n rGU

Tf oHOftntnvnt,C-
s .
:r
07Xf30
Qf 7 X!30
2
2
140
140
1,6
1,0
i,!
0,7
-

1
)1504]
�
aU;s (16)
� '
.
'
~
The divergences are presented in the vertical and horizontal planes for
a plate element.
Key: (1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(iz)
(13)
(14)
(15)
(16)
(i>)
(18)
Type of glass
Lasing mode
Type of actiire element
Size of active element, mm
Fulse repetition frequency, hertz
Pumping energy per pulse, joules
lasing energy, joules
Efficiency, %
Angular divergence*, minutes
References
Plate
Silicate
KGSS-7
LGS-...
Free .
Gioat pulse
Cylindrical
Vertical 7, horizontal 28
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h'UR Ut'h't(:IAL UhL UNLY
Table 5.9
(11'
(12
TtapKe ODH
71111 CTPN:IY
~1 )
PcacNm
it)IPF~9LLNIf
(2)
7H(1 A3
(3)
P+aNrP A3.
py
(4)
9ocTOra
~ON70{1P-
HNA lIM-
nyTuOe,
'nit-i,ri+ii
II:IGH'i1H
P 1 AM'
n)-ll*r,
~
~ =
c-~
~ c ~
�
q
~
~�~;,~nar
~wC~i;lll-
~fOCTL

ilu.
I~fTb411NN
AAIUINY
(10)
!�JIG22
MonojimnynLC-
llaacrna-i.
4Y.24x145
2
500 I
i,!
0,23 I
14(0.5)
(SQS)
1~1C-'~2
njau 14
p
~~16~
4Y,24Y.145
5
500
0,75
045
-
1':I(:'':.'
CDOGu;uii,u
]..lc:iilitup.
01UX130
5
151)
1,5
!.0

176J
ITII'C-11 .
� (15)
(17)
O8X100
lU
7U
1,0
1,4
-
1158,591
ZII'C-11
A'fuvolimuvnbc-
A
08X100
fU
40
0,6
1,5
22(0.9)
1
ubW (14)
.
(j-$g� '
Cuo6ouetui~
�
.0 6,3x76
5
!f
0,24
2.2
f ~
~.gg� �
(15 ?
s
06,3X76
15
!f
0,18
1.6
~
(81J

11'1UU011"U1)'1[LC-
i
06,3X7E
i)
il
0,09
0,8
~ f
~bdi (14)
(1�88� (13).
*
r
06,3X76
15
f 1
0,065
1.i-nd-Y(l)
CuoGomH u
�
05x50
fo
fon
u,(;S
u.6 5
-
1497)
l.i-Nd.~'Q~
�~1~~ '
1 A
05x50
!
0.155
1.!,0

} (499J
].i-.Nd-yq)
Tfoauunun�nbc-
�
05X50
f
0,15
0,47
-
Hf.iu (l41
The proportion of the lasing energy in the given solid angle is indicated
in parentheses
Key: (1) Type of glass
(2) Lasing mode
(3) Type of active element
(4) Size of active element, mm
(5) Pulse repetition frequency, hertz
(6) Pumping energy per pulse, joules
(7) Lasing energy, Joules
(8) Efficiency, %
(9) Angular divergence*, minutes
(10) References
(11) GLS-...
(12) LGS-I
(13) Li-Nd-UF
(14) Giant pulse
(15) Free
(16) Plate
(17) Cylindrical
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The poesibility of obtaining aho+:c pulsea investigated in Chapter 4(pulses on
the order of 10-10 to 10'11 sFCOnds in duration) in phosphate glass can also
be realized in the pulse-periodic mode. In [506], high power up to 0.5 giga-
watt with a pulse duration of about 5 to 100 picoseconds and a pulse repeti-
ti.on frequency to 12 hertz was obtained on "athermal" phosphate glaes LHG-7.
The most rigid requirements are imposed on active elements during operation of
the laser in the continuous mode. As a result of large temperature gradients
in this case it is necessary to mak.e maximum improvement of the cooling condi-
tions, which is achieved with amall transverse cross section of the active
elements. For effective abaorption of light in the case of transverse pump-
ing, high activator concentration is necessary. In this version the thresh-
old pumping power ethreshold using the narrow-band radiation source with con-
- tinuous mode is equal to [229]
Gr ~~~o ' � lu-;
"th i.P 2r.,1,:%'1jk11 ' (5.10)
where I'o and I'p are the nonresonance and resonance losses in the resonator,
respect3.vely, for a double pass, h is the Planck constant, c is the speed of
li ht, apump is the pumping wavelength, T1 is the luminescence lif etime of
Nd~+, N is the relative population of the upper half-level 4F3/2, kpump is
the absorption coefficient in the pumpiiig band, L is the length of the active
element. The resonance losses Tp = 2Lo.lii0$11'l, where X is the activator con-
centration, sl ie the Boltzmann factor for the lower laser level, Z is the
dfatribution function. For glass with a concentration of Nd3 on the order of
1021 cm 3 the resonance losses are significant, and they amount to several
thousand cm 1[48, 229, 232].
The product T1Q~pump which enters into formula (5.10) and must be maximal de-
pends to the highest degree an the composition. Since for cmall active ele-
ments kp~p must be large, glass is required whh ha3 long luminescence life-
times of Nd3+ with concentrations to (2-4) � 1021 cm and large induced emis-
sion cross section and, correapondingly, high quantum yield of luminescence.
The magnitude of the quantum yield which depends weakly on the glass matrix in
the dehydrated phosphate glass for a concentration of Nd3+ (4-6) � 1020 cm 3
(only if there is no inclinati,on of the glass toward microstratification char-
acteristic, for example, of zinc phosphate or boron phosphate glass) varies
sharply with the glass composition at high Nd203 contents. It was demonstrated
in Chapters 2-4 that the least luminescence quenching is observed in ultra-
phosphate and metaphosphate glaes with approximately identical content of the
oxides of univalent and trivalent metals under the condition of careful dehy-
dration of the glass. Stronger quenching occurs in glass containing bivalent
cations. When selecting the base of the glass for continuous microlasers, it
is necessary to consider also the technologicaZ, thermooptical and physico-
chemical properties of glass. Absorption coefficieuts on a wavelength of 0.8
micron for phos?hate ilass reach approximately 70 cm 1 with Nd3 concentration
of (3.8-4) � 10 1 cm , and the maximum luminescence lifetime for such activa-
tor concentrations in the case of complete dehydration of the glass is 40 to
60 microseconds. Calculation shows [229] that for pumping by the emission of
semiconductor light diodes the active elements of optimal size made of
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phosphate glass with specially selected ac_tivator concentration and small in-
active absorption can have lasing thresholds in the continuous mode which are
comparable to lasing thresholds for YAG: Nd3 crystals. The lasing on phos-
phate glass in the continuous mode is rea.lized only for longitudinal pumping
of the active elements by the emission of an argon laser [229].
