NBS SPECIAL PUBLICATION 341

Damage

in Laser Materials

UNITED STATES DEPARTMENT OF COMMERCE • Maurice H. Stans, Secretary

NATIONAL BUREAU OF STANDARDS • Lewis M. Branscomb, Director

Damage in Laser Materials

Proceedings of a Symposium Sponsored by

the American Society for Testing and Materials

and by the National Bureau of Standards

June 24-25, 1970, NBS, Boulder, Colorado

Edited by

Alexander J. Glass

Wayne State University

Detroit, Michigan 48202

and

Arthur H. Guenther

Air Force Weapons Laboratory

Kirtland AFB, New Mexico 87117

National Bureau of Standards Special Publication 341

Nat. Bur. Stand. (U.S.), Spec. PubL 341, 126 pages (Dec. 1970)

CODEN: XNBSA

Issued December 1970

sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 (Order by SD Catalog No. C13.10:341), Price $1.25.

Foreword

These proceedings report in detail the formal papers and discussions presented at the 2nd Annual

Symposium on Damage in Laser Materials held at the National Bureau of Standards, Boulder, Colorado on June 24 and 25, 1970. This meeting was jointly sponsored by the National Bureau of Standards and the American Society of Testing and Materials. The major topics covered were Diagnostic Development,

Damage Testing and Assessment, Damage Theory, and Physical Characteristics of Optical Media of importance in controlling damage.

The co-chairmen. Dr. Alexander J. Glass of Wayne State University, Detroit, Michigan, and Dr. Arthur H. Guenther of the Air Force Weapons Laboratory, Kirtland AFB, New Mexico, take full responsibility for synopsis of comments following each paper as well as the summary and conclusions of the meeting.

I It is suggested that individuals interested in the subject obtain publication NMAB-271, "Report

of the Committee on the Fundamentals of Damage in Laser Glass" which is available for sale

from the National Technice: Trf.rrn-.ation :;ervice. Springfield, Virginia 221'?] . at a cost of $3.00. Proceedings of the 1969 ASTM Symposium were published in December 1969 as "Damage in Laser Glass", ASTM Special Technical Publication No. 459 "Library of Congress Catalog Card

No. 74-102757".

It is our intention to convene another symposium next year in Boulder during June to update and document the state of the art in Damage in Laser Materials at that time. This meeting will cover the subject historically presented at these symposia as well as attempt to attack new areas such as thin

film coating damage, newer non-linear optical materials and crystalline laser materials (such as YAG

,

FAP, SOAP, in addition to ruby). Of particular importance will be discussions on damage thresholds

in picosecond times. We wish to encourage the reader to contact us on matters pertinent to the intent

of these conferences.

A. H. Guenther

Library of Congress Catalog Card Ntunber: 73-609162

iii
Contents

Page

Foreword «,•-••• i,° iii

A, If. Guzntrnfi Summary and Conclusions ^

A. J. Gl(U!> and A, H, numtli?A

Introductory Remarks 1 A. J. Glass

Keynote Address „ , 3 J. D. Myers , ,

Recent Developments at American Optical Corporation in Glass Lasers 5 E. Snitzer

Laser Glass Damage Testing at Owens-Illinois 11

R. W. Beck

Laser Glass Testing at NRL , , 19 T. H, DeRieux and J. M. McMahon

Experimental Investigation of the Behavior of Neodymium-Glass Laser Amplifiers 28

C. R. Jones, P. V. Avizonis , and P. Sivgals

Filamentary Damage in Glasses.... 37

J, Davit

Measurement of the Nonlinear Index of Glass Using Picosecond Pulses., 45

M. A. Duguay and J. W. Hansen

Absorbing Centers in Laser Glasses..., = 51 H. S. Bennett

The Inclusion Problem in Laser Glass 55

R. W. Hopper, C. Lee and D. R. Uhlmann

Role of Photo-Electrons in Optical Damage, , 67

R. W. Hellwarth

Damage Threshold Studies in Ruby and Sapphire , 76

C. R. Giuliano and L. D. Hess

Laser-Induced Damage to Nonlinear Crystalline Materials , 90 M. Bass

Raman Scattering in Microscopically Damaged Quartz „ 97 David F. Edwards, C, Y. She, J. D. Masso, Y. D. Harker and H. C. Schade

Exoelectron Emission from Optical Surfaces. , 102

P, Braunlich

Appendices

I. Pulse Duration Dependence of Laser Damage Mechanisms 105

E. S. Bliss

II. Participants 118

iv
Abstract

The second ASTM Symposium on Damage in Laser Materials was held at the National Bureau of Standards at Boulder, Colorado on June 24th and 25th, 1970. About 150 attendees heard papers by

fourteen speakers, representing the major manufacturers of laser glass, government, industrial and "university laboratories. Although the primary emphasis was on Ndrglass as a laser material, damage

mechanisms and morphology in ruby, sapphire, and nonlinear optic materials were also considered. It was clear that substantial advances have been made in the last year in the production of damageresistant laser glass for use in conventional Q-switched lasers. New diagnostic techniques have been

developed, and in some cases, adopted as quality control procedures by the glass manufacturers.

Theoretical understanding of the fundamental damage mechanisms is beginning to emerge, and material

properties relevant to these damage mechanisms are beginning to be measured. It was equally clear

that a great deal of effort remains to be expended to develop techniques suitable for nondestructive

testing of laser materials, and that many properties of laser materials at high energy density are presently poorly understood.

Key words: Ferroelectric materials; glass; laser damage; lasers.

Summary and Conclusions

1. Principal Conclusions

In the course of the two days of discussion, certain points emerged which might be termed "highlights" of the meeting. It was dramatically clear that both major domestic manufacturers of laser

glass have improved the damage resistance of their product significantly in the past few years. Laser

glass is presently commercially available from both the American Optical Company and Owens-Illinois

which will withstand from 20 to 30 joules/cm^ in a 30 nsec pulse. Selected samples are capable of operating at higher flux densities. Facilities now exist at these companies, and at the Naval

Research Laboratories, for testing large sized samples of laser glass at energy densities of 40 to

50 joules/cm2, unfocused, in 30 to 50 nsec pulses. In addition, new quality control procedures have

instituted by the manufacturers to select glass of better homogeneity, free of striae, bubbles,

stones, and other imperfections.

A point which was continually emphasized throughout the symposium was the importance of carrying

out damage tests with mode- control led lasers. In both ruby and nonlinear materials, damage thresholds

under illumination by single-mode lasers were from 10 to 100 times greater than those reported under

multimode illumination where average energy densities are computed. The scatter in the values

obtained for damage thresholds was also greatly reduced by using well controlled and reproducible

lasers thus eliminating scatter due to flucuations in the irradiating source.

Two speakers reported theoretical analyses of the stress induced in an otherwise homogeneous

medium by the presence of an absorbing inclusion under intense illumination. Although there were

points of disagreement between the two analyses, certain conclusions were obtained from both. The most damaging particles range in size from 10"^ to 10"'^ cm, and it is precisely in this range that

the non destructive detection of particulate inclusions is most difficult. Larger particles do not

get heated to a temperature sufficiently high to cause damaging stress concentrations, while smaller

particles do not intercept enough of the incident energy to cause damage. Increasing the thermal

conductivity of the medium increases the damage threshold, as might be expected. It is significant

that detailed modeling of this most fundamental damage process has only been carried out recently,

although the role of particulate inclusions in the damage process has been known for many years. The

models, though approximate, show trends and parametric dependence which are useful to guide experimental research and device development.

An apparently new phenomenon which was reported at this symposium was the presence of a so-called

"gain anomaly" in high energy, glass amplifier systems. At high pump energies, the gain measured in power amplifiers was up to 207„ less than that expected from theory. This anomalous gain reduction

could not be attributed to increased superradiant losses, spectral shift of the flashlamps, or the existence of any broad, pump-induced absorption in the laser medium. It appears in all laser glasses.

New diagnostic techniques were proposed for nondestructive tests of laser materials, including

holographic identification of large inclusions, changes in the Raman spectrum as evidence of fatigue

or residual stresses, and exoelectron emission as a tool for studying surface states. All these

techniques are currently under further investigation.

V
Sv'vor.il I'd rt i 1 p.u\t ;i in tho Sym|H>ti liiw i'v^ihmI oil \i\i\isiiroi\\out s i> I t ho uonliuiMi' linlox cm* f I' t o i out ol

jilatit!. 'l'l\o v.ihios oM.iiuovl Ivm' l.U'ior j^UlSSOti c.iuy.o I li'iw to .1 \ 10" ' osu lor u.,. I'lio v.iluo ol no Is wot !iou;!tt Ivo t v> t I v'h.u\i;.oti 1 1\ tillloillo oovihh>m i t i ou .

Ktu.illv, thoio w.iti I ,\c uioro I n I vnmat I ou ou otv st 1 1 t uo matovialt! aC tills year's symposium tliau was availablo a voac a>^o . I'Ktoustvo tuvo;;t IvAat tous ot tho wox-pho lo):;y of surface ilamago iu luhv ,uul sa(^)<h(ro has hoou oarrtovl out usluj; a soaivnluj^ olootrou mioroscopo. Damage throshoUis havo boon

dot ormluovl , usUis a stui^lo movio lasor, for l>v>th surfaoo ami voUuuo iiamaj.\o tu ruby; wlt:h oxit surface

vlamajio showluii tho lowest throshoUl, theu bulk ilavHage, aiul thou eutvauce surface (.taiuagte with t:he htjihest thresUolvl. St\rtaoo davtutjio was general ly acoompauleil by vilaswa fonnaCioiv, aini voUmio damage

acpearovl to bo in'oo I (>t tat i^d lu part by beam frappiug. The surface damage threshold for hiNhO.^ vi/as vHoasui-ed to bo ;vSO Mw/ow' for st»\gle mode ( 1 1 umluat iou . Uslug multlmode il lumluatiou , KOV vvas found

t v» bo much wore damage I'oststaut thou l.lNbO>, while tho damage thi'oshold iu lv'>,,NaNbt.O^ i- was about

tho same as tu liNbO..

2. Summary ot Vapors

U\ provtvlivig a suiwuary of the coutet\ts of the papers, it is iuteuded to give the iutorested

rvvuler svmwo flavor of the topics discussed at the Symposium, and to direct his attention to the papers appropriate to his particular Interests. I'he papers are svmmiariaed in approximately tho order they wore given at t Uo Svmpv^sium.

Pr . Klias Snit^er of the Americavx Optical Company reported ov\ tho status of their glass mav\ufacturlug and testing pvogccUH. Hy melting glass in a wullite crucible, with reduced pot attack, they are vwanufactur tv\g plat vnum- free glass with an absorption coefficient of as lovv? as 0.2~X./cra. He outlined tho details of the vuelt pxvcednre. He described their expanded procedure for improved quality

control, inclndivxg inspection techniques for tho elimination of bubbles, stones, and striae, and outlined the holograVbic test procedure used to find large inclusions. Results were given for damage

tests tvi variovis tost geometries.

Ivobort Ueok, of Owens-X llinots , in disovissing their laser glass development program, described

tho high-powor oscillator-amplifier system used for testiv\g, as well as their measurement techniques. He stressed the importance of considering overall system performance in establishing damage criteria.

Results of davnage tests on large s,'uv\ples were reported, as \\'ere plans for future investigatioix

.

John McMahon , of the Naval Research l^aboratory, reported results ^f damage tests carried out on

the iSRl. test device.^ This laser is capable of testing rods up to 4 cv\\~ in area at energy densities

greater than .^0 d/cwr In Q-switched operation, A full set of Owens-Illinois ivds have been tested in tho device, avxd results on d.-unage, beam divergence, pulse broadenitxg, and gain were reported. Results wore also given for American Optical glass rods. McMahon reported results on the aforementioned gain

anomaly. Vvirther results on the gain anomaly were reported by Capt. C. R. Jones of the Air Force

We^spons laboratory. Sevex-al possible explanatiovxs of the anomaly, includiixg superradiance , flash

lamp spectral shift, and pvwxp-induced losses iu tho host material wore ruled out by experimental test. Results were also given for the amplification of YAG laser output using an axial gradient glass

avwpltfior

.

fr, Joan l\\vit of tho Oampagnio G&^\^rale d' Electricite" shared elegant new results on the

vwrphology of self-tracking damage. By eraployiitg the Reiehert niicxvscope , he showed that the damage

track consists oC a tube of high index of a few ^m in diameter in wlxich an intermittent damage track

of less than one jJm. in diameter is evident. Davit has measured the noi\llt\ear index coefficient n., for several glasses, and rep\>rted that glasses with essentially^ the same value of but different

Cv^xsvvsitions show different thresholds for self tx-acking dam^ige.