�5.3. Glaes for fligh-Energy Laser Systems
When studying the propagation laws of coherent radiation in the atmosphere,
for experiments on the interaction of emission with the material and obtaining
a thermonuclear plasma, lasers with an energy of more th3n 103 joules per
pulse are required. Naturally, the divergence af the emission must be quite
small, and the energy density in the laser bea.m the ma.ximum possible. Since
the ILN radiation energy flux density in the range of 0.3 micron to 1,000 nm
is about 0.2 megavolt/cm2, and in the best case 10 percent of the pumping en-
ergy or under giant pulse conditions:l percent, is converted to induced emission
under free lasing conditions, in order to obtain the indicated energy multi-
tube, multistage laser systems are used with large total ILN surface and ac-
tive elements, respectively. In these lasers the total nwnber of ILN exceeds
102 to Z03, and the total length of the active elements reaches several me-
ters.
Let us consider the basic requirements imposed on the physical parameters of
laser glass used in active elements of large laser systems.
For lasers operating in the free lasing mode, in accordance with what has been
discussed above it is necessary to select glass which for the given magnitude
of the absorption coefficient has minimal luminescence band width of the
transition 4F3/2 4I11/2 and large quantum yield, that is, glass with maximum
product QT1. As was demonstrated in �1.1, this glass will have minimum energy
losses connected with luminescence processes and maintenance of threshold pop-
ulation. 1
Since the surface strength and nonlinear properties of the glass limit the op-
erating energy density of the induced emission to values that are smaller than
or equal to hv/v, application of glass with high induced emission cross sec-
tion in giant-pulse lasers promotes more efficient use of the energy stored in
the inverse population of Nd3'f', especially in the preamplification stages.
The increase in laser emission divergence (above the diffraction divergence)
is determined by the following factors: distortions of the wave front of the
emission on nonuniformities in the glase, deviation of the form of the working
surfaces of the active elements from given, thermooptical and nonlinear ef-
fects.
Modern technology enaures high quality of active elements during series produc-
tion of them. The distortion of the emisaion wave front on passage through an
active element 100 cm long does not excaed O.Sa (a = 1.060 run). Therefore
thermooptical and nonlinear distortions are becoming the basic factors in-
creaeing the emission divergence.
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The magnitude of the thermooptical distortions and the active elements (91.4)
is d etermined by the expression
Op(x, y, z) _(D(T(x, y) - T)L
where (D = P t Q for a plate active element and ~D = P�_q/2 for a cylindrical
active element, L is the length of the active element, T is the average tem-
perature, T(x, y) is the local temperature in the active element. Let us es-
timat e what value of 4~ the glass must have which is used in a laser with total
length of the active element equal to 1 meter so that Ap S 0.5 � 10-4 cm, that
is, so that the thermooptical distortions will not exceed the distortions of
the wave front caused by nonidealness of the glass. In giant-pu1sA lasers the
energy (per unit volume) stored in the inverse population, as a ru:,e, does not
exceed 1 joule/cm3, and at the time of achievement of the indicatec'. population
it goes for heating t:e glass as a function of the shape and duration of a
pumping pulse of 1.5 to 2 joules/cm3. Consequently, the maximum value of
(T(x, y) - T) does not exceed 1� C, and the value of 4) must be less than
_ 5- 10-7 K-1. In powerful lasers operating under free lasing conditions, the
active element is heated by no more than 5� C. Therefore the magnitude of 4~
must not exceed 10-7 K-1. If the lasers operate in the repeated pulse mode
with repetition period less than the time of complete cooling of the active
elemen ts, the established temperature gradient is tens of degrees, and more
rigid requirements are imposed on the thermooptical characteristics of the
glass: in addition to the condition ~D z 0 for T= T, it is necessary that
a(D/aT z 0, for the latter value determines the temperature range inside which
the conditions of smallness of the thermooptical distortions are satisfied.
In the case where the laser e*.nits a series of pulses (after which total cool-
ing of the active elements takes place), the value of (T(x, y) - T) increases
continuously during the course of the working cycle, and the average tempera-
ture increases by AT >(H/8T)-1, it is possible to minimize the thermooptical
distortions as follows.
I'or active elements, glass with 4) _-(H/at)LT is selected; the heating of the
active element during lasing leads to a gradual decrease in the absolute mag-
nitud e of 0, and at the end of the series, where tiie temperature gradients are
maximal, 0 z 0 and correspondingly Ap(x, y) z 0.
As the measurements show, the thermooptical distortions in the active elements
- in th e form of a plane parallelepiped with a cross section of 40 x 240 mm made
both f rom phosphate and silicate glass with neodymium concentration (1.4-2.0) �
I020 cm 3, and the greater part of the cross section are close to cylindrical.
They are about 0.2a in an actlve element 720 mm long with pumping of 250
kjoul es. In giant-pulse lasers which use these active elements, the thermoop-
tical distortions can be compensated by a cylindrical lens, the curvature of
TJt11Ct1 is connected at the time of lasing to the curvature of the wave front of
- ttie emission. In lasers operating in the free lasing mode, the thermooptical
clisto rtions are equivalent to a lens with variable focal length; therefore in
order to compensate for the distortions, an optical system coupled to the
tliermooptical lens is required, the focal length of which varies proportionally
- to th e pumping energy absorbed by the active element. It must be noted that
thc thermooptical distortions at the edges of a plate active element (in an
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area making up 20 to 30 percent of the area of the output end) have complex
form, and therefore they cannot be compensated by cylindrical or spherical op-
tical.system. In active elements of cylindrical form excited by the emiseion
of illuminators with 4 to 6 tubea, nonuniformity is observed in the inverse
population distribution and heat release both in the radial and in the azi-
muthal directions. However, the indicated nonuniformities can be decreased to
20 percent of the values at the conter even in an active element with a diame-
ter of about 100 mm by selection of the configuration of the reflectors and
decreasing xhe Nd3+ concentration in the glass, and the thermal lens can be
made almost spherical.
In lasers with disk active elemeiLts, the basic thermooptical distortions are
caused by heating of the air betiaeen the inaividual aczive elements (dn/dT of
the air is on the order of 10'6 K-1), by the ultraviolet part of the pumping
emission. In order to attenuate the pumping in the ultraviolet region, pyrex
glass filters are used. The volumetric: thermooptical diatortions in disk ac-
tive elements are small, for with uniform pumping with respect to aperture of
' the active element, the variation in the optical path in the glass as a result
of volumetric thermooptical effects must have the same magnitude over the en-
tire cross aection of the laser beam even for poor thermooptical parameters of
the glass. According to the experimental data, the total (surface and volu-
metric) thermooptical distortions in the laser containing aix disk elements
with light aperture of 10 cm and total glass thickness of 18 cm, amount to ap-
- proximately O.Sa for pumping of 70 kjoulea [349].
The distortions of the wave front of the emiasion caused by nonlinearity of
the index of refraction significantly increa8e the divergence of the emission
and decrease the flux density which can be obtained, focusing the laser beam,
- if nonlinear variation of the phase on propagazion of the emission in the la-
ser system is much greater than w. Here the maximum radiation flux density
which can be obtained for a given quality of the wave front, as was noted
above, is proportional to (QNi)2/Y. (The induced emission cross aection a and
the nonlinearity coefficient Y are constants of the glass.) Obviously, the
nonlinear phenomena are manifeated completely for pulse durations such
that the condition
L
2;tnyJ(1)d1 >n
u
is satisfied for flux densities less than the threshold of optical breakdown
of the glass surface.* For phosphate glass, the duration of these pulses is
less than (0.5-1) � 10'9 seconds.