Dr. Michel IXiguay, of tho Poll Tolophone Laboratories, also gave results obtained on the value

of n^. For SchoCt he fouiul » 2 x 10~'-'" esu, in good agreement with Davit's values. He

fv^vuxvl the relaxation time assc>ciateiJ with n.^ to be less than 5 psec. Us;^n§ the values measured, he

calculated trat^ring lengtlxs of 29 ciu for a power density of 10' watts/cift~ in a 30 nsec pulse, and

O.^^lcw for •^10''- watts/citt~ in picosecond times. The exact mechanisius, which accounts for the value

of n^ in glasjs at different pulse leixgths, remains uxxclear. Dr. LXiguay also reported an experimental

technique of attractive simplicity for ultra-high speed photography, using a picosecond shutter

driven by the optical Kerr effect. He exhibited a photograjrfx of a mode-lock*vd laser pulse in a scattering mediwu, eiaployirig this technique.

Dr. Herbert Bennett of tho National iJuroau of Stat\dards. and Mr. Robert Hopper of MIT both

described detailed calculations of the stress resulting frora the heating of a spherical psrticle

etubeddovi ix\ an otherwise hoGJogeneous nxeditua. These calculations provide valuable guidance both

for understanditx^ particle- iudvicod dam^i^e and evaluating the application of the h>^lographic test procedure reported by l>r. Suitaer. Both calculations identify particles from 10~" to 10" (JOxn in

diastoter as beitxg uvst likely to cause damage. While Dr. Bentrett found Sb and dielectric inclusions

to be slightly Kvre davaaging than Ft particles. Mr. Hopper found Ft inclusions more damaging than

vi
dielectrics. Dr. Bennett concluded that the damage process was more sensitive to the thermal con- ductivity of the host medium, compared to the thermal expansivity. He also concluded that "strengthening" the host by increasing its Young's modulus did not in itself ensure greater resistance to damage. Mr. Hopper concluded that great care had to be exercised in extrapolating damage results

obtained with /isec pulses to the nsec pulse regime. He also commented on the effect of non-sphericity

of the particles on the computed damage threshold.

Dr. Robert Hellwarth of the Hughes Research Laboratory and the University of Southern California

discussed a theoretical investigation of the heating of electrons by intense light pulses, in polar

crystals. Using the Frohlich-Hamiltonian to describe the electron-phonon interaction, he concluded

that there would not be significant production of "hot" electrons, but that the electrons would rapidly

transfer the absorbed energy to the phonons . He estimated that the intensity of the resultant acoustical waves could be sufficient to cause damage. He also found that the presence of cold electrons

could greatly enhance the excitation of impurity levels, and that an added multi-photon absorbtion

by impurity centers could result. These results were in disagreement with those previously reported

in the literature. Dr. Hellwarth also commented on the influence of conduction electrons on selftrapping, and identified the lack of experimental data on the photoconductivity of ruby and sapphire

over an extensive range of light intensities as a serious deficiency.

Dr. Concetto Guiliano, of the Hughes Research Laboratory, showed scanning electron microscope

pictures of surface damage in ruby samples. He found evidence of exit surface damage, accompanied by

plasma formation, at a lower threshold than that observed for volume damage, which could be attributed

to self-trapping. At still higher power levels, entrance surface damage, with plasma formation, was observed. Electron micrographs showed evidence of both crazing of the surface and of melting after

repeated exposures. Dr. Guiliano conducted his tests with a mode-controlled ruby laser, which he

described in detail. He also reported preliminary results for damage in optically pumped samples.

There was no discernable difference in the damage threshold under these two conditions or when the samples were chemically treated. There was, however, a marked difference in the morphology of damage

as exhibited in ruby and sapphire. Finally, in direct opposition to the findings of Nath and Walda,

the addition of the suggested amounts of TiO^ to ruby did not improve the damage threshold and in fact,

a decrease was observed.

Dr. Michael Bass, of Raytheon, discussed the questiorj of damage testing in nonlinear optical

materials. He emphasized the importance of detailed characterization of the material tested, and of

careful control and measurement of the intensity profile of the irradiating laser. Evidence of the importance of laser mode-control was given by the fact that in samples of Lithium Niobate which were

tested, the threshold for surface damage was 350 Megawatts /cm^ in a single mode beam, but only

6 Megawatts /cm^ in a multi-mode beam. These figures refer to average power density at the focus. In these experiments, surface damage was detected by the presence of a visible spark, and the subsequent

microscopic detection of a damage pit on the surface. Other materials investigated include KDP, ADP,

and Barium Sodium Niobate. No dependence of damage threshold on temperature or on the atmosphere to which the sample was exposed was observed. Dr. Bass pointed out that in most Q-switched lasers or frequency doubled systems, the nonlinear crystal is the Achilles heel of the system, and that damage

considerations often force one to the use of KDP, which has a higher damage threshold, in place of the

riiobates , which exhibit greater nonlinear coefficients.

Three short papers concluded the symposium. Dr. David Edwards^ of Colorado State University,

discussed the use of Raman scattering as a tool for detecting local stress in crystalline materials.

Stress accumulation is a precursor to catastrophic damage. In crystalline quartz, he has seen line

broadening, line shifts, intensity changes, and even the occurence of new lines in stressed samples.

Observations on laser-damaged quartz correlate with those made on samples subjected to thermal and uniaxial stress.

Dr. Peter Braunlich, of the Bendix Company, reported on the use of exoelectron emission as a diagnostic tool for the study of surface states. By recording the emission of electrons from a surface as a sample is heated from low temperature, information can be obtained on the presence of electrons in shallow traps and defects near the surface. Using a Channeltron* imaging device, a spatial image can be made of the variation of the work function on the surface. Results were reported

for ED-2 glass.

Capt. Erlan Bliss, of the Air Force Cambridge Research Laboratory, discussed the influence of the various mechanisms of nonlinear index change on laser damage, as a function of the time duration of

the laser pulse. An expanded version of his comments is included as an appendix to the symposium

proceedings

.

vii
3. Recommendations for further work

It is appropriate to end this summary of the conference with some observations on those features

of damage In laser media not fully resolved. In which more examination is suggested. Obviously

additional effort Is necessary in the development of nondestructive diagnostic techniques for quality

control purposes. It was pointed out on numerous occasions that as yet there is no convenient method

to determine the presence of sub-micron sized inclusions in laser glass, which are the lowest threshold

sites for the onset of inclusion damage under short pulse (i.e. < 30 ns) conditions.

In regard to bulk damage, due to nonlinear effects such as self focussing, no clear evidence has been advanced which delineate the temporal domain over which a certain mechanism (e.g. A. C. Kerr

Effect, electrostriction, etc.) is dominant as to its Influence on the nonlinear refractive index n . Only the generally accepted thesis as to which is obviously the principal cause at either very short or very long times, leaving unclear the mechanism effective for many materials in the time regime in which most Q spoiled high power lasers operate.

With the rapid growth of applications for mode locked pico-second lasers, damage thresholds at these short times should be assessed to determine how the damage mechanism is modified by enhanced

nonlinear optical behavior. This information is most crucial to the scientist Interested in plasmas

produced by lasers.

To people Interested in high total energy, high peak power application, the new well documented

evidence of a decrease in extraction efficiency under hard pumping conditions is most disconcerting.

One must elucidate the cause of this anomalous behavior before one can determine whether he has to live with it or can, in some manner, correct it.

Finally, while it was reported that much higher damage thresholds are obtained when employing

well-controlled single mode systems as compared to multimode lasers, the full danger of extrapolation

of small area or small volume damage investigations to usable dimensions has not yet been conclusively

demonstrated. This is particularly Important in crystalline media which are less reproducible in the growth process than glass melting and fabrication.

A. J. Glass

A. H. Guenther

viii
Introductory Remarks

Alexander J. Glass

Wayne State University

Detroit, Mich. 48202

Welcome to the 2nd ASTM Symposium on Damage in Laser Materials, The ASTM

Subcommittee II on Lasers and Laser Materials is charged with the responsibility of

formulating standards for laser materials, components, and devices. it is essential

that these standards be realistic, realizable in the laboratory, and wherever

possible, be based on a full understanding of the fundamental processes involved in

device performance and material properties.

In high power lasers, the damage level under various operating conditions is

the material property of paramount interest. But before damage standards can be

enunciated, substantial advances are required in the understanding of damage

phenomena, and in the techniques of testing laser materials at high power. It is

the concern of this symposiiim to inform the participants of the latest developments

in laser materials and test procedures, and to reach a consensus on the state of

knowledge regarding damage phenomena

.

During the past few years, the level of understanding of the damage mechanisms

in glass lasers, operating in a Q-switched pulse of 10 to 50 nsec duration, has

greatly increased. Three principal mechanisms of damage have been identified,

damage to particular inclusions, damage to surfaces, and failure of the material in

bulk due to the intense electric fields generated in self-trapped optical filaments.

The principal source of particulate inclusions has been identified as platinum coming

into the melt in the form of platin\am oxide. A few different manufacturing techniques have been developed to circumvent this problem, either by preventing the

formation of damaging inclusions of platinum, or eliminating platinum from the

manufacturing process altogether.

As evidence of the success of these techniques, laser glass is now commercially

available capable of withstanding light fluxes in excess of 20 j/cm^ in 30 nsec pulses, which represents an increase in damage level of a factor of 10 over the

laser glass of a few years ago.

There have also been significant advances in the understanding of surface

damage. There is general agreement that surface damage arises from the formation of

a micro plasma at or within the surface. A somewhat empirical approach to treating

the surface, to inhibit this plasma production, has proved successful in raising

surface damage thresholds in excess of 100 j/cm^ in 30 nsec pulses.

The phenomenon of self-trapping is inherently complex, depending on the nonlinear index coefficient of the glass, the beam profile, and the length of path

available. The underlying mechanism is a combination of effects, including electronic

polarizability , molecular libration, Kerr effect and electrostr iction . Basic

measurements of the effective non-linear index as a function of pulse length are just emerging, and will be reported at this meeting.

There still remains a great deal of work to do on damage mechanisms. There is

a scarcity of data at pulse lengths on one nanosecond or less. The question of

surface damage as a function of surface condition and treatment is still somewhat

open. There is still hope of further improving the damage level in glasses by

L
reducing the size and frequency of occurence of inclusions. Test procedures must be

developed if uniform standards are ever to emerge. When we turn our attention away

from glass to crystalline materials, less is available in the way of systematic data.

These materials, ruby, sapphire, and the materials of non-linear optics, are less

homogeneous than glass, and reproducibility and materials specification are important

problems. We shall hear two papers on damage in crystalline materials at this meeting.

The idea of this symposium is to bring us up to date on the subjects discussed.

I want to thank all the speakers who have contributed papers, and all the attendees

who will contribute to the discussion. We are grateful to the National Bureau of

Standards for their hospitality. Our particular thanks go to Mrs. Pauline Smith

and Dr. Harold Boyne of the National Bureau of Standards for their help and advice

in the organization of this symposium, and their efforts in the preparation of the

symposium proceedings.
Keynote Address

John D. Myers

Chairman Subcommittee II, Lasers, ASTM

The American Society for Testing and Materials is sponsoring another Laser Damage Symposium for a number of reasons, most of which are intimately connected with the interests of the membership.

The primary reason, however, is simply in response to the rhetorical question, "How can we pre- pare standard methods for measuring the damage threshold if we are not really sure of what we are talking about?" On the other hand, one might well ask, "Why do anything at all?"

The situation which motivates most of us to action is, in this case, typical of new technologies.

This situation can best be described as one of incomplete communication. What usually transpires is that some company makes a claim about one of its products. Other companies make counter-claims

based upon their particular bent, until the air is filled with claim, counter-claim, and counter- counter-claim. . .all using the same words, but within entirely different context. We all remember

when the output of a laser was not so much dependent upon the electronics involved as whose calorimeter was used.

To elaborate further - one can imagine the following one-sided telephone conversation between

a laser material user and the Ersatz Company who has just made a claim that its laser material has

a damage threshold of .3 BTU/in^...

"Hello, Ersatz Company, I want to talk to one of your technical people about your

laser material. Dr. Schwartz? That will be fine. Hello, Bernie, how are you?

What is this I hear about indestructible laser material? How did you run the test? Uh-huh . . . long focal length lens. What was the pulse width?... 127 nanodays? How did you manage that? I see, it just came out that way. What would

be an equivalent damage threshold at 2 picoseconds? You haven't the faintest

idea? Well, in any case, it must be pretty good stuff... I imagine you tested

quite a few samples. How big was the sample .. .microscope slide? Well, this

is the same material you sell isn't it ... .almost? Can I buy some to try in my

system? Problems...? What kind of problems? Man who made the stuff quit...

to start a chicken farm?"

And , so it goes . .

.

I am sure everyone here is familiar with similar episodes which have resulted in warped per- spectives and agonizing frustration for all concerned. It seems clear that what is required to alleviate these misunderstandings is simply a clear presentation of the purpose for which the claim

is made, along with the context within which the claim applies. And, this is precisely what ASTM

attempts to accomplish. True, we do add a bit. We not only explain the purpose and scope, but also

suggest a pre-tested measurement method.

So far, our efforts in this area have resulted in the following specifications which are now

undergoing review and preparation for inclusion in the ASTM standards.

1) "MEASURING THE OUTPUT OF A HE-NE LASER OPERATING AT 6328A."

2) "INSPECTION PROCEDURE FOR SURFACE FINISH OF POLISHED CRYSTAL OPTICAL ELEMENTS."

3) "METHOD OF TEST OF BEAM DIVERGENCE FOR OPTICALLY PUMPED PULSED LASERS."

4) "DETERMINATION OF PARALLELISM OF SURFACES OF TRANSPARENT MATERIALS."

5) "METHOD OF TEST FOR EFFECTIVE FLUORSCENT LIFETIME OF NEODYMIUM AND ERBIUM LASER

MATERIALS .

6) "METHOD OF TEST OF SLOPE EFFICIENCY AND LASING THRESHOLD FOR RUBY LASER RODS."

7) "METHOD OF TEST OF LASING THRESHOLD CURRENT AND SLOP EFFICIENCIES FOR DISC LASERS."

Plus more to come...

3
These standards have been prepared by the various sections of the subcommittee. The sections

are: Optically Pumped Section, chaired by Arthur H. Guenther, U. S. Air Force Weapons Laboratory;

the Electron Impact Section, chaired by Sheldon Minkowitz , The Perkin-Elmer Corporation, the Diode

Section, co-chaired by Jack Ludman, Air Force Cambridge Research Laboratory and Robert J. Mahler,

National Bureau of Standards, Boulder; and the Modulator Section, chaired by Allan E. Carlson,

Gould, Inc.

We approach these subjects in a rather pragmatic manner. For example, if two solutions to a problem exist, rather than choose between them we suggest them both. Our mission is to foster understanding within and promote the well being of the laser industry as a whole, rather than restrict

or regulate. All of us are volunteers, (although I suppose some are drafted) who feel the job needs

doing and really can't find anyone else to do it.

WELCOME, on behalf of ASTM, to the second Laser Damage Symposium.
Recent Developments

at American Optical Corporat

in Glass Lasers

ion

E. Snitzer^

Central Research Laboratory

American Optical Corporation

Southbr idge^, Massachusetts 01550

A description will be given of the quality control procedures

used to obtain laser glass from an all ceramic melt facility which

IS suitable for use at 20J/ cm in a 30 ns pulse. A non-destructive

holographic method for the identification of damage sites will be

presented. Finally, some results will be given on recently prepared experimental glass which appears to be entirely free of

damaging inclusions and which has an absorption coefficient at 1|J, of 0.2f°/cm.

Key Words: Glass damage, glass lasers, holography,

inclusions, lasers.

1. Introduction

A review of the work done on laser induced damage in glass at American Optical

Corporation up to last year was given at the First Conference on Damage in Laser

Glass held here in Boulder a year ago [ll. Since that time, our efforts have been

directed primarily towards the problem of damaging inclusions in neodymium laser glass.

In this report, the quality control procedures that are used for obtaining glass

suitable for operation up to 20j/cm^ in a 50 ns pulse without damage are described.

Since damaging inclusions within glass are essentially a statistical problem, some data

is given on the density of damage sites as a function of incident energy density. The

second topic to be covered is some preliminary results on a nondestructive method for

identifying potentially damaging inclusions by the use of holographic inter ferometry.

Finally, some results on recently melted experimental glasses are given in which there

appear to be no damaging inclusions.

2. Quality Control and Damage Test Results

Laser glass suitable for efficient operation in large oscillator-amplifier systems

should not only be free of damaging inclusions but should have a low loss coefficient

at 1.06[X and be of sufficiently good optical quality to permit output beams approaching

diffraction limited performance. To obtain a low loss coefficient, the batch from

which the glass is reacted contained less than 5 PPni of iron and copper. The ceramic

melter was made of high purity mullite, which is sufficiently insoluble in the glass so that the pot attack is low enough to permit effective homogenization of the glass. The

glass was produced by a batch process in a mullite crucible with a bottom orifice [23.

Eight liters of glass are reacted, fined and homogenized in a ten liter crucible.

Typically only five or six liters of finished glass is extruded at one time. The

^Director of Basic Research

5
remaining glass in the crucible serves to plug the bottom orifice for the next fill.

The billets are cast in a graphite mold 7-5 cm in diameter and approximately a meter in length. After the ends are ground and polished for preinspection and the

billet found to be reasonably free of bubbles and striae, the billets are placed in a transparent rectangular chamber filled with index matching immersion oil. A photographic record of the striae in the glass is then taken in the form of three shadowgraphs, one through the length of the billet and the other two photographic records

perpendicular to the axis of the billet. The preinspection yields 60 to 80^ of the

billets produced. An average of 10 billets can be made with one crucible. Of these,

60 to 80^ are sufficiently free of striae and bubbles to warrant further inspection in

the liquid immersion tank. The glass coming from the tank typically contains no more

than one bubble per two liters of glass with the bubble size less than O.5 mm in

diameter. The density of stones is of the order of one per ten liters. The yield from

both the preinspection and the striaegraph test in the liquid immersion tank is between

50 and 40^. The higher yields are for low neodymium content glass, that is, glass with

either 0.8 or I.5 wt^ Nds O3 . The specification on the loss coefficient at the laser

wavelength of 1.06|i is that it not exceed 0.35^/cm; however, most of the glass has a loss coefficient of about 0.2/^/cm. The glass of good optical quality is then damage

tested

.

The damage tester was described in detail by Young and Woodcock [l]. By use of

pulse forming networks and a Kerr cell, the peak portion of the spontaneous emission

from a meter length rod can be admitted to the subsequent amplifying stages with a total gain of I50 dB . A schematic representation of the device is shown in Fig. 1. Three different pulse durations have been worked with as shown in the table in Fig. 1. Most of the damage testing was done with an energy per pulse of between 80 and 100

joules with a total pulse duration of lOU-s. Due to gain saturation, one half of the

energy is contained in the first 4|j,s. Gain saturation in the amplifier does not occur

for the shorter pulse durations. Less energy was produced per pulse in the shorter

times as shown in the table. The output diameter of the last amplifier was 38 mm and

the full beam width at one half intensity was 1.8 milliradians . To obtain uniformity

across the aperture only the central 30 mm was focused into the billet to be tested.

The lens for focusing the energy into the billet depended on the energy generated in

the pulse. For the three time domains, focal lengths of 4, I.3 and 0.5 meters were

used to test the glass. The most extensive tests were carried out with the 10|is pulse.

A 4 meter focal length lens has sufficient depth of focus to sweep the entire length of

the billet in one shot.

The test results on ten billets with 80j/cm^ in lOp-s gave between two and six

damage sites per billet. The sites appeared to be randomly distributed. The average

density of damaging inclusions was one per liter. The glass which survived this test was then subjected to the next shorter pulse time. The density of damage sites as a function of energy density in the pulse is shown in Fig. 2. Curves A and B are for

two different glasses and represent the typical spread in the average density of damage

sites for various glasses. Glass which survived 80j/cm^ in 10 ns did not damage at

30j/cm for pulses between 0.5 and l|j,s in duration. However, for energy densities

above JOj/cm^ in this shorter time domain, the density of damage sites rose abruptly.

The glass was then tested at 25j/cm^ in a 100 ns pulse and no damage was produced.

Finally, tests at 20j/cm^ in JO ns produced no additional damage sites. The damage

sites which were produced in any of these time domains grew larger on subsequent

irradiation at the same energy density, but no new damage sites appeared, which

indicated that fatigue effects were not present.

A density of one damage site per liter is sufficiently low to readily permit

fabrication of rods 30 cm or more in length, but a higher density of damage sites

restricts the rod sizes that could be obtained. Hence, a practical restriction on the

laser glass commercially available from AO at the present time is that it be used in

systems operated up to 20j/cm^ in a J>Q ns pulse. At higher energy densities in this

time domain, the glass may damage.

The damage produced as a function of pulse duration and energy density can be

used to infer the approximate particle sizes for inclusions. In the paper to be

6
presented at this conference by Hopper and Uhlmann, they calculate the temperature of a metallic inclusion as a function of energy density, pulse duration and particle size.

From the temperature distribution, they obtain the stresses in the glass which can lead

to fracture. Their analysis indicates that the damaging particles are about l\xs in

radius

.

5. Holographic Testing

Although recently, some experimental melts of glass have been prepared which are entirely free of inclusions, the ability to identify the composition of the inclusion

would be of great help for the production of large volumes of damage free glass. At

present, by testing the glass with 80j/cm^ in lOp-s when a damage site is identified by

fracture of the glass, it is not possible to then determine the composition of the

inclusion. This is because when damage occurs, a large surface area is presented over which the material in the inclusion is spread. Attempts have been made on damaged

glass both with an electron beam probe and a laser spectroscopic microprobe to determine the composition of the material at the damage site. These attempts have been

unsuccessful, probably because of the aforementioned problem of dispersal of the

inclusion over a much larger volume.

By a holographic inter ferometric technique, it should be possible to identify the

positions of the damaging inclusions within the glass without producing damage. Even

though the particle size is of the order of l[is , if enough energy is absorbed from an incident beam of relatively long pulse duration, the heated glass in the vicinity of

the particle could constitute a sufficiently large phase object to be seen optically.

With care it is possible to see phase objects of less than X/lO Cjl. Energy densities

of thousands of joules per cm^ in several milliseconds may be required.

In the holographic inter ferometric technique, two holograms are superposed on the

same film. The first exposure is taken just before irradiation with a high energy

density and the other shortly after irradiation. In the reconstruction of the hologram,

the fringe pattern in the vicinity of the particle would indicate the presence of an absorbing inclusion. An inclusion which is nondamaging, such as a small piece of

refractory or a bubble, would not give a fringe pattern.

A feasibility experiment was conducted with the damage tester operated with a

10|jLs pulse. The glass for this experiment was known to contain particles whose

diameter is of the order of 10 to 15(1. The apparatus used for the experiment is shown

schematically in Fig. 3. A Spectra-Physics Model 125 He-Ne laser with a power output

of 20 milliwatts at 0.628(1 made the holograms. The first hologram was made with the

removable mirror and the removable light absorber out of the beam. These two elements

were then replaced and the billet irradiated with the output of the damage tester. The

second hologram was then quickly taken with the mirror and the light absorber again

removed. The film used was AGFA-GEVAERT 8e70 with a resolution of I5OO lines/cm and a sensitivity of 200 ergs/cm^. To avoid excessive noise from the nonlinear response of

the film, by attenuation before the beam splitter an exposure of 3(ij/cm^ was used such

as to give a 6oi modulation on the film. The length of each of the exposures to the

He-Ne light which was 1 ms and the time between irradiation with the 1.06|i beam and the

second hologram was HO ms

.

In Fig. 4 are shown a series of pictures taken of the reconstructed image in the

neighborhood of an absorbing inclusion which was irradiated with 40J/cm^ . Figure 4 is

a series taken with the plane of the focal region of the microscope moved successively

by 1 mm increments. In Frame A, the focal plane is 1 mm in front of the inclusion, in

B in the plane of the inclusion, in C one millimeter behind the plane of the inclusion,

and in D two millimeters behind the inclusion. In the plane of the best focus on the

particle, two fringes are present which is indicative of absorption by the inclusion.

The evidence in Fig. 4 was much more clearly indicated in the direct observation of the

reconstructed image, because it was possible for the observer to focus through the

plane of the particle and in this way clearly distinguish between particles with fringes

and those without them.

7
To identify particles of

energies. Longer pulse times

the surrounding glass without

the order of 1 to 2[i in diameter would require much highe:

could be used so as to develop observable phase delays in

damage.

4. Recent Experimental Glass

Three experimental melts have been made of low loss glass which appeared to be

entirely free of inclusions. The largest melt was a two liter volume in which only

about 1/5 of the glass was sufficiently free of striae to be useful. This volume was

swept with 100 to 120j/cm^ in 100 ns and no damage produced. In ten additional shots

in which two cc' s of glass are irradiated at up to 5OOj/cm^ in lOO ns, no damage

resulted. Self- tracking damage occurred at 5OOj/cm^ in an 80 ns pulse. The measured

value of the loss coefficient was 0.2f>/cm. This glass will not be commercially available until reasonably large volumes of striae free glass can be fabricated.

5. Acknowledgement

The author gratefully acknowledges the work done by C. Padula in testing the glass

and the holographic work by R. van Ligten, J. Levitt and K. Lawton. R. Hopper and

D. Uhlmann are acknowledged for helpful discussions on the damage mechanisms due to

inclusions. The cooperation of R. Woodcock, G. Young and E. Deeg is gratefully noted.