The authors of [507] propose selection of the glass for laser systema in the
picosecond range by the cost of 1joule of focused energy Zj, using for this
formula
* According to the data presented in [507], the aurface b r eak do wn thresh-
old of the glass for different typee of ~lass is 50 to 120 gigawatts/cm2 with
a laser pu18e duration of about 2- 10-1 seconds.
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y, i " S (R,vj)"
_n y
where C is the cost of the glass, S is the area of the output end. For lasers
with a pulse duration of 10'9 to 10-10 seconds, the optimal phosphate and
fluophosphate glass with n2 =(1-0.5 � 10-13 cm2/volts2 and Q> 3.5 � 10'20
cm2, and with a laser pulse duration of :510'10 seconds, the fluoberyllate
glasses with n2 < 0.5 � 10'13 cm2/volts2 are the best.
In lasers in the nanosecond range, nonlinear effects are not so significant,
and the cost of the focused energy is determined by the ratio of the product
of the energy_density for which breakdow n of the surface of the glass
takes place, Ep for the energy stored in the inverse population, to the magni-
tude c,f the saturating signal, ES = hv/v multiplied by the thermooptical con-
stant of the glass:
i:jn'iv
z,,' 'r ~
i: cu),
where V is the volume of the active element in the laser system.
The types of phosphate laser glasa priduced in the USSR are distinguished by
good optical properties (and the LGS-M type glass also has a small value of
d(P � Q) /dT z 0.09 � 10'7 K-2 they have high values of the induced emissioi
cross section of neodymium, and therefore they are used successfully in lasers
in the nanosecond and millisecond range. For lasers that emit pulses ahorter
than 10-9 seconds, glass of the KGSS-1161 and LGS-M types, for which n2 z
10-13 cm2/volts2 are the most suitable.
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CHAPTER 6. ERBIUM-DOPED LASER GLASS
�6.1. Specific Nature of Erbium Lasers and Requirements on the Active Medium
- The induced emission of Erg+ ions in glase was ~irst obteined in 1965 by Snitzer
and Woodcock [312] on the resonance transition I2.3/2 I1-5/Z+ Xlase = 1.536
microns (Figure 3.3). The effort~ [204, 5081 to obtaln lasin~ on transitians
from higher4excited4states of Er3 ions, for example 53/2 I~3/Z (XTase % 0.85
micron) or Fy/2 I13J2 (Xlase ti 1.1 microns), in contrast to crystals, did
not yield poaitive results inasmuch as the luminescence from these states in
glass is sharply quenched " by the processes of multiphonon nonradiation re-
laxation of excitation (�3.4). The specif ic nature of erbium lasers consists
primarily in the fact that the accumulation of the excitation energy on the uppir
- laser level in erbium glass is realized predominantly (or completely) through
the sensitization channeL for the effectiveness of direct excitation of the
Erg+ ions is extremely low as a result of rElatively weak and rare abaorption
bands of the latter and the necessity for introducing erbium ione into the active
medium in the smallest ~oseible concentrations on the basis Of the thr.ee-1eve1
lasing syatem. For Er9 ions, the Yb9+ iona turn out to be effective sensitizere..
Yb3+ ions have a unique, but powerful (especially for high Yb9+ concentration)
absorption band in thI range of 0.9 to 1.02 microns with "effective" width on
the order of 1000 cm (Figure 3.3 and 6.1). At the same time, the Yb3+ ions
can be in turn sensitized by Nds+, Cr3+, Ce3+1 Mo2+ ions, and so on [48, 821,
which theoretically permits the use coeff icient of the emission of the pumping
tubes to be increased still more. Under such conditions, the energy charac-
teristics of erbium lasers (EL) are determined to a deciaive degree by the
BPV efficiency in the Ybg+-Er9+ pair. The laCter limits the minimum admis-
sible concentration of the Ers+ ions, it forces $n increase to the limit of
.M,rb and basically gives the choice of the chemical composition of the glass.
The maximum concentration of the Yb9+:�ions which can be introduced into the glass
without having a sharp negative effect on its technological properties (crys-
tallization capacity, optical uniformity, and so on) usually is (1.5 to 2) �
�1021 cm 3(relatively rare glass compositions in which .MY6 can be increased
to (3-4) � 1021 cm 3, unfortunately, do not have the required level of adapta-
bility to manuf�eture). For such ./Nro hifh quantum yield of the excitation
energy transmission in the pair Yb9t - Er3 _(q 1) can be insured (depending
on the used matrix) for drEr >(1,5-5) ' 1019 CM-9 dA(�3.3) . Consequently, con-
sidering the losses in the laser cavity, in order to reach the lasing thresh-
old it is necessary to excite at least (1-3) �io19 cm 3 Er3+ ions. These
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Figure 6.1. Standard abaorption apectrum
of Erbium-doped phosphate laser glass._
. ~
(1b r~-
Key: (1) Transmission, %
(2) Microns
(3) Absorption edge of the
OH band
I
OA
;a,zo
a s0
0,40 0,50 0,60 0,70 0,80 0,90 1,00 l,40
12)
11BO A,MKM
excitation levels are already quite high. For comparison let us point aut that
in neodymium glass lasers with blind resonator mirrore the lasing threshejld can
be reached with a opulation of the metastable state of the Nd3+ ions on the
order of (1-2)�101~ cm73 , and under optimal operating conditions, the latter
doe not usually exceed 1�1018 cm 9 under free lasing conditions and (2.5-5) �
�10~8 cm 3 under the amplification conditions of short pulses (Chapter 4). In
erbium glass, even the best wlth respect to BPV efficiency, the minimum Erg+
ion concentration must in,pr:zctice be greater than the above indicated values,
within the limits of (.iWs,)m,p > (2,5--5) ' 1019 cx'8. The fact that is at high
excitation levels, as the Er3t. ions accumulate in the metastable state under
the effect of a pumping pulse, the BPV process' efficiency decreases signifi-
cantly. Frequently this is connected with impoverishment of the population of
the ground etate. Another effect appeara to be more important. This effect
consiste in primary knockout af the acceptor centera from the'quenehing process
with maximum probability of donor-acceptor intefactions. According to what
has been discussed in Chapter 3, for the above-indicated ratioa of the Yb3+
and Er9+ ion concentrations in erbium laser glass, the kinetic phase of the BPV
process is realized, that ia, excitation energy migraCion with respect to the
donor subsystem is so intense that the limiting factor of the quenching process
is the excitation runoff rate to the acceptor subsystem. At low pumping levels
the runoff Cakes place primarily through the acceptor centers, the donor vicinity
of which approaches them to the maximum (to the minimum admiasible distance Rmin
(�3.2)). At high pumping levels, under conditions where the migration process
is absent in the acceptor subeystem (JI�s, is small) and t � T , where
tp~P is the pumping pulse duration, such centers, beingpumpexcitederto the
first stage, are knocked out according to the pumping pulse effect from the
BPV process, and the effective rate of the BPV process can drop signif icantl;
faster than would be expected beginning with the dynamics of the decrease in
population of the ground state of the Er9+ ions. It is also possible to men-
tion other important principles of the accelerated decrease in W during intense
pumpings. In order to compensate for the indicated effects, it is also neces-
sary to increase
Thus, if we- also consider the relatively low use coefficient of the emisaion
of the pumping tubes (in spite of the presence of sensitizera), the lasing
thresholds of erbium lasers with the traditional system of their execution
using pulse tubes turn out to be very high, and under the conditions of limited
reserve with respect to etrength of the latter they are in practice reachable
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only for cylindrical emall-diameter active elemente (d < 10 to 15 mm). The
diameter restrictions are also imposed by the large values of the Yb9+ concen-
tration, inasmuch as the active elementa with d> 7 to S mm usually are pumped
very nonuniformly. Thus, the possibilities of the tube version of the aerbicim
laser (ELL) are highly limited. Introduction of sensitizers into the g'1?ss
doea not change the situation for the most effective of them, Nd3+, cannor be
used in sufficient amount as a result of the appearance of quenching of the
luminescence of Erg+ with respect to the Er9+ (IIl8/L-~1I1e~2) ,-Na3+
03.3), and the others have low Offectiveness. Ae a result, the energy charac-
teristics of ELL are greatly ir.ferior to the characteristics of neodymium glass
lasers: the emission energy is less than one ,joule, the efficiency is 0.2
to 0.4 percent [48, 85, 450]. At the same time, they f ind defined application
as a result of absence of other, more efficient lasers f or the 1.5 micron band,
and also as a result of safety of their emission for the vision [48, 5091, the
presence of windows of transparency of the atuwsphere [510, 511] and good radia-
tion receivers [512].
Cardinal improvement of the energy characteristics of erbium lasers has been
achieved by transition to excitation by the emission of neodymium glass lasers
operating in the free running mode [247]. The pumping radiation in this case
is absorbed by Yb3+ ions during the electron transition between the upper Stark
component of the base level 2 F7 12 and the lower component of the metastable
level 2F5/2 (Figure 3.3). The initial level of the absorption transition at
room temperature is weakly populated (about 1.5 to 2) � 10-2 JY'Te but as a
result of the large values of ,N�Yr it is possible to insure an absorption co-
efficient on the pumping frequency of kpUMp approximately equal to (5 to 8) �
� 10 2 cm 1, for which the threshold den2ities of the stimulating emission,
although quite high (30 to 100 joules/cm are entirely attainable by neodymium
glass lasers and, the main thing, they do noC exceed the light strength of the
glass (see � 1.3). At the same time, small absorption level permits uniform
excitation of large volumes of the active medium. The theoretically possible
energy coefficient of conversion 1.06 1.54 microns is defined by the ratio
of the quantum energies of excitation and pumping, and it is n1Aa'X 0.69.
Although in a real experiment such values are hardly attainable, the applica-
tion of the laser excitation system permits creation of erbium lasers with high
energy characteristics as a result of high efficiency of the neodymium lasers
in the free-running mode (to 5-6 percent) and elimination of restrictions on
the thickness of the active elements. As will be demonstrated below (�6.5),
the advantages of erbium laser reemitters (ELP) of neodymium lasers are espe-
cially perceptable when constructing powerful systems for the amplification
of short and aupershort pulses (KI and SKI). Indeed, high quantum yield (no
less than 0.9), long excitation lifetimes in the metastable state (on the order
of 1'10-2 sec) and moderate yalues of the traneverse cross section of the induced
emission not exceeding 1�10-10 cm2 make the set of excited Er3+ ions almost the
ideal medium for these operating conditions, and the application of the laser
method of exciting the active medium to a high degree eliminates a number of
the harmful effects accompanying tube pumping (for example, heating of the
active elements or transverse nonuniformity of the distribution of the excited
particles), and it permits achievement of rscord values of the specific stored
energy in the amplification channel (to S to 10 joules/cm3).
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i.et us consider in more detail the requirements imposed on erbium glass as an
nctive medium in orde�r to maximize the energy charac.teristice of erbium lasera.
l.et ue perform a theoretical analysis of the processes of accumulating Er3+
ions in the metastable iatate and lasing of stimulated emission in the example
of the model of the ELP excited by a monochromatic square pulse of emission of a
_ neodymium laser (IpuMP (v,t) = I080 - vpumP)t, 0 E t< tpumP, where vpuMp end
Ipum are the emission frequency (sec-1) and intensity of the photon beam
(cm sec 1) in the pumping laser pu1ae). The strict kinetic model of ELP is
quite complicated. Figure 6.2 shows a simplif ied equivalent diagram of the
levels and transitions between them de-:ermining the dynamics of the accumulation
of the excitation energy in the metastable state and the lasing process. When
compiling it, along with the excitation processes, consideration was given to
BPV and lasing and also the presence of induced absorption of the Er3+ ions in
the metastable state on pumping and lasing frequencies (v lase) for which the
wings of the absorption bands corr%Wonding to the transitions 4jl3/,--}`F%
(vo t: ggpq cm-1) and (vo p., 6100 cnc-1) are responsible. In the
diagram in Figure 6.2 con~sideration is also given to the fact that in order to
obtain lasing in the Erg ion system in glass, according to the analysis of the
structure of their lumineacence spectra (see below �6.2) the most favorable are
the transitions from the 4I13/, level for one of three low S tark components of
the level 4116/2 separated energywise by 40 to 50 cm 1 (L1E � kBT) . The transi-
tions to the components_t-8 of the 4I15/2 level lagging behind the lower com-
- ponent by 200 Lo 500 cm (AE > kBT) have significantlq smaller transverse
cross sections (by 5 to 20 times) and, in addition, they overlap more sharpZy
- with respect to energy with the induced absorption band. Therefore the condi-
_ tions for obtaining effective lasing on them, unfortunaCely, are unfavorable.
It is also considered that according to the data diecussed in �3.4, the proba-
bility of direct nonradiating tzansitions from the upper excited states of the
Er3+ ione (states 3-5) to the ground state is negligibly small by comparison
- with the probab ilities of staged relaxation with the participation ef all of
the intermediate levels.
Using the notation introduced in Figure 6.2, the system of kinetic equations
describing the variation of the populations N of the levels of the Xb3+ and
Er3 ions during excitation accumulation on tAe metastable level 4I13/2 (2 A)
and generation of stimulated emission, can be written in the following form:
(T ~~n (N:~I - N374) - NaAi,u - wReN3u+
11'In Rd; (NCA " N1A) d' TOAN:A - wunNau + U'21N2n,
u13 sNsn - (ioe -f- wa1) N:n - a~,Ir (Ns, - N,A) -
- a';al,, (Nsn - Nan) - azolu Ma - Nbn),
U'RpNyIx - u'39N8A lU4JN4Ar (6.1)
:Y 1:1 1"6.,N6A d" Q941r (Nzn - Nan) ` ID43N4A,
A15A - Q:610 (NRA - N6A) - w64N6Ar
~'2A = lyIA eXp ~k 1T COIISt K.JY'Yb,
S
i NtA = .Mc.r�
{_1
Key: (1) lase (2) pump
211
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A(01 A(Lr3*)
~ 5 4Fg1a
~ � N w
o ' 4 s` 41er/z
~WJ l6;N \1)
~o ZFsi 3 a
' ~ ~ ~jr
4lu1a
Qr jr 1;A
f 2 ~ 2)
p zF~/21 1 1~ 4~I5/t
wAA .
Figure 6.2. Equivalent diagram of the energy levelp of the aystem of ions
Yb9+-Erg+ and transitions between them describing the operation of the ELP.