References

[1] Young, C. G. and Woodcock, R. F. , "Laser Induced Damage in Glass, " Damage

in Laser Glass , A. J. Glass and A. H. Guenther, Eds., ASTM STP 469, American

Society for Testing and Materials, 1969,

pp. 84-99.

[2] Deeg, E. W. and Silverberg, C. G. , "Melter for Optical Glasses, " J. of Glass

Manufacturing, April 1970.

[3] van Ligten, R. F. , "Holographic Microscopy

for the Determination of Failure Mechanisms

in Monolithic Circuits, " Final report on Contract No. NAS 12-584, NAS Scientific

and Technical Information Facility, College

Park, Maryland.

1 .8 mrad

= k, 1.3, 0.5 m

Fig. 1

PULSE DURATION TOTAL energy/pulse

h -10 lis 0.5 - 1 .0 ^LS 100 ns

80-100 J

55- 80 J

15- 25 J

Schematic of amplified spontaneous emission device used to test glass billets for mclusion damage. The total energy available for the various time domains are indicated in the table. The focal length for the lens used to focus into the billet decreased with decreasing energy in order to provide the necessary energy density withm the glass. ^

8
T

J/cm2 in Ips

Fig. 2 The density of damage sites produced in currently available AO commercial laser

glass. The glass that was tested had previously survived 80j/cm^ in 10 ys.

Fig. 3 Schematic of holographic apparatus for nondestructive identification of the positions

of damaging inclusions.

9
Fig. 4 Photographs of the reconstructed image of a hologram when focusing in various focal planes in the vicinity of an absorbing inclusion. Frame A is 1 mm in front of the inclusion, B at the inclusion, C 1 mm behind the inclusion and D 2 mm behind the inclusion.

COMMENTS OAi PAPER 6V ELJAS SWITZER

T/ie nmcauKejfmyiti n.e.ponJ:e,d heAn weAe pnolAyritncuuj , and MOJie. du-cgmd to dmonitAcute, the {^zailbUxZy

0(5 iLi,-LiiQ thd liotogfLapkic mutkod to locatz. abio^b^ng poAtxclsA -tn the. glcLii. At pKej^ent, pcuvUcleJ,

0(5 dA-CumeXeA^ ai malZ cu. 1 0 to /5 ym can be deXncXnd . Thui pcuvUaleA yield a dlitonJU.on pcuUeAn o^

2 ifu.ng<iM when ^AAadA,ated ax a level ojj 40 joulei /m^ . To iee paAtU.cJLe6 o^ one pm i^ze, mWi the

ionie 6eni>-utLVAjiLj, would fiequAJie 100 timei> g>ieat an energy detuUy. It ^ po-iilble, M-Uh caAe, to

Y^ietea^e the ienA-UUvAXy oi the pie^ent appoAatm to detect a 6lvt{^t o/J a (^nacXlon o{^ a inA.nge. The

hologiapivLC expoiuAe -a, taken 40 to 50 mi,ec a^teA the heaAxng puUe. The fiecoAdlng expoauie dan.aJu.on

-u. about one mec. It moa (^eU that negligMe cooling oceans on ttvu time icale. Te^U u)eAe n.un on unpwnped ianip£e,5 only.

iJo {^attgue e(,(,ecti> wexe obieAved In ceAamtc-made gloM, although oldeA iamplei o(, gla^i, made -Ln plaUnutn unde,n. a contAoUed atnwiphsAe d<.d exlu-bU {^atcgue e^ect^ . In all ca^ei>, the damage i>Ue giom M^th each iubiequent expoiuAe.

10
Laser Glass Damage Testing

At Cwens-Illinois

R. ¥. Beck

Owens-Illinois, Inc. Toledo, Ohio

Owens-Illinois is continuing to test a variety of glass samples to determine

their damage threshold to laser irradiation.

Active damage threshold tests in the third amplifier stage of the OwensIllinois oscillator-amplifier system indicate that selected samples may withstand

peak energy densities of 50 joules/cm^, for 50 nano-sec pulses. The increase in the peak energy densities for damage result from improved .melting processes in

the period from February of to February of 1970. The effect, thus far, is an increase in the laser glass damage threshold.

Active life tests in the third amplifier stage at peak energy densities of

36 Joules/cm^ indicate that no degradation of the lasing properties, notably, ef- ficiency, beam profile, pulse duration, and beam divergence occur for a 200 shot sequence. These results imply that for current state-of-the-art laser glass,

system output degradation characteristics should at least be a part of any criterion for laser glass damage.

Passive damage tests on samples approximately O.5 cm thick by 2 cm square indicate that micron to sub-micron inclusions are most easily damaged. A sample,

which contained no visible inclusions at lOOX magnification with side lighting,

did not damage at a peak energy density of 70 joules/cm^.

Self-trapping and surface damage measurements on a 91 cm long unpumped

sample resulted in no damage with an unfocused beam of 75 joules/cm^ average energy density. With the sample placed ahead of the focus of a 2 meter lens, orange peel damage appeared on the output face at an average energy density of 136 joules/cm^, pitting damage appeared at an average energy density of ihk joules/cm^, and self -trapping damage occurred at an average energy density of

128 Joules/cm^. No input face damage was noted for a maximum average incident energy density of I'j-O joules/cm^.

Key Words: Active damage threshold, inclusion damage, life test,

passive damage threshold, self-trapping damage, surface damage.

1. Introduction

Laser glass testing at Owens-Illinois is directed toward the characterization of laser glass damage, first, to provide the users of laser glass with reliable damage threshold data and, second, to internally utilize the information for further laser glass quality improvements.

There are several possible mechanisms responsible for the observed internal damage in laser glass,

such as absorption and subsequent heating, plasma formation from multiphoton absorption and avalanche

breakdown, stimulated Brillouin scattering, and others. Each process exhibits its own characteristic

dependence on several critical parameters, such as pulse duration, wavelength, beam profile, and the degree of focusing, and each process is in turn enhanced by self-trapping. This then presents a rather

complex experimental environment and any valid testing program must define and control the many experimental conditions which prevail during damage testing. In this vain, the experimental configuration

with which the damage measurements at Owens-Illinois are performed and the techniques used to determine

the experimental conditions are first defined. As the discussion proceeds, the experimental conditions

which prevail during each damage measurement are indicated, noting such parameters as the lasing energy, pulse duration, beam profile, beam divergence, whether the beam is focused or unfocused, and i.riiether the test sample is pimped or unpumped, which is referred to as active or passive testing.

11
2. Experimental Configuration and Measurement Techniques

The principal test facility for the damage measurements, shown in Figure 1, is basically a Qswltched, neodymium glass, laser oscillator-trebble amplifier system. The system is Brewstered and all

rod diameters are 19 mm. The rods are pumped with helical flashlamps and each lamp delivers a maximum

of k060 joules at 6.0 KV. The rotating resonant reflector, Q-switched, oscillator will deliver a maxi- mum of from 10 to 12 joules, full aperture, in a hO nano-sec pulse. To enhance the beam uniformity, an 11 mm major axis elliptical aperture is placed after the oscillator output mirror. About 5 joules passes through this aperture. The beam is then expanded and recollimated by a 1.5X telescope after

which it passes through the three amplification stages. Elliptical apertures with l6 ram major axes are placed on the input faces of amplifiers one and two to lessen the probability of output face damage and to keep the beam away from the rod sidewalls.

The average energy density within the system is sampled both at the input and the output of the

amplification stage using beam splitting components. The energy is monitored with TRG thermopiles and

recorded on milli-volt strip chart recorders. The maximum average energy density which the system will

deliver is approximately 75 joules/cm^.

The lasing pulse duration is monitored with a TRG 105B photodetector and a 519 Tektronix Oscilloscope and the system generally emits a 50 nano-sec pulse.

The system beam divergence is determined by burning exposed film placed 100 cm behind a pinhole

grid. The system typically has a slightly better beam divergence in the direction across the TIR roof

edge than along the edge. For an oscillator cavity length of 135 cm, the vertical and horizontal full

angle beam divergences are 0.5 and 1.5 milli-radians for a 30 joule output, and 1.0 and 2.0 milliradians for a 60 joule output, and 1.0 and 2.0 milli-radians for a 90 joule output.

The device used to measure the lasing beam profile is a United Detector photodiode array consisting

of 13 photodiodes in the form of a cross. The diodes are spaced on 3-8 mm centers and each diode is 2.0 mm in diameter. Each diode is part of a separate channel consisting of a light sensing circuit, an emitter follower transistor stage, and an RC storage network. The array is calibrated with uniform

laser energy and the stored voltages are normalized to the center diode to provide relative profile

measurements. As shown in Figure 1, a wedged beam splitter samples the lasing output, a negative lens expands the beam to fill the array, and neutral density filters are inserted to control the beam intensity incident on the diodes. The distance from the output end of the third amplifier to the array is nominally 50 cm. To convert voltage readings to energy densities in joules/cm^, a computer program was written which integrates the volume contained by a surface generated from 11 voltage measurements. This

volume is then divided by 2 cm^, which represents the circular cross-section of the beam within the amplifier rods, and is equated to the measured average energy density. The resulting energy density

equivalent to one stored volt is then applied to each measured capacitor voltage, completing the con- version to energy densities. Typically the profiles have peak to average energy density values of 1.3j

1.2, and 1.1 for respective system energy outputs of 30, 60, and 90 joules. A typical profile for a system output of approximately hO joules/cm^ peak energy density is shown in Figure 2.

In the damage statistics which follow, the damage thresholds will be given in both average joules/cm^ and peak joules/cm^, the conversion factors for which are obtained from profiles similar to

the one shown, but recorded during the particular measurement.

Active damage thresholds are observed in samples pumped in the third amplifier stage. The occurrence of internal damage is noted by the presence of a visible inclusion with the sample illuminated

with a microscope lamp, which easily detects 10 p, size inclusions. Passive damage measurements are per- formed on samples placed external to laser system, either with or without the aid of focusing optics.

3. Active Damage Tests _

,

During the course of the period from July of 19^9 to the present, l8 third amplifier rods were actively damage threshold tested. The rods were selected equally from each of three melts between

February of I969 and February of 1970. Table 1 summarizes the damage results obtained for the three

melts. The figure indicates both the average and the peak energy density at the threshold of damage

for each rod tested. At the onset of damage no more than two damage sites were ever noted and these were generally in the order of from 100 \J, to 200 |j, in size. It is significant to note that the range

of damage thresholds within a melt is of the same order as the melt average, indicating that the damage sites are not uniformly distributed throughout the melt either in size, location, or both. The

highest damage thresholds obtained to date have been samples one and five of melt C which damaged at peak energy densities of 52.6 and 55. 1 joules/cm^ respectively.

12
Table 1. Active Damage Summary

Melt "A" (February 1969)

Sample No. Avera^ Damage Threshold Peak Damagf5 Threshold

(Joules/ cm ) ( Joules/cm^)

1 8.0 12.8

2 10.8 17 3 12.0 19 2

k 6.8 10 9

5 9.8 15 7

6 23.9 31 1

i-VV trl ct^;e = 11.9 Average = I7 8

Melt ' B (.October lyby

j

1 25.0 - 9-1- Ru

2 20 J 5 XD . 0 21 5

T 8 8 q 18 2

u 25 7 Avera^;e = 17-5 Average = 23 9 Melt ' C' (February 1970)

1 41.6 52 6 2 13.8 16 6

3 19.4 23 1 26.1 33 1

5 46.9 53 1 6 13.8 18 6 Avera^ = 26.9 Average = 32 8

An analysis of the data also indicates that the average of the peak damage thresholds for melt C is 84^ better than the corresponding figure for melt A, indicating a significant improvement in melting

capabilities in the time period February I969 to February 1970- When the thermo-dynamic analysis of

the melting environment is completed, it is hoped that the results will dictate further improvements

in the ensuing months.

4. Life Test Results

In the preceding measurements, laser glass damage is defined as the appearance of an inhomogeneous

physical defect within the material resulting from the transmission of a laser pulse. An alternative

definition is a degradation in the output performance of the laser system in terms of some system variable such as efficiency, beam profile, beam divergence, or pulse duration, and it is such a performance

deterioration which is of most importance to the users of laser material.

To determine the significance of such a proposed degradation definition of laser glass damage, a rod from melt B and a rod from melt C were actively life-tested in the third amplifier stage for 200

shots each at a peak energy density of 36 joules/cm^. TJo system deterioration in efficiency, beam profile, beam divergence, or pulse duration was noted in these tests. The rod from melt B had a total of

11 inclusions at the end of the test, one having grown to O.5 mm, while the rod from melt C had only

the original one inclusion at the end of the test, and th^ inclusion had not enlarged. These results

strongly imply that for the current state-of-the-art of laser glass, output degradation characteristics

should at least be a part of any criterion for laser glass damage.