IpU and IlSBe are the intensities of the pumping and laeing emission
(cM T�sec 1). crpUMp and Qlase 8re the effective transverse cross sections of
absoiption on the pwnping.frequency and induced emisaion on the lasing frequency
(cm Qij are the transverse absorption cross aections between the levels I
and J of the acceptor (cm Z). w i is the rate of nonradiating relaxation of
excitation between ~he levels i d j(sec-1), w is the effective BPV
rate in the pair Yb9 -Zr3+(sec T~ is the luinescent lifetime of Ybs+
on the levels 2F5/2 (3D), TDA is the radiating lifetime of the Er3+ ions on
the metastable level 4I13/2 (2 A).
Key: (1) pump
(2) lase
The strict solution of the system (6.1) must be found jointlywith the solutions
of the equatinns for the emission density in the laser resonator (see, for
example, [3]). Considering the complex forni of the function wDA(N2A), it is
difficult to obtain it However for the stationary pumping mode (t ;
tthreshold � wDA ' W32' W54' W43' where tthreshold is the time inteTvai
from the beginning of pumping until the threshold inverse population is reached
pN threahold i(N 2A - N lA )threshold ) under acceptable conditions
wes, w43, wb4 >'1'+Ir1 01e10(6.2)
Key: (1) lase (1)
it is possible to replace system (6.1) by the equation for inverse population
dsN + Tni)�AN (6.3)
ar - 1
_ TnAJY'Er+ l cslo TnA wAe
Key: (1) lase (2)
(2) pump 212
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where 'r1A m TOA + w21. Equation (6.3) is nonlinear, for wDA ' f(ON). If the
form of the function f is known, ita solution can be found hy numerical methods.
At the same time it ia obvious that for miaimization of ANthreshold it ig neces-
~ sary to insure satisfaction of the conditian
wAA ~ ~ lll
2
Key: (1) pump
(6.4)
In this case the solution of (6.3) presents no diff iculties. In the initial
phase of operation of the laser when the induced emission is absent Ilase = 0)
_ and the process of chargP accumulation takes place on the level 2A,
(6.5)
AN (t) .MEr)
where X = 2(1) ,~'rr:AT:1n.
(6.6)
- Key: (1) pwnp
Hence, it is easy to determine the time tthreshold'
I
tn= '[JiA 111 -~A,\ (6.7)
Key: (1) threshold (1) and the threshold pumping energy density of the active medium of volume V:
)'nnop = hvaVlo [arsNsA -I' Pu -1-
. (1) (2) Qn .0,25 (Y',.r -I- A ~3~)1 te0v, (6.8)
Key: (1) pump threshold
(2) PumP
(3) threshold
which must approach the minimum value
OPunopjmin 0,5hvaV (MEr -f- ANnop) X �
~1) X r1 + pn 0,25% (ANn~p ~f- X~r) (6.9)
Key: (1) pump threshold
(2) PumP
(3) threshold
on satisfsction of the condition tthreahold 8,2 � 1022 cm-2 � sec (77 joulee,/cm2) . These conditions are less rigid than for
silicate glass, but they are also quite stressed. Their satisfaction is com-
plicated with a decrease in tpUMp. IC is also necessary to note that the
pumping-energy densities requ3red for realization of high efficiencies are
- very high even for the laser method of excitation. For silicate glass, they
exceed the radiation breakdown thresho2d of the glass with respect to platinum
inclusions (700 to 1000 joules/cm2).
Thus, the performed analysis demonstrated that under optimal conditions the
er_ergy efficiency of the ELP can approach the theoretical limits.. Here the
integral brightness of the emission of such ELP can exceed by one and a half
to two orders the brightness of neodynium lasers [247, 413, 5351. However,
the achievement of high energy charaGteristics of the ELP in the free running
mode is possible only under very rigid conditions requiring optimization of
the chemical composition of the glass and concentrations of the activators,
216
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high radiating strength of the glass, high energy densities of the pumping
emission and maxi.mum shift of the emission wavelength of the pumping laser
to the shortwave side (to 1.050 to 1.054 microns). The best matrices for
the working material of the ELP are phosphate materials haviag decisive advan-
tages over silicate. Only borate glass could compete with them with respect
to BPV efficiency, but in borate glass the quantum yield of the Er3+ ion
luminescence, unfortunately, is extremely low 0.07) as a result of the high
efficiency of the MFR processes (�3.4). In the phosphate glass series prefer-
ence must be givez to the compositions permitting introduction of the largest
possible concentrations of Yb3+ ions having both high cY pume 61ase and maximum
transfer efficiency in the Yb3+-Er3+ pair without having negative effects an
the technological characteristics. According to the results of �3.3, they
should be found among the systems permitting maximum approach of the rare earth
ions, that is, having minimsm Rmin'
� 6.2. Spectral Luminescent Properties of Erbium Glass
Figure 6.1 shows the standard absorption spectr..,.., of erbium phosphate laser
glass. It consists of a small number of relatively weak and narrow bands in
the visible and near intrared regions of the spectrum. The most intense are
the bands with peaks about 522 and 378 nm (the oscillator strengths are
5.7�10-6 and 12�10-6, respectively). The remaining groups of the bands are at
least an order weaker. A detailed analysis of the absorption spectra, detailed
data on the powers of the oscillators of the transitions and positions of the
band peaks and also the parameters calculated by them (in some cases) for the
crystal field, can be found in the following papers: for silicate glass [361,
364, 516-518], phosphate glass [191, 193, 204, 361, 405, 411, 508, 516, 5171,
borophosphate glass [193, 361, 517], fluophosphate glass [191, 345, 5171,
borate glass [405, 411, 508, 5171, germanate glass [405, 411, 508, 5171,
tellurite glass [361, 403, 411] and fluoberyllate [361, 517, 521, 522]. A
comparison of the data presented in them permits the conclusion to be drawn
that the chemical composition of glass has less inf].uence on the form and the
position of the bands than was observed for the Nd3+ ions. For example, in
metaphosphate glass with different modifiers (elements of the first and second
groups) and also in borophosphate glass the form and the position of the
absorption bands of Er3+ do not change in practice [193]. Only on comparison
of them with other tvpes of glass are differences noticeable. It is possible
to be convinced of this in the example of the resonance absorption band corres-
ponding to the laser transition (Figure 6.3). The resolution of the transitions
varies more signiFicantly. With some exceptions, it increases in the series
of: fluoberyllate-alkali and alkali earth silicate-aluminocalciumsilicate-
fluophosphate-borophosphate-phasphate-germanate-borate-tellurite glass (7-8
times for "supersensitive" transitions 'I,.~2:;t4I�/2 ; 2Nii/,; 4G11/2 with
!'~J = 2 and 2 to 3 times for the remaining transitions, including for
which, accordina to [518], correlates w-tth the decrease in symmetry ot the
1_ocal crystalline field in the vicinity of the rare earth ions in this series
of glasses. The resolution of the transitions varies noticeably also as a
function of the type of modifier. For example, in ti:iary alkali earth phosphate
g].ass (50.5 MeO, 49.5 P 0 molecular percent) the integral absorption cross
section of the transitions 4Iid/,-4I13/2 increases bS 1.35 times in the Mg-Cd
ser.�ies (to 4.2�108cm2�sec-1), then it decreases somewhat for Ba [519].
217
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In the luminescenoespectra of the majority af compositions, a unique intense
band is observed with peak at 1536 nm corresponding to the resonance transi-
tion 'll~~,-'I,~/~ (Figure 6.3). Only in fluoberyllate and especially in tlie _
tellurite Plasees do the bands correspondinQ to the transition ~Ss~~-'1~~~~
(550 nm), `jll/1-'hal ; (about 990 nm) and ~p'/~-'fi~~~ (about 320 tun)- L345,
361, 521, 5221 liave noticeable intensity, which is caused by lower probability
of nonradiating degredation of the high excited states of the ions in these
- types of glass (Chapter 3).
In contrast to the corre~ponding absorption band, the form of the resonance
luminescence band of Er3 ions depends strongly on the glass composit;on (Figure
6.3). Its halfwidth in. phosphate glass is greatar than in silicate glass
Av 135 and 115 cm 1 respectively), and depends insignificantly on the type
of modifier. In fluophosphate and especially in borate glass, the value of
N l increases sharply (in the latter, to 400 cm 1), which is connected first
of all with growth of tht relative intensity of the transitions from the upper
Stark components of the I13/2 level forming the h{gh frequency wing of the
luminescence band at 300K. Simultaneously, in the series of silicate-phos-
phate fluophosphate-borate glass, the transve�-ae cross section of the induced

~
~
~
F
Figure 6.3. Luminescence (1) and .
absorption (2) bands of Er3+ ions
corresponding to the transition
4I13/2 f 4I15/2 in Li-Mg-silicate
(a), Ba-Al-phosphate (b),
fluophosphate (c) and Na-borate
_ (d) glass. 300 K.
Here and in Figure 6.4 the absorption
cross sections are multiplied by
-1.
o,ti
C,,-,
, CM"/
~ 6tR70 N 6:5110 %000 v Cer-~
-0,4
C)
dj
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emission decreases at the luminescence band peak a . Let us note that this
- series is almost inverse to the one presented aboveawfiere we were talking about
the integral cross sections of the absorption bands of Er3+ ions. This apparent
contradiction is explained by differences in width and shape of the luminescence
bands. In Table 6.1 complete information about a and the positions of the
_ maximum resonance luminescence band taken from var~ous sources are collected.
The differences in the presented values of Qlase do not exceed 50 percent. This
is much less than the observed differences for neodymium glass where they reach
three times (and even more) (Figure 4). Among phosphate glass, according to
[519j the value of Qlase increases from 6.3�ZO-Z1 to 8�10-21cm2 in the series
of modif iers Mg-Ca-Sr, then decreases to ~ 7.5�10-21 cm2 for Cd and Ba. How-
ever, the indicated differences are not too significant. Thus, it can be con-
cluded that the possibility of a significant increase in 61ase by f inding the
_ optimal compositions for erbium glass obviously is excluded.
= Measurements of the absorption and luminescenoespectra for low temperatures
permit us to obtain information about the position of the Stark components of
the levels 4113 2 and 4I15/ and also the magnitude of the nonuniform broadening
of the ban.ds co~responding ~o the transitions between these components. In
Figure 6.4, the spectra of this type that we obtained are demonstrated for a
temperature of 4.2 K for Na-K-La-Ba-silicate and Na-Mg-phosphate glass and also
approximum expansion of these spectra into individual components. It is obvious
that the degeneration of the indicated levels in glass is completely removed,
and each of the terms is expanded in 2J + 1 halflevels. The opposite conclusion
drawn previously in [517] is explained obviously by low accuracy of the record-
ing. In Table 6.2 the positions of the Stark components on the energy scale and
estimated values of nonuniform broadening of the absorption or luminescence
- bands connected with them are presented. The obtained values of Av for
phosphate glass turned out to be larger than for silicate glass, anRuLopgously
to the results found by us for the Yb3+ ions, and opposite to the situation in
neodymium gl ass. On the whole, the magnitude of the nonuniform broadening of
the E-r3+ ion bands is appreciably less than for the Nb3+ ions.
Few experimental studies have been made of the induced absorption spectra of
Er3+ ions in glass. A strong band in the 20,880 cm 1 region was detected in
reference..[525]. This band was attributed to the transition to the ZK15/2,
2G7~2 levels, and weak bands were detected in the regions of 19,250
cm 4G9/2) and 15,400 cm 1(the transition is not established) in multi-
componPnt silicate glass. More complete and exact data were obtained in
[361, 5261 f or Li-Mg-Al-silicate and Na-Al-phosphate glass where the induced
absorption bands corresponding to the transitions on the 419/2 level (about
6100 cm 1),4S3/2 (approximately11,~50 cm 1), 2H11/21(122450 cm 1), 4F7/2
(13,950 cm 1 4F5/2 (~5,550 cm 1 F3/2 (15,~50 cm G9/2 (18,050 cm 1),
_1K15/2 (21,550 cm 1 bands
4G11/2 (19,850 cm G9/2 (20,850 cm 1) and G7/2, 2
(Figure 6.5). Here the band with maximum at 6100 cm turned out to be one of
tlie most int ense. Let us note that the authors of [361, 526] diverge with the
generally accepted classification of Er3+ ion levels (see, for example, [95,
219
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rvK urri'LInL ubr, uivLY
Glass compositYon I
Q , tor20ca2
-t I
Data
molecular X
1�ase

Source �
79,5 Si02, 8,1 Na2O,
2,0 BaO, 2,4 YbsOs,
0,50
'6510
[312]
8,0 KyO, 0,04 EyOs
57 SiQ3, 26,4 Li,O,
.
1,8 A1103i 13,8 M90,
0,77
6510
,
1339, 5191
1 ErsO8
119,5 P206i 49,5 SrO,
�
l Er,09 �
0,80
L 6510
1501
,
49,5 P903, 49,5Cd0,
. .
1 Lr&Os
0,76
6510
15191
49,5 P206, 49,5 MgO, '
1 EyOs ,
0983
6510
(50] .
56,3 P206r 25 ZnO,
'
12,5 A1,03, 5,2 La,O,,
0,74
8510
[519] '
1 ErzO3
84 BsOs, 14,8 Na;O,
0,50
6650
[519]
1,25 Ers08
� O,42
6510
�
58,9 PaOa, 24,7 ZnO,
,
' .
11,2 A1403, 5,2 Yb80�
1,11
,6510
[528J, :
0,18 Ey03
50 F905, 37 BaO, .
.
12,5 A120� 0,5 ErsO'
0,70
6510
[101, 2/t7]
The measurements were Derformed for 77K
Table 6.1

,
100, 338] and so on), according to which the induced absorption bands with peaks
in the vicinity of 18,050 c~ 1 and 20,850 cm 1 must correspond to transitions
to the leve~s zH9/2 4nd 2G912, respectively. The band corresponding to the
transition I13/2 4- F9/2 (near 8800 cm 1) was not detected in these experiments.
On the cyntrary, in [527], the presence of induced absorption in the 9400 to
9250 cm region in erbium glass was noted, which was later related by the
authors to the indicated Cransition [413] (Figure 6.6). However, as a result
of experimental difficulties, they were unable to reproduce the absorption band
curve completely, and the presented data are limited to a segment of its short-
wave wing. From Figure 6.6 it is obvious that on the pumping frequency of the
ELP (1.055 micons) phosphate glass with a concentration of .ML,, = 3- 1019 crc-3
with specific absorbed energy of about 5 ioules/cm3 has an induced absorption
level approximately equal to 7.5'10-3 cm I, which is 1.3 times less than in
220
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~
~
~
e~
~
C'
~
~
t
' p)
Figure 6.4. Luminescence (1) and absorption (2) bands of Erg+ ions in
Na-Mg-phosphate (a) and Na-K-Ba-La-silicate (b) glass at 4.2K and the
approximate position of the Stark components (dotted lines).