5- Passive Dcimage Measurements

At the outset of the current laser damage program one of the primary goals was to generate inclusion size and type versus damage threshold data. To attain this goal small samples approximately 0.5 cm thick by 2 cm square were polished and mapped at lOOX magnification with side lighting. The samples were then irradiated and remapped. The evaluation of many such samples concluded that such a technique

is not practical. First, due to the small density of inclusions present in the material, large volumes must be mapped to locate the desired inhomogeneities . Second, when inclusions are found they rarely

damage when irradiated, rather, small micron to sub-micron inclusions which show up irith side lighting

produce the majority of the damage and wash out the original inclusion. Third, quite often damage

13
results in areas where the glass was thought to be inclusion-free. Attempts are presently being made to locate the inclusions with holographic techniques, but if the lowest damaging inclusions are in fact

those of a micron to sub-micron size, then even holography may not have the necessary resolving power

One test of the passive damage measurements worth noting was a sample which was visually inclusionfree at lOOX magnification and subsequently showed no damage at a peak energy density of TO joules/cm^.

This indicates that if the sample was indeed inclusion-free, then the damage threshold of homogenous

glass is quite high. ;

' ' '

6. Self-Trapping And Surface Damage

Preliminary self-trapping and surface damage measurements have been performed on a 91 cm long un- pumped sample. For the first test, the sample was irradiated with the unfocused output of the

oscillator-amplifier system. With this configuration, a maximum average energy density of 73 joules/cm^

incident on the front surface of the sample produced neither surface or self-trapping damage. Assuming

a worst case beam divergence of 2 milli-radians, this is equivalent to an energy density of 63joules/cm2

on the output face of the sample.

Having produced no damage with the unfocused beam, a 2 meter lens was placed in the system immediately after the third amplifier and the test sample was placed ahead of the focus with its front end

100 cm from the lens, as shown in Figure J- As the output energy of the laser was increased, the first occurrence of damage was an orange peel effect on the output face of the test sample. The appearance

of this type of damage is shown in Figures k and 5- In Figure k, the surface is slightly out of focus

to more effectively show the waviness of the surface while in Figure 5 the surface is in focus and both

orange peel and pitting damage are apparent. Sampling the output surface at several locations showed

that this type of damage occurs at an average energy density of 136 joules/cm^.

As the output energy was further increased, pitting damage began to appear on the output face. The onset of such damage on the average occurred at an energy density of 14^+ joules/cm^, somewhat above the

level for the orange peel damage. The appearance of this type of damage at threshold was generally

marked by the presence of crater type damage surrounded by a larger region of crazed glass. Several

such sites are shown in Figures 6, T , and 8 as the damage progresses from threshold to several times

threshold. No front surface damage was noted during these tests for a maximum average energy density

of l^J-O joules/cm^.

Throughout the surface damage testing, self-trapping damage was noted. The trapping damage occurred anywhere from the front end to the exit end of the billet and generally occurred only after exit

surface damage was noted, such that the exit face damage does not appear to be trapping limited. The average trapping threshold was found to be 128 joules/cm^. Figures 9, 10, and 11 are typical of the

trapping damage noted. As shown, the bubble type damage characteristically has a diameter of a few

tens of microns and the spacing between bubbles is generally not uniform. A summary of the self- trapping and surface damage results is shown in Table 2. The table primarily indicates the rather

Table 2. Self-Trapping and Surface Damage Results

Orange Peel

(Average Joules/cm^)

Surface Pitting

(Average Joules/cmS)

Trapping

(Average Joules/cm^)

154 123 B3 171 154 63 112 150 170

113 150 194 1^7

broad variation in the damage results, especially those related to the trapping threshold which varied

from 63 to 194 joules/cm^. Because of these rather large variations, this data should be considered as tentative only. Further tests are presently being prepared and in the near future the range for the

damage threshold values will hopefully be narrowed. It cannot be ignored, however, that these damage

levels are generally higher than those previously reported by others.

7. Future Plans

The planned research program for the next twelve months can be conveniently broken into four main

phases as shown in Table J14
Table J- Future Program

1. Inclusion damage in the 1 to 5 nano-sec time domain.

2. Thermodynamics of the melting of laser glass in

platinum.

3. Kinetics of self-trapping induced stress patterns.

4. Surface damage characterization.

The inclusion type damage measurements in the 1 to 5 nano-sec time domain will follov/ the same general procedure as that previously described for the 50 nano-sec work. Active tests will be per- formed in the third amplifier stage, while passive tests will be performed on unpumped samples ex- terior to the oscillator-amplifier system. The attainment of accurate data in this time domain to- gether with the 50 nano-sec results should yield experimental information as to the effect of the time

parameter in laser glass inclusion damage.

In the thermodynamic study the activities for oxides in laser glass and metals in platinum will be

determined to assess the feasibility of melting laser glass in platinum for various partial pressures

of oxygen. The basic problem is to lower the P02 as low as possible without reducing the laser melt

oxides and allowing the metals to attack the platinum. The one shortcoming of this approach is that it does not include the kinetics of the reactions so that after the activities are determined, some experimental work will be necessary to isolate the optimum melting conditions.

The kinetics of self-trapping induced stress patterns will be observed using the techniques of interferometric holography. The hologram will be produced with a 10 to 15 nano-sec ruby pulse at different time intervals during a 100 to I50 nano-sec pulse from our neodymium oscillator-amplifier

system. The laser induced stress patterns and their temporal evolution will be observed as a function

of the laser energy and the sample physical parameters which could be relevant to self-trapping (such

as density. Young's modulus, refractive index, and others). Possible correlations of the stress pattern

formation and evolution to the physical parameters will be explored with a goal to delineate these

parameters which are relevant to self-trapping. Since self-trapping appears to be the precursor of laser glass damage, such a characterization would appear to be a meaningful contribution.

The fourth and final phase of the program will be to investigate those factors which may be ex- pected to alter laser glass surface damage. Based upon the ambiguity as to whether such damage is caused by thermal or mechanical failure, the effects of such processes as etching, vacuum drying, and

mechanical strengthening will be determined. In addition to quantifying the relationship of each process to the damage threshold, the long term benefits of each process will also be investigated.

8. Acknowledgements

The support of the Advanced Research Projects Agency of the Department of Defense is gratefully

acknowledged for both the current and succeeding twelve month programs. I would also like to acknowledge many fruitful discussions with Haynes Lee and Alex Glass, and I am most grateful to Ted Phillips

who spent many endless hours obtaining the data for this paper.

I05B PHOTOOETECTOB

Fig. 1 Oscillator Amplifier Optical Configuration

15
SYSTEM PROFILE

30.7 JOULES /cm^ AVERAGE INTENSITY

DIODE NUMBER

Fig. 2 System Profile - 30.7 Joules cm^ Average Intensity.

I6nnm MAJOR AXIS DIAMETER BEAM

L. luu cm

91 cm LONG SAMPLE

2 METER LENS

PULSE DURATION 50 x 10"' SECONDS BEAM DIVERGENCE 2 x iO'^ RADIANS

Self-trapping and Surface Damage Experimental Arrangement
Fig. 4 Orange Peel Damage Fig. 5 Orange Peel Damage
Fig. 10 Trapping Damage Fig. 11 Trapping Damage

COMMENTS ON PAPER BY ROBERT BECK

^)u^ to the. meXhod u^>^d to m^cu,uA& the, int&mvty pio^-vtc, ovte^iivtLj data weAe taken ovity at

d^^icn^ete oo-tnti along penpend^catoA axei>, latheA than co ntA.no mty. No detcuJLed ^ine 6tAuctu/ie

woi soLvohte. b'f ziiUs method. The uA.ode oAAay conA^ted OjJ S diodes, each w-Uth a diayneXeA o{^ &0 thoLUandthi o{, an uich, ipaced 2 mm apanX atong each ax-c6. Onty the -entente centAol pofitioyi o(^ the beam mai mea^uAed. The beam waj, eJUU-pttcaJL due to the u6e o^ a BteuJiteA- angle iyitem, with a

majon. dumeteA 16 otm. The Intensity at the (^ocat 6pot MitlvLn the gtai>6 iomple wai, computed

^Kom the seconded ^.ntem vty pfiof^-ile, knom (^ocal length and mea^uAed total enexgij.

The 91 oil long iomple wai moved towoAdi the (,ocal ipot, to -tncieaic the energy dem-Uty tMitiu.yi the ^mriple. At a g<.\)en i>a}i]ple position, the IxueA eneAgy woi ^.nc>iea^ed antxl Viapp-tyig damage wa^

icen. Su^f^ace dan^age o^ten occuAAed at the output ^ace o^J the 6antple p'vtoA to the appeoAance

tAapp^ng damage. No 6uA{^ace damage u)a4 ieen at the entAance iace ojj the ianiple at eneAgy deiU-itteA up to 140 joul&i /ay/

.

CoAl ?AXha 0^ AFCRE fiepoKted i>eeA.ng flapping damage oi iapphlAe nuJiAoAi, accompanied by "oAangepeel" doinage at the exAX 6uA{,ace. Ma. Beck Aeponted that, -tn iuJ> te^ti, tAapping neaA the exit {^ace

0(5 tiie ioinple geneAally moa accompanied by pitting at the 6uA(^ace AotheA than "oAange-peel" damage.

18
Laser Glass Testing at NRL

Thomas H. DeRieux and John M. McMahon

Naval Research Laboratory

Washington, D. C. 20390

Damage thresholds exhibited by several different laser glasses are reported

using the VD 320 system. The performance characteristics of these glasses when

operated in the VD 320 laser is discussed. Of particular importance was the anomalous gain noted when very high population inversion was attempted as well as severe pulse broadening.

Key Words: Glass damage, laser amplifiers, ceramic hosts, optical gain,

laser characteristics, pulse broadening.

1. Introduction

This report covers activities in laser glass evaluation during the past year. Test reports are included on test series on Owens-Illinois and American Optical laser glasses. During this period,

the CGE VD 320 was modified by the addition of another amplifier to produce 115- joule, 30-nanosecond

pulses. With this system 4 cm^ areas can be tested at fluxes in excess of 20 joules /cm^. Fairly

complete tests on presently available 01 laser glass were completed during this period. Some limited (and promising) tests were conducted on American Optical glass but the planned extensive

test series has had to be postponed at American Optical 's request.

No samples of Schott laser glass were tested during this period because an improved glass was supposed to be in the works. This glass has recently been announced and a rod is being purchased.

The technical data supplied by Dr. Neuroth (Schott Jenaer Glaswerk, Mainz, DFR) shows this glass to be very similar to A00835 in its basic properties with a very low claimed loss coefficient

(~1 X lO'^cm"^) .

Preliminary tests on a sintered ceramic neodymnium laser host, Yttralox from General Electric,

are being reported separately.

The CGE VD320 laser system has in excess of four thousand shots at this point and has performed

well throughout. No failures have occurred in the optical train although there have been a number

of faults in the electronic system. These have in general been random component failures rather

than a systematic degradation of the system. There have also been some failures due to poor original

assembly techniques (e.g. HV connectors crimped but not soldered). The French high voltage leads have been replaced with Amphenol 21-412 cable to ensure long term alignment stability of the laser

heads. The output face of the final amplifier was repolished after ~3000 shots as the surface had

degraded somewhat, presumably because of residual scarring left by exploded dust particles. The

degradation appeared to be rather slight and was only visible with strong illumination on the surface.

2. Owens-Illinois Laser Glass

Early in the fall a set of laser rods was received from Owens-Illinois for all three stages of

the CGE laser. The sequence followed was to first tune up the oscillator then the first amplifier

and finally the last amplifier.

It was expected that the oscillator would require less pump energy because of the larger induced

emission coefficient and lower passive loss in the glass. In fact the oscillator could be tuned up

to produce a 30-35 nanosecond pulse with about 65% of the pump energy required for the French glass.

It was found necessary to aperture the rod to ~14 mm to suppress scattering from the rod barrel. Even under these conditions the optimum beam divergence from the oscillator was approximately twice

what it was with the French glass. In addition, the near field fringes lacked contrast and the far-field pattern was more Lorentzian than Gaussian in shape. This behavior is characteristic of

a situation where there is excessive small angle scattering in the laser rod. [l]

19
It should be noted that there was no selection procedure performed by Owens-Illinois on this lase: rod which is in direct opposition to the procedure employed by CGE. The French fabricate a number of rods and test all of them in a standard oscillator to select those which perform at or better than

their beam divergence specification (late in 1968, this represented less than 207,, of the rods

fabricated [2]). Homogeneity in an oscillator rod is especially important since it is a multipass

situation and an active testing specification may be necessary for low divergence systems. It was decided to use the oscillator rod as the larger beam spread (~0.5 mr) was still acceptable for the test series.