Data on the cf oss section are increased by five-fold in figure b in the
6000-6200 cm range.
,
silicate glass. Hence, it is possible to obtain a value of a 25 -S 3�10-22cm2
which must be considered as the lower limit, for the population of the metastable
level is explicitly below the value estimated by the absorbed energy.
As was already noted in S 6.1, an important characteristic of erbium glass is
the absorption coefficient kPUMP in the region of emission of pumped neodymium
lasers (1.055 to 1.06 microns). The form of the abaorption band of Yb3+ ions
in phosphate glass with high concentration of them is illustrated in Figure 6.1.
221
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Table 6.2
FOR OFFICIAL USE ONLY
Na-B-aa-Le-81os� glas
-
en-AI-PaOb..glass
Level
~
v~ y~, ~ cx-~
1
ev cu
-v t or-1
v
~ /
ev , cM-t .
pUmp
u m
Compon ints
0
13
0
,.17
2
~ Zg
. i8
29
, 26 `
3
.62 .
30
' 5i �
. ~
y
107
35
74
64
5
0
.2
2
m60
~l30
rtI3
8
6

~j
~YiJDV
SVI~/O
N270
~
NIO
'
7
w440 ' .
:70 '
as320
.70
, 8
M500
z,75
' s070
sw80
Compon in~"s"
0
17
2
33
46
18
~i8
�
g
51
18
41
.
. 26
4
75
25
89
35
5
a230
ce40
m}32
.
m(f0
6
as280
;J+S
Rs190
ft85 .
_ 7
%030
z9.2
.250
=SO
~
J
K
7.6�1o-3 sec, q " 0.9, $41.5�10-3 cm l, S ~ 2.Ox10-3 cm
_ kl Er M 6�10-Z cm 1. er lase pump
PuMP
� 6.3. Tube-Pumped Erbium Lasers
As has already been noted above 6.1), the energy possibilities of ELL are
highly limited. The basic efforts have been applied to improving them after
the appearance of the first reports on obtaining the lasing effect in Na-K-
Ba-silicate [514, 5291, Li-Mg-Al-silicate [530] and fluophosphate [531] glass.
Generalizing the conclusions of theoretical analysis of the energy characteris-
tics of ELP to the case of ELL, it is possible to state that conditions 2)
and 5) (6.14) in this case lose significance on the basis of the wideband
nature of the pumping. On the contrary, condition 6) acquires decisive weight.
In the given case this condition can be written in the form
230
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~'"Lr I nNthreshold '
f u~v) l~a dv ~ lyr c fo~ u(''1 dv = const,
v (1) (1) u" pump v (1)
0E UNLY
aZ
Figure 6.16. Diagram of an erbium converter with intraresonator symmetric
excitation of the erbium element [247]. 1--erbium active element; 2,2'--
neodymium active element; 319 32--neodymium resonator mirrors; 33, 3 4
erbium resonator mirrors.
Key: (1) X pump = 1.055 microns
(2) X lase - 1.536 microns
Figure 6.16 shows one of the optical systems of ELP with intraresonator loca-
tion of the erbium active element [101, 247] which we investigated. The latter
was made of phosphate glass typQ LGS-E containing .MYb = 1.5�1021 cm 3 and
J',r - 2,5 .1019 cri-3 (k = 6� 10-2cm 1. R � < 2� 10-3cu-1~ Tl E= g+p~~lp-3
sec), in the form of ~a p~~ism with side faggsPbeveled at angles of 45 _5 . The
pumping radiation was introduced into it normally to one of the beveled faces
and, undergoing several total internal reflections, it exited through the op-
posite face. The length of the erbium active element with respect to the pumping
channel was 12.8 cm. The pumped volume was 8.2 cmg. The resonator of the
pumping laser consisted of a prism 3 and dielectric mirror 3 and also two
active elements made of phosphate neodymium glass LGS-I made in the form of
rectangular plates 2 and 2' with dimensions of 1Ox32x280 mm3 and ends beveled
at the Brewster angle arranged symmetrically with respect to the erbium active
element. The base of the pumping resonator was 150 cm. The ELP resonator with
base s 20 cm was made up of flat dielectric mirrors 3 3(R = 1) and 3 4(R = 0.6).
The pumping pulse duration tpUMp = 1.6�10-3 second.
Two methods of compensation of k' (X) were used. In the first method, a
plane parallel plate of Sm203 puipeg glass (5 percent by weight)was placed in
the resonator at the Brewster angle to its axis: By selecting its thickness,
it was possible to stabilize aPumP, but the laser efficiency was reduced by 10
to 15 percent as a result of introducing additional losses into the resonator
at the lasing frequency (Figure 6.15, b). The second method gave better re-
sults. A dielectric mirror with reflection band selected so that R(1.54
microns) = 0.95, and R(1.070 microns) = 0.45 (Figure 6.15, c) was made. In
this case no noticeable decrease in pumping laser efficiency was observed. In
- both bases the lasing spectrum remained twice as wide as with a flat mirror,
and it occupied an interval of 1.054 to 1.056 microns.
Measurements o� the energy characteristics of this ELP demonstrated that the
threshold absorbed specific pumping energy is 5.3 3oules/cm3, the lasing energy
is about 40 joules with triple excess over threshold. The standard dependence
238
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of the lasing energy lase) on the specific pumping energy absorbed in the
erbium active element (7ty' ) is presented in Figure 6.17. From this rela-
tion it is possible to dete~ine the differential eff iciency of the ELP, reaching
30 percent. With somewhat altered resonator layout and greater pumping dura-
tion and excess over the threshold, the lasing energy of about 80 joules in a
pul.se with a duration of 3.5 milliseconds was achieved later wit~i differential
efficiency of about 39 percent and radiation divergence of 3'10 rad [515].
The lasing spectra consisted of three lines: 1.536 microns with
n~i lase -7 cm l, 1.543 microns with A~ lase -7'S cm 1 and 1.538 microns with
nvlase - 6 cm-l. With a pumping density of ~ 700 to 800 joules/cm2, local
deterioration of the glass of the erbium active elements with respect to platinum
inclusions was observed.
Attention is attracted by the small divergence of the lasing emission achieved
without the application of any special measures with a short resonator base
and small cross section of the lasing beam of the ELP (about 1.4 cmZ). This
is promoted by high uniformity of excitation and low specific heat release, which
are distinguishing features of ELP.
In references [413, 535], a study was made of the extraresonator system of the
G[,P (Figure 6.18). A phosphate glass laser with active elements 45 mm in
diameter by 620 mm (X = 1.543 microns) raas used as the neodymium pumping
laser. In order to iRcrBase the pumping density, a telescopic system 2 with
multiplicity of about 4 was used. The pumping was done through the end of the
ELP element (3) at an angle of approximately 20' to the axis of the ELP resona-
tor. The latter was formed by the prism 4 and the flat mirror 5 with R= 0.2
to 0.8. The length of the resonator of the erbium laser was about 150 cm. The
pumping pulse duration was (2 to 2.5)110-3 seconds. The erbium active element
wasmade of phosphate glass with the following parameters: .MY,, = 2,2 � 1()21
cm3, ,4"1!, = g . qp k pump = 0.054 cm l, T 1 Er = 7.5�10-31 Rlase = 0.006
cm I. Under such conditions with absorbed specific pumping density equal to
31 joule/cm3, a conversion efficiency was achieved which is equal to 35 percent,
and the differential efficiency was 43 percent with a specific energy pickup
of about 11 joules/cm3, total emission energy of 27 joules (through a S mm
iris) and divergence of 2.6'. The use of higher pumping densities led to the
Figure 6.17. Standard dependence of the lasing
energy )r lase of ELP in the free lasing mode on
ttie specific pumping energy absorbed in the active ~t
- el.ements, ~p' in the diagram with intraresonator .
abs
- 20
Lucation of the erbium active element.
(1)
Kcy: (l) 'or lase' Joules
(2) w abs' j�ules/cm3
(3) Efficiency with respect to slope ~ 30 percent
239
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!0 !.'U
(2)
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APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500080015-2
. - V� � ~~.~~.u Vyu VI \V �
1 z ~
4 3 054~ ~
' ~ �
liv
� ` ~ I
.f~ ~`'4~-~:(1~ ~
Figure 6.18. Diagram of an erbium ELP with active element outside the
resonator [4131.
1--Neodymium laser; 2--telecope; 3--erbium active element; 4--rectangular
reflector prism; 5--output mirror.
Key: (1) microns
- appearance of local damage to the investigated glass. The integral brightness
of the emission of the ELP is almost an order greater than the brightness of
the emission of the pumping neodymium laser. The emission spectrum consists
of two spectral components with peaks at 1.536 and 1.545 microns, 8 and 16 cm
wide, respectively.
Thus, the performed experiments demonstrated that the ELP permit not only crea-
tion of laser sources in the region of 1.5 microns with good energy characteristics,
but even an increase in the limiting values of the specific energy pickup from
the active element (to 10 to 20 3oules/cm3) and integral brightness of the
radiation to levels that are record levels for lasers in general, which opens
up the prospects for their use in powerful laser systems. At the same time,
a number of factors were discovered which prevent the achievement of maximum
operating efficiency of the ELP in the free lasing mode. Above all, these in-
clude the following factors:
1) Extremely high required pumping emission densities (to 1000 joules/cm2)
commensurate with the radiating strength of the glass and complicating the
problem of optical coupling of the ELP and the pumping lasers; 2) the necessity
for operation with minimum possible concentrations of Er3+ ions, which does
not permit insurance of suff$cient efficiency of the excitation energy trans-
mission in the pair Yb3+-Er3 , especially for high excitation levels; 3) rela-
tively small cross seEtion of the laser transition 4I13/2 } 4I15/2 which sig-
nificantly increases the requirements on the level of inactive losses and the
optical quality of the glass; 4) the presence of induced absorption on the
lasing frequency.
The indicated difficulties are softened to a significant degree on using ELP in
the lasing mode and on amplif ication of short (KI) and supershort (SKI) pulses.
� 6.5. Possibilities of the ELP Under Lasing and Amplification Conditions of
KI [Short Pulses] and SKI [Supershort Pulses]
In � 6.1 it was already noted that erbium glass is an almost ideal medium for
amplif ication of KI and SKI. This fact was first indicated in [513]. The
advantages of the erbium medium consist primarily in high quantum yield and
240
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large values of T1 Er permitting easy realization of the pumping mode
tpump 10 nanoseconds, values of n-_ 0.15-0.2 are entirely attain-
able; thus, the e?f iciency of zhe neodymium laser of about 3 percent can be
counted on for a total efficiency of up to 0.4 to 0.6 percent.
(1)
110
48
Figure 6.20. Experimental dependence of is
the specific abeorbed pumping energy. ~ y
W'abs threshold corresponding to fhe ,
threshold of achievement of inversion as `
a function of the Er9+ ion concentration ~
in LGS-E glass; .MYe=1,5x SOS' cH`i.-
Key: (1)'!+abs thresh' 3oules/cmg
242
FOR OFFICIAL USE ONLy
g 4 6'
o ,o
~ME~~IO~yCM'J
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- Figure 6.19 shows the experimental dependence of the gain of an erbium active
element made of LGS-E phosphate glass with different erbium ion concentrations
as a function of the relative magnitude of the absorbed speciric pumping energy.
The measurements were performed by sounding the active layer 5 cm thick uni-
formly excited by an external converging beam of neodymium laser emission
(tpUMp a 0.8 milliseconds), by a short pulse from the external ELL with Q-
switching (the delay with respect to the beginning of pumping is about 1.0
millisecond). As we see, for amall �Me the investigated relation is non-
linear in a large range of values of yr /w . On the other hand,
19 -3 abs abs thresh 1
for 'Mer = 8.6�10 cm , it is linear to va~ues of al se a 0.26 to 0.3 ~9 _ '3
which corresponds to a level populaCion of I11/2 of ~pproximately 7�10 cm .
The obtained maximum value of oc = 0.44'cm is not limiting. For large
Xg, and "W ab8 it can reach uplto 1 cm 1.
The threshold specific absorbed pumping energy as a function of the erbium ion
concentration in the glass is illustrated in Figure 6.20. From this relation
it follows that for small X$, the value V abs thresh is somewhat higher than
expected for qDASe-~- l. These data agree with the results presented in Figure
6.12, and they independently confirm the contribution of the accelerated de-
crease in probability of BPV in the pair Yb3+-Er3+ as the Er3+ ions are accumu-
lated in the metastable state with low concentration of them.in the glass.
The lasing characteristics of the ELP in the Q-switching mode will be illus-
trated in the example of the system used earlier to obtain free lasing (Figure
6.16). When using a rotating prism, output mirror with R= 0.5 and specific
pumping energy of about 9.5 3oules/cmg, this ELP emitted 5.1 joules per pulse
with 30 nanosecond duration. -
Figure 6.21. One version of the optical
system of the power amplification stage
for KI and SKI based on ELP.
1--erbium active element, 2--90� prism
of erbium glass, 3--neodymiun active
element, 4--selective dielectric mirrors.
x 4

,
r,r
i ~ ar
Figure 6.21 shows one of the possible versions of the optical system of the
output stage of a power amplifier based on ELP. The erbium active element is
made in the form of a plate 14.1 mm thick and 60 nm long, on the two lateral
faces of which 90 degree prisms made of glass of the same composition activated
only by erbium ions in a concentration of 2�1020 cm 3 are seated on a deep opti-
cal contact. Emission from two symmetrically arranged plates 20 mm thick made
of neodymium glass which are placed in a common resonator with the erbium
243
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N'UK UN'MII;IAL Ubh. UIVLY
active element is introduced through the indicated prisms into the active
element. The manufacture of these prisms from glass with Er3+ permits
efficient suppression of spurious lasing on the internal modes. It is obvious
that the amplified beam of radiation can be transmitted at any angle of
incidence with respect to the working planes of the active elements. The
degree of nonuniformity of distribution of the inverse population in it does
not exceed 5 percent. The total stored energy depends on the width H of the
excited part of the active element and the erbium ion concentration. For
example, for H= 60 mm and .Mer = 8.6�1019 cm 3, it can reach 500 joules. The
amplifying characteristics of the active element are analogous to those pre-
sented in Figure 6.18, that is, the gain per pass on incidence of the beam
at the Brewster angle will be about two.
244
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literatury, 1980
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