In setting up the first amplifier of the system consideration was given to the fact that the

fluorescence lifetime (~ 300 i-isec) of the Owens-Illinois was much shorter than the pump pulse

duration (750 |asec) . For this reason the bank capacitance was varied to observe the effect of pump

pulse width on the performance. The peak voltage ratings of the capacitors, 12 kV, limited the energy

at the shorter durations to 8 kj at 360 |j.sec and 12 kj at 480 (jsec, compared to the normal 20 kj at

750 Usee. Figure 1 shows the results of this exercise. The outputs at 12 and 20 kJ were identical

and it appeared that 10 kJ at 360 Usee would also have given the same output. Removing the potassium

chromate ultraviolet cladding and using distilled water alone increased the output by 5-l07o in all cases at these levels although this was not true at higher levels. The curves all had very similar

shapes. In terms of a model relating the energy storage efficiency to the ratio of fluorescence

intensity to pulse duration including changes in the spectral distribution of flashlamp radiation at different loadings on the lamp, the results were somewhat more dependent on pulse width than was expected, in that somewhat more energy was required at the longer pulse widths than would be expected

from the model. This may be due to amplified spontaneous emission at the fairly high energy densities

stored in this rod (~1 j/cm^). This amplifier rod appeared to be of excellent optical quality and

did not noticably degrade the beam divergence.

The output of the device was run up to 13 J/cm^ average and 20 J/cm^ peak with no signs of

damage

.

Experiments were also performed at 1.15|J and 6328 A to determine whether or not there was any appreciable pump induced absorption at these wavelengths. The experiments to date indicate that any pump induced loss must be less than 0.002 cm"''' at 1.15 |-i and 6328 A at pumping levels up to 100 J/cm^

(lamp energy per cm of laser material).

It was realized from this and other data that the VD 320 did not have a high enough output

energy density to function as a damage testing system for presently available laser glasses and an additional amplifier was fabricated to raise the total output to ~ 120 joules. This amplifier was designed for 32 mm X 250 mm long laser rods. The previous data on the effects of pulse width

variation led us to choose a 500 M-sec duration pump pulse. Flashlamp design data [3,4] led us to choose a maximum input of 7500 joules to each helical lamp at 17.3 kV. The French lamp life data

gives an expected lamp life to 10,000 shots for this system.

The expanded system was then run with French glass in the first three stages and the O-I rod

in the final state. The amplifier was run both with and without the potassium chromate cladding

solution. Figure 8 shows the measured small signal gain coefficients (cm-y)^ for both cases. Without the cladding (an-y)^^ was about YL higher than with the 2.5 gm/liter solution. The measured

output energies vs pump input are shown in Fig. 9. Here the total output was higher with the cladding

by about 5 joules (115 J vs 110 J) . The system was also run with the intermediate expander (between

23 and 32 mm stages) removed and the output over 4 cm found to be slightly in excess of 21 J/cm^.

During all tests at and around this level no damage was noted which implied that the density of

inclusions which would explode under 20 j/cm^ was less than 1 per 50 cm^ of glass.

Figure 10 shows the input-output curves for this amplifier at 5, 10, and 15 kJ pump energies.

Several interesting facts were observed about the operation of this amplifier:

1. The energy storage efficiency (joules of inversion per joule of puirip energy) decreased

markedly at higher pump energies. It was 1.4% at 5 kJ , 1.1% at 10 kJ and 0.9% at 15 kJ . From the model we would have expected 1.40%, 1.27%, and 1.17% at the three input energies.

2. The fluroescence intensity at 30^* to the optical axis (Fig. 8) was nonlinear. It could

be linearized by use of the small signal gain coefficient and an effective length. Figure 11 shows

the linearized results for an effective length of 11 cm. This is a longer length than the direct

view of this detector (i.e. the light must have been scattered off the wall).

3. The differences in input-output curves and small signal gains with and without the potassium chromate ultraviolet cladding were suggestive of the original active loss hypothesis.

20
4. With the beam expander removed the input to the last amplifier was ~ 1.5 times the saturation flux and the output was ~ 3 times the saturation flux. The pulse shapes and timing were measured using ITT FW photodiodes and the results are shown in Fig. 12. Not only does the pulse

leading edge move forward in time with a "phase" velocity of ~ 25c (which is an effect first noted by Basov and Zuev in ruby [6]) but the pulse also broadens by ~ 70%. The theoretical results of Franz

and Nodvik [7] would predict a broadening of no greater than 30% for this situation.

Several approaches are being pursued to understand these results:

1. The model of Xenon lamps pumping neodymnium laser material is in the process of experimental validation to insure that it accurately represents the actual physical situation as part

of another program.

2. The effect of axial and near axial superradlant coupling between the oscillator and the amplifiers has been investigated by placing saturable absorbers between stages of the laser. These

experiments showed no difference with or without the dye cells. The results of a simplified

calculation for fluroescence lifetime shortening due to superradiance indicate that for our case, this

effect is negligible in the rod itself.

3. Experiments are underway to evaluate the role played by transverse superradiance and whispering modes in the pump cavity in limiting the peak inversion achievable. This will be done by

placing a 1.06 M. absorber between the flashlamps and laser rod and evaluating the change in small

signal gain.

4. The active loss coefficient will be measured in a more favorable experiment with

improved s/n ratio. Mirrors have been obtained to run our Spectra-Physics Model 125 at 1.06 \s, 1.08 \1 or 1.15 (J for this experiment. In addition, low noise PIN diode detector-amplifier combinations have

been designed and fabricated to give s/n better than 5000:1 at 1 MHz bandwidth.

5. Duston's results giving a lower laser level cross relaxation time of ~ 11 nsec for the

01 glass [7] could affect both the extraction efficiency and the pulse shape. Our computer programs

show that the measured pulse broadening is consistent with - 10 nsec but some additional

active loss still appears to be present.

6. The result of Vance shows that in at least one laser glass excited state absorption

from the upper laser level is an important factor in reducing the gain. [8] This effect needs to be evaluated for 01 glass in that physically it exhibits appropriate behavior.

3. American Optical Laser Glass

In November, American Optical told us that they had several amplifier rods to test. Mr. Charles

Padula accompanied the rods and assisted in the experiments. Two rods were brought to NRL and time

permitted detailed measurements only upon one of these. One rod was a standard C835 glass and the other was a new type, number 2378 doped with Cerium (~ 2 wt . %) . Both rods had numerous bubles.

Figure 13 shows the results obtained with the new glass in the second amplifier. The Cerium

addition seemed to help only at the low pumping level. No inclusion damage was noted in this case. Figure 13 corresponds to the case where French glass was used in the oscillator. The system was

also run with an 01 oscillator and in this case the small signal gain coefficient was only half as large implying the ct(1.0621) =i3.5 a(1.057) for the AO glass. This is lower than Duston's measure- ment of the relative fluorescence intensity profile would imply.

The passive loss coefficient was measured after ~ 50 shots and found to be ~ 1.9 X 10

^ ± 2 X 10 cm"-"- . C. Padula had measured the passive loss at AO before running the rods and found

Y ~ (1.3 ±.2) X 10 "^cm"-'' . After returning to American Optical he measured this value and found,

on the same apparatus, it to be (1.8 ± .2) X 10"^ cm"''' .[9]

It was hoped to run a further test series with AO glass in the spring out several difficulties

prevented this. AO found that their testing procedure was not relevant to operation at 30 nanoseconds

and, is, at present, understandably unwilling to submit any more glass for testing until they have

established satisfactory testing procedures. Hopefully, they will be back in business by the end of

the summer.

4, Future Plans

Several more amplifiers are being fabricated in-house to allow the testing of glass at levels up to 40 J/crn^ . These should be ready by the middle of the summer.

21
5. Summary

Tlie results to date on the Owens-Illinois ED-2 laser glass are that:

1. Large volume of glass can be fabricated with a damage threshold above 20 j/cm^ for Q-switched pulses.

3 —1 2. The absorption loss was typically ~ 2 X 10" cm for the glass tested but there seem

to be some problems in obtaining large rods with good optical quality.

3. The active (pumped) performance of this glass is still not completely understood.

The results to date on the American-Optical laser glass are that:

1. The sample tested withstood fluxes of 15-20 J/cm^ without damage.

2. The net optical quality left something to be desired in that there were numerous bubbles

in the glass which might be a problem in a very high gain amplifier train. The total loss coefficient

was of the same order as for the Owens-Illinois laser glass (~ 1.9 X

10""^ cm"''- ) .

3. The overlap of the two glasses was investigated and it was found that the induced

emission coefficient of the AO 2378 glass at 1.0621 where 01 glass lasers was ~ 50% of the peak

value (1.6 X lO"^'' cm^ ) . [10]

It would therefore not be recommended to have an 01 oscillator with AO amplifiers but our earlier result on the 01 glass pumped by the French (which has the same peak fluorescence wavelength

as the AO glass) indicates that the reverse setup; AO, French or Schott oscillator and 01 amplifiers

would work as well as with an 01 oscillator . [11]

6. References

[1] McMahon , J.M., Laser Mode Selection with a Slowly Opened Q-Switch , IEEE, JQE , QE-5, 10,

October 1969, pp. 489-495.

[2] Sturel, J. (CGE) , private communication.

[3] Flash Pour Barreau 32 mm" Centre De Richarches , Companie ' General d' Electricite ' , Division Technique Report

JS/AL - No. 66-A-149.

[4] Emmett , J. L. and Markievicz, J. P., Design

of Flashlamp Driving Circuits, IEEE JQE,

Vol. QE-2, No. 11, November 1966, pp. 707,

711.

[5] Ambartsumyan , R. V., Basov, N. G.

,

Zuev, V. S., Kryukov, P. G., and Letokhov,

V. S., IEEE, JQE, Vol. QE-2, 9, September

1966, pp. 436-441.

[6] Franz, L. and Nodvik, J., Theory of Pulse

Propagation in a Laser Amplifier, J. Appl.

Phys. 34 2346 (1963).

[7] Duston, D. K. , Factors Influencing the Gain

in Neodymnium Glass, Ph.D. Thesis, 1969,

Renassaleur Polytechnic Institute, p. 125.

[8] Vance, M. E., Saturation and Excited State Absorption in Neodymium Laser Glass, IEEE,

JQE, QE-6, _5, May 1970, pp. 249-253.

[9] Duston, D. K. , Ibid., Fig.- 4-3.

[10] Padula, C. , (American Optical) private

communication

.

[11] Young, C. G., Kantorski, J. W. , Padula, C. F. and La Marre, D. A., paper number 10-1,

Conference on Laser Engineering and Applications, May 26-28, 1969, Washington, D. C.

[12] McMahon, J. M., Glass Laser Materials Testing

at the Naval Research Laboratory, Damage in Laser Glass, ASTM STP 469, (1969) pp. 117-

127.

22
10 INPUT IkJ) Fig. 1 Laser output of the intermediate

amplifier (23 mm) of the CGE laser

with Owens-Illinois glass as a function of pump pulse energy with

pump pulse with width varied. Also

shown is the output with and without

a ultraviolet absorber (2.5 gm/liter

of potassium chromate) . Input was

2.5-joule, 30-nanosecond pulse.

Fig. 2 Laser output of second amplifier

(32 mm diameter) of CGE laser with

Owens-Illinois glass vs pump energy

for various pump pulse widths. Input was 19-joule, 30-nanosecond pulse.

9 8.0 k J

y\l 6.25 KJ

X3 3.6 kJ

1 1 1

1 2 3 INPUT (J/fcm2) Fig. 3 Laser input vs laser output for the second amplifier with a 480 fisec pump pulse at 3.6, 6.25, and 8.0 kJ pump energies.

1 2 3 INPUT (J/cmZ) Fig. 4 Laser input vs laser output for the second amplifier with a 580 jUsec pump pulse at 5.35, 8.4, and 12.0 kJ pump energies.

23
Fig. 7 Far-field energy distribution of Fig. 8 Small signal gains coefficient vs input

entire system with 750 /isec pump energy for third amplifier. The

pulse (20 kJ input) . fluroescence intensity at 3CP to the optical axis is also shown.

24
0. 60

6 9 12 PUMP ENERGY (kj) 6 9 12 INPUT ENERGY DENSITY

Fig. 9 Total output vs pump energy to final

amplifier with and without cladding

solution. Beam area was 7.0 cm and input pulse was 57 joules in 35 nano- seconds .

Fig. 10 Laser input vs laser output for third

amplifier at 5, 10, and 15 kJ pump

inputs

.

6 8 10 PUMP ENERGY (k J)

12 16

Fig. 11 Fluroescence data of Fig. 9 renormalized using small signal gain coefficients and -teff 11 cm

.

25
osc

AMP# 1

AMP#2

AMP#3

PULSE SHAPES

Fig. 12 Oscillator pulse shape and amplified

pulse shape at various places In amplifier train. The pulse is not appreciably broadened in the first

amplifier, is broadened 20% in the second amplifier and ~ 50"L in the third amplifier.

0 2 ENERGY DENSITY IN Fig. 13 Laser input vs laser output for AO

2378 laser glass at pump energies of

8.8, 13.8, and 20.0 kj with and with

out ultraviolet filtering.

26
CCMMEVTS O'i PAPE!? 8V VlH^l Mr^AH'i^

The. £ocaZ b^am expandeAi coyii^deAably idduce. thz normal oicAlZcUofL beam diveAgmce abouX 3 mn.ad, conAzcXing {^on the naXu/iat 6phefu.cjJ:y o{, the wave (^lonZ <u well. cu> thenmal dhstombion

^ntAoduced by the ampti(,-ieA itageA. The tatteA ti, a {,unctton o(, the fiepetUtA^on tcute.

It -U, not appnopniate to make a dtAect companAJ>on the peA(^onmance, e.g. bexm\ dtveAgence,

Omevn-llLino-u, and C.G.E. gtajii, -in the C.G.E. iyitent, i-ince iti> mode opeAatton Moi optAmized {^OA

the choAacteAtittci a ielected, high quatoty oicuLtaton. nod o{^ C.G.E. gloM.

MexuuAementi at AFCRL -tndx-cate matt angle icatteAtng ui Owem-ItttnoAj) glaa in agKement. voiXh the value -cn^^eAAed (,n.om the WRL meoiuAementA

.

A dii(^(^Kaction patteAn -u, intAoduced ^n the moA (^-teld the lai,eA output by the bh.eak edge ojj the rotating TlR pnjjim.

The ton, o{^ de^iinttion thti, dii^f^n-acXion patteAn obieAved uiing Owen-s-JttLnoii gtaa oveA that ex.hibiXed with C.G.E. gtoM td pfiobabty due to paiiive diitonZion n.aX.heA than i>matt angle

icatteAing. Tkii, wa4 veAA.(^ied when the tej>t nod Moi iub^equenZty examined at Oixieiu,-lttinoi^ u^ing

an inteAi^eAometAic technique iimiZaA to that o^ BaiAd [L.R.L.]. A (^utt imve Ojj dtdtontion iMoi obieAved in the tej>t nod. Thii tzit ihoutd be a uAe^ut quatoCy contAol indtcaton o/j nod peA(,onmance,

and ii noM in oie at 0ue.n6-JllA.noii . Vn, Snitzen alio po-tnted out that impnoved qualiXy contAot

pAoceduneM have been ^mtituted at AmeAican Opttcat Company and that the nod iupplied ^on testing at

M.R.L. contained thnee bubbles leM than onz rm -tn dtameJieA, which had no majon e(^{^ecX on the

peA^onmance that ipecA.{,ic gtaa nod.

M^. 'IcMo-'iod ^elX that the obieAved puLf>e bnoadeyiing wai due to the long neJLaxaZion time the toweA loMZA lev\iX., which impeded the evident extnaction eyiengy at high eneAgy demitieji { 100

j outeji / cm^ ] . It woi atio po-tnted out that gneat cane had to be exeActied to eLimiyiate (^eedback due

to ne{,tecting iun{,acei. Putie bnoadening ha-i been obieAved at Oweni-IttinoiA due to neltection

(^nom amplA.(jieA Aod endi cut ai much aj, 10 degneeA o^ axii, ai wett ai ^nom tangeX backicaJXeA. The

{^eedback e^f^ect wa& pnecluded -tn the ML te-it^ by monitoning the oiciltaton and ampli^^-ieA output

pulieA iynchnonou^ty with two dA.odej>

.

The anatyiii the pulie bnoadening cannied out. at hlRL wai ba^ed ioleJLy on the uie of^ the nate

equation dey!>cAA.ption o^J the level population change-i , and the obi^Avcd 80% put&e bnoadzniyig wai, attnibuted to a {jilting the lowen la^eA level, when the nod wai pumped at a high level. Vn. Snitzen

po-tnted out that undeA the^e coyiditiom , a {^ull quantum-mechayvtcal deni-tty matnix deicniptcon o(j the nelaxation pnoce-iiie-i ii neqa-tned, -tncluding both quantum-mechayucal neZaxation (T^) on well ai population changes (TJ.

27
Experimental Investigation of the Behavior of Neodymium-Glass Laser Amplifiers

C. R. Jones, P. V. Avizonis, and P. Sivgals

Air Force Weapons Laboratory

Kirtland AFB, N. M. 87117

Anomalies observed in gain measurements on Nd: glass laser amplifiers are

reported. The investigation, which was undertaken as part of a high-energy

laser program, revealed a significant gain fall-off at high amplifier excitation energies. Efforts to determine the origin of this phenomenon are

described. The discrepancy between the observed gain and that predicted

theoretically for an Nd:glass laser amplifier is found not to be due to superradiance or flashlamp spectral shift. Furthermore, a pump-energydependent loss process in the glass matrix is shown not to contribute to the gain roll'-off. The underlying physical process remains undetermined.

Key Words: Amplifier, flashlamp, laser, Nd:glass, optical gain,

optically pumped laser

1. Introduction

A segmented-glass laser system similar to that sketched in Fig. 1 is currently under development in this laboratory. The available gain from the optical amplifiers in this high-energy system is obviously

of prime importance. Moreover, the capability of predicting the gain over a wide range of flashlamp

energies and laser input energies is certainly desirable from a design point of view. These considerations led to a recent investigation into the behavior of Nd:glass amplifiers with emphasis on the comparison of the experimental data with the theoretical predictions.

The expression which describes the spatial evolution of an optical pulse in a four-level laser

amplifier is [I]-'-

where E(x) = pulse energy density in joules/cm at position x in amplifier,

3 = inversion density in joules/cm in the active medium at time of pulse,

gain coefficient in cm /joules, usually defined at peak of fluorescence curve, and

a = loss coefficient of the laser medium at the operating wavelength.

This expression has been modified from that for the three-level scheme derived in the reference.

The application of expression (1) to a particular amplifier is quite straightforward on a desk computer

if the relevant parameters are known.

The literature revealed very little in the comparison of the theoretical amplifier equation above

with experimental results on Nd:glass material. It seemed worthwhile, then, to experimentally verify

the equation above with an amplifier experiment incorporating solid glass rods. The results should be

relevant to a segmented laser system with the proper adjustment of the loss coefficient.

2. Experimental

The experimental apparatus is presented schematically in Fig. 2. Several Nd:glass rods were used

as the amplifier, each being pumped in a flashlamp enclosure as drawn to scale in Fig. 3. The

s

Numerals in square brackets indicate literature references appearing at the end of this paper.

28
reflector surface is polished silver foil and the cladding is deionized water. Each set of two lamps

in series is driven by a 300 uF capacitor bank through a 100 yH air-core inductor, producing a smooth

current pulse of about 400 ysec duration. The excitation efficiency typically exceeds 1%. The 50- nanosecond laser input pulse has an intensity profile of about 6 mm diameter.

3. Results

3.1 Gain Results

Most of the amplifier measurements entailed monitoring the dependence of amplifier gain on flashlamp energy at a selected laser input energy density. The results of the first measurements, shown in Fig. A, are for three ED-2 rods of lengths 4, 8, and 12 inches. (All rods used in this investigation

are 0.75 inch in diameter and are Brewster-Brewster.) The input energy density is in each case 1.25 joule/cm (average). The abscissa units of flashlamp energy have been normalized to the rod pumped

volume. The theoretical curve generated by eq. (1) has been fitted to the lower energy data points of each experiment through adjustment of the pumping efficiency. A loss coefficient of 0.005 cm"-'- and a gain coefficient of 0.14 cm^/joule were used. It is apparent that for the shorter two rods there is a growing discrepancy between the theoretical curve and the observed data beyond about 50 joules/cm^

energy input. The departure of the experimental curve from the theoretical one does not seem to be

dependent upon the laser input to the amplifier: The small-signal gain curve for the 8-inch rod (Fig.

5) departs from theory at about the same point on the flashlamp energy scale. Subsequent sections will

explore the physical basis of the observed discrepancy.

3.2 Fluorescence Results

The most popular explanations for gain fall-off of this type are superradiance depletion and flashlamp blue shift, both of which diminish the inversion. Hence, a series of fluorescence measurements on

the Nd:glass amplifiers was initiated. The experimental arrangement is included in Fig. 2, which shows

the pumped-rod fluorescence at 1.05y monitored by a photodiode through a light pipe. The fluorescence

is observed, as shown, along the geometrical rod axis and not along the optical axis. Thus, hopefully,

spontaneous emission from only a small end-segment of the rod is being detected.

The observations on the 4-inch rod are presented in Fig. 6. The plot of relative fluorescence

peak against the pump density is agreeably straight, with an expected leveling at high excitation. The

flashlamp emission was found to be an insignificant contributor to these readings. Significant super- radiance was checked by observing the fluorescence with and without a 100% reflecting mirror placed

near the opposite (to the photodiode) end of the amplifier rod and normal to its optical axis. There

was no effect from the mirror on the signal at any excitation level, although on-axis fluorescence was markedly affected.

The results of the fluorescence measurements on the 8-inch ED-2 rod are presented in Fig. 7. The

straight line is rather boldly drawn through what is more of an S-shaped arrangement of data points,

although the sharp break (from gain results on this rod) appears to be real. Again, the 100% mirror

had no effect on the fluorescence signal. A correction of the gain curve for the apparent inversion

nonlinearity shown in Fig. 7 still indicates a distinct departure of experimental gain from theoretical

gain at the same value of about 50 joules/cm-' pump density.

Fig. 8 is the graphical fluorescence data on the 12-inch rod (no straight line attempted). Perhaps

significantly, the curvature of the fluorescence data increases with pumped length of the rod. Correction of the gain curve of Fig. 4 for this pronounced nonlinearity produces a gain fall-off for the 12- inch rod very similar to that of the shorter rods, and, in fact, the departure from theory begins at about the same value of pump energy density.

In order to determine how much of the laser rod contributes to the fluorescence signal for this

configuration, the 12-inch rod was placed in the pumping enclosure of the 8-inch rod. By varying the distance the rod protruded from the enclosure and monitoring the spontaneous emission at each distance,

an indication of the contributing volume was obtained. The results for this measurement are presented

in Fig. 9, along with the data for a 12- inch rod with a polished barrel. (All rods in other parts of the experiment have roughened barrels). The smooth rod clearly demonstrates its shortcoming while the roughened-rod data indicates that it exhibits some light-gathering capability. The data, while not completely analyzed, does emphasize the desirability of a 1.06)j absorbing cladding around a high-gain

rod.

3.3 Other-Glass Results

A possible pump-dependent absorption process in the base glass, which could certainly explain the observed gain roll off, was checked as follows: An ED-4 (base glass of ED-2) rod of the same dimensions was substituted for the 4-inch ED-2 rod used in the gain measurements. The variation of gain

29

I
(loss) with excitation was observed under the same conditions as before. To within experimental error

(5%) no pump-dependent absorption could be detected over the same energy range covered in the ED-2 amplifier experiment.

That the apparent gain anomaly is confined to Owens-Illinois glass was checked by performing the gain measurements on a 3% doped American-Optical laser rod and a French glass laser rod borrowed from

Hadron, Inc. These gain results, plotted in Figs. 10 and 11, also show the severe gain fall off observed above.

3. A Flashlamp Effects

The blue shift of the flashlamp spectral output with increasing current density is certainly one

of the foremost of the possible explanations for the observed gain fold-over. The first effort in attempting to isolate this phenomenon, as it applies to the gain results, involved measuring the gain

while using flashlamps of different bore. Fig. 12 shows the data for the gain of the short ED-2 rod using three types of flashlamps with the same driving circuitry. The current waveforms through the different lamps were observed to be essentially Identical, which means that only the current density

changed when the lamps were changed. Quite apparent is the greater pumping efficiency of the smallerbore lamp^, although the important feature of this data is that the departure of the observed gain

from theory occurs at about the same flashlamp input for all three lamps, despite the difference in current densities. Not surprisingly, however, the 7-mm flashlamp curve seems to be folding over faster

at energy levels above 100 joules/cm^. Above this excitation peak, current densities exceed 5,000 A/cm^

in the small-bore lamp.

3.5 Temperature Dependence of Gain

The high-average-power requirement on the laser system under development dictates that thermal

effects will be of considerable importance in the design of the device. Although the segmented-rod

configuration tends to alleviate many of the thermal problems, the interior of each disc will, nevertheless, be at an elevated temperature that will be a function of the operating power. The Increased

temperature of the laser material could critically affect the gain realized with a high-average-power

amplifier. An experiment was recently begun which will determine the variation in gain of an Nd:glass

rod with temperature.

The first results are shown in Fig. 13, in which the gain as a function of flashlamp energy is presented for two rod temperatures - 5''C and 88°C, The temperature range is being extended upward to include the anticipated temperatures of interest in segmented-glass-laser operation, since the foregoing data indicates a significantly reduced gain at elevated glass temperatures.

3.6 Nd:glass Amplifier with Nd:YAG Input

As Fig. 1 of this report indicates, the high-average-power laser system under development may incorporate an Nd:YAG oscillator-amplifier driver section. It is hoped that the Nd:YAG system output will

have an acceptably low beam divergence, although mode-control measures may be required. In any case the amplification of an Nd:YAG pulse by an Nd:glass amplifier is an Important consideration, but there appears to be no reported investigation in this area.

The narrow spectral range of the Nd:YAG output, relative to the fluorescence linewidth of Nd:glass,

will possibly bear upon the utility of an Nd:YAG laser as the driver stage for Nd: glass amplifiers,

particularly beyond the small-signal-gain regime. Thus, an experiment to observe the gain characteristic

of an Nd:glass amplifier with an Nd:YAG laser input has been set up. The experiment will compare, at equal laser input levels, the gain of the amplifier using a YAG input pulse with that using an input

pulse from a glass-laser oscillator.

The first results obtained were for the small-signal-gain regime (30 mJ/cm input at less than

10 dB gain) with the two inputs producing almost identical gain curves. Preliminary results in the intermediate-signal-gain regime (0.2 J/cm^) reveal, however, a smaller gain for the Nd:YAG pulse over

the full amplifier excitation range. This data is shown in Fig. 14.

4. Discussion ' " --

4.1 Other Investigations

The data in Fig. 4 clearly indicates that the disparity between actual amplifier performance and

The EG&G 13mm lamp data is not corrected for the unused one-third of its length. This correc- tion reveals that this lamp has, in this situation, a 20% greater pumping efficiency that the 7mm lamp,

which in turn, is 25% more efficient than the ILC lamp.

30
the theoretical predictions can be quite significant. The first literature, of which we are aware, that reports a discrepancy between observed amplifier gain and that predicted theoretically, for Nd:glass

amplifiers, is a paper by Young and Kantorski presented at the 1964 DOD Conference on Laser Technology

[2]. More recently this phenomenon has been examined rather extensively by Beck at Owens-Illinois, Inc.

[3] and McMahon at NRL [4]. All the above investigators have noted essentially the same effect in the gain behavior, although there seems to be no agreement as to its origin. The data of Young and Kantorksi

I2J supports their conclusion that within their operating range the cause of the gain fall off is a de- crease of the flashlamp output in the useful pumping regions with increasing energy input. Their

observed small-signal gain, 3 (%/cm), normalized fluorescence, and lamp emittance in the green and red exhibited identical dependences on the flashlamp input. Beck I3J , after noting a gain fall-off in his

amplifier data, examined the effects of the flashlamp spectral shift on the excitation efficiency. His

analysis, based upon the flashlamp emission spectrum and the absorption curve of the Nd: glass, indicated

a gradually decreasing pumping efficiency with increasing energy input to the lamps. However, this

decrease was not enough to cause the full gain discrepancy, there apparently being other underlying

processes such as superradiance and/or upper-level absorption losses, as suggested by the author. After

observing a gain roll-off with increasing pump energy in an O-I glass amplifier (particularly pronounced

when no ultraviolet-absorbing cladding was used), McMahon [4] ran a series of input-output curves on the amplifier rod. This data did not depend upon the excitation efficiency, since the flashlamp energy was

held constant, and the output energy monitored as the laser input was varied. By fitting eq (1) to the observed results for a sequence of flashlamp inputs, it was shown that an increasing absorption

coefficient, a, with pump energy could account for the abserved gain fall-off. It was shown that the proposed increase in a closely followed an observed increase in lamp UV-blue emission with pump energy.

4.2 Fluorescence

In section 3.2 results were reported for the fluorescence measurements, which were motivated by the gain discrepancy shown in Fig. 4. Unfortunately, the fluorescence curves become more S-shaped as the

rod length increases, casting the long rod spontaneous emission data into doubt. Also, it appears from

the data of Fig. 9 that the fluorescence detected with the experimental arrangement used here does not arise only from a small segment of the rod; in fact, perhaps one-half of the energy comes from the geometrically occluded portion of the rod, apparently being light-piped to the detector. This situation

is of course undesirable in this type of measurement since it indicates that some superradiance may be

affecting the results. Light piping, of course, can seriously degrade the achievable inversion in a laser medium as pointed out by Sooy et^ al. , who observed the marked degradation of achievable gain in

a ruby amplifier brought about by substituting a smooth-barrel ruby rod for one with a rough surface. Further analysis is being performed on the fluorescence results, although tentatively it seems that

the spontaneous emission signal for low-gain rods (4-inch rod) has a direct correlation with the actual

inversion. For higher-gain rods the curvature of the fluorescence curves in Figs. 7 and 8 may indicate

a distortion of the data by superradiance. Unfortunately, perhaps, Important measurements of laser

parameters have been based upon similar observations of rod fluorescence, notably the experiments of Michon [6] and Belan,

^ al . [7]. 4.3 Base Glass

McMahon [4] has shown that the gain fall off could be due to an increase in the loss coefficient

with flashlamp energy input. The absence of a pump-dependent loss in the O-I base glass ED-4 strongly

indicates that the gain fold-over is not due to an interaction of the host with the pump light. This

does not rule out any pump-dependent loss process, however, in that the neodymium ion itself can interact with the lamp radiation with other than a positive effect.

4.4 Population Inversion

The fluorescence results, as discussed in section 4.2, indicate that only the short-rod data

unambiguously relates to the gain portion of this experiment. The spontaneous emission measurements

on the four-inch rod show that the gain fall -off is not a manifestation of a population inversion falloff. McMahon's experiment [4], particularly the input-output amplifier data at constant flashlamp

energy, supports this conclusion. In his experiment each family of data points (output energy density

versus input energy density) was fitted with a theoretical curve by adjustment of the parameters , 5g, and a. This was accomplished for several flashlamp energy input values, an increasing a with pump

energy affording a proper fit of the theory to the data. However, the stored energy, C^, was found to be almost linear with flashlamp energy over the full range of population inversion. Similarly, Beck's

experiment [3] showed that the inversion should fall off slightly with increased pump energy over this range, not nearly enough to account for the observed gain fall off.

^ The amplifier data of both Beck and McMahon encompass an inversion range very close to that of this experiment. Beck, however, noted a larger decrease in excitation efficiency over his energy^range,

which can be explained by the fact that his pumping efficiency was about one-half that in McMahon's

experiment. The doubled flashlamp energy range undoubtedly caused additional spectral shift.

31
4.5 Flashlamp Effects

The shift of the spectral output of the flashlamps must, at some point, produce a decrease in the pumping efficiency of the laser system, which will in turn lead to a gain fold-over. Apparently, the experiment of Young and Kantorski was performed over an energy range in which the lamp blue-shift was

the dominant mechanism behind the observed gain suppression. Their energy input range, corrected for current pulse length, exceeded that of this experiment by a factor of about four.

The effective color temperature of flashlamps is a strong function of the current density, as determined by Goncz and Newell f8J. Their results for FX-47A-7.5 lamps are reproduced in Fig. 15 for

two current densities. The large blue-shift is evident, and in fact, the lamp radiant output in the spectral region between 0.6v and 0.9p even appears to decrease with current density.

Within the operating range of this experiment the shift in spectral output of the flashlamps has

little effect on the amplifier gain. Were the gain measurements performed over a region of significant

lamp blue-shift, the current density through the flashlamps would have pronounced effect on the gain

discrepancy. However, as Fig. 12 illustrates, the gain fall-off for the 4-lnch amplifier rod is not noticeably altered by a change in lamp current density of a factor of 3.5. Aside from efficiency, the only apparent change in gain characteristic incurred by replacing the large bore lamps with the smallbore lamps is an additional flattening of the gain curve at the top end. In this region the 7000 A/cm^

peak current density in the small lamp probably leads to a substantially reduced excitation efficiency.

5. Conclusions

The results indicate that the theoretical gain equation in its present form does not adequately

predict the gain behavior of an Nd:glass amplifier. The discrepancy between the observed gain and the theoretical gain was found to exist in several types of laser glass and over a range of laser input

pulse energies from small-signal through 2.5 joules/cm^.

Fluorescence data on a short, low-gain amplifier rod, indicates that the gain discrepancy was not due to an inversion-limiting process over the operating range of this study. The negligible effect of fluorescence being reflected back through the amplifier rod helped substantiate the conclusion that superradiance depletion was not significant in this experiment. Furthermore, by employing lamps of different bore, it was observed that a marked change in current density through the flashlamps at the same lamp input energy had no effect on the gain discrepancy. This suggests that the spectral shift

of the flashlamp radiant output with changing current density did not noticeably contribute to the observed gain suppression. This flashlamp blue-shift is, however, expected to affect the gain at greater

lamp inputs than those of this experiment. The recent studies by other investigators support these

conclusions

.

By placing a sample of base glass (no Nd doping) in the test amplifier fixture, it was shown that

no measurable pump-dependent loss process in the host matrix was responsible for the gain fall-off.

The measurements on the off-axis fluorescence from amplifier rods of different lengths indicate

that the observed signal may not be proportional to the population inversion except in the case of short, low-gain rods. This observation is substantiated by the measurements of the fluorescence signal

from a pumped rod as a function of its protrusion from the lamp enclosure, with the excited length held

constant. Even for a roughened rod, the entire rod volume was found to contribute significantly to the detected signal, although only a few centimeters were geometrically allowed by the position of the detector. The increased probability of superradiance reaching the detector suggests that the results

of previously reported experiments based upon fluorescence observations may be in error.

Finally, the results presented herein suggest that an anomaly in the gain behavior of Nd: glass

laser amplifiers, which is not explicable by the usual explanations of superradiance and flashlamp

blue-shift, does exist. The origin of the discrepancy has not been determined.

6. References

[1] Avizonis, P.V. and Grotbeck, R. L., J. Appl.

Phys. 37^, 687 (1966).

[2] Young, C. G. and Kantorski, J.W., "Optical

Gain and Inversion in Neodymium-glass

Lasers," presented at the First POD Con- ference on Laser Technology, 1964.

[3] Beck, R.W., "Damage Threshold Studies of Glass Laser Materials," Owens-Illinois, Inc.,

Semiannual Technical Report under ARPA Contract Number DAHC15-69-C-0303 , January, 1970.

[4] McMahon, J.M., "Studies on 32mm OwensIllinois Amplifier Rod," Naval Research

Laboratories, Interim Report under ARPA

Order 660, March, 1969.

[5] Sooy, W.R., Cougleton, R.S., Dobratz, B.E., and Ng, W.K. , Quantum Electronics III , (Columbia Univ. Press, N.Y., 1964) P. 1103.

[6] Michon, M. , JQE QE-2, 612 (1966).

32
[7] Belan, V. R. , Grigoryants, V. V., and Zhabotinski, M. E., Opto-Electronics 1, 33-

35 (1969).

S] Goncz , J, H. and Newell, Pe . B. , J. Opt. Soc. Am. 56, 87 (1966).

YA6 OSCILLATOR

AMP. COMBINATION (1=1 GLASS AMPLIFIER

I 1/2 X 24 SEGMENTED

GLASS AMPLIFIER

SMALL SEGMENTED

GLASS OSCILLATOR

LOW BEAM

DIVERGENCE 10 JOULES

50 JOULES

Basic components for high-radiance, repetitively pulsed laser system now under development

at AFWL.

POCKELS / CELL APERTURES

WEDGED \-^-/fffffff-"<^^^ *r ^BEAMSPLITTERS

OX BREWSTER —t-|--

««n PI iTF? Fn-?

100 . MIRROR PLATES ED-2 GLASS ' 35 %

ROD MIRROR

^A»^PHOTODIODE # 1 f-K*.)

^

(INTEGRATING)

SCOPE

TR6

THERMOPILE

AMPLIFIER ROD 53--a

^'^ LIGHT / PIPE

PHOTODIODE #^ 2 (INTEGRATING)

SCOPE

Experimental set-up for investigation of Nd : glass laser amplifier behavior.

PYREX CLAOOrNC

Cross-section of flashlamp assembly used in amplifier investigation. The sketch is scale

for a 0.75-inch diameter laser rod. The coolant is typically water and the reflector

surface is polished silver foil.

33
°- 7 o

S 6

. *-> S 5 o

2

EO-2 ROD CM PUMPED

50 iOO CaPaCITOR EHERGY / JOULES ) ROD PUMPED VOLUME \ CC J

Fig. 7 Peak of fluorescence waveform as a function of flashlamp energy input

for the 8-inch rod.

10

9

<tUJ

o- 7

UJ

UJ 6 oCO

UJg 5

=>

1^ 4 >

5 3

-JUJ

I

ED-2 ROD

28 CM PUMPED

_L _L _L

50 100 CAPACITY ENERGY /JOULES\

ROD PUMPED VOLUME I CC /

150

Fig. 8 Peak of fluorescence waveform as a function of flashlamp energy input

for the 12-inch rod.

34
ROD PUMPED AT 90 J/CC.

15 CM PUMPED 0-ROD WITH ROUGH BARREL O -ROD WITH SMOOTH BARREL

LITE PIPE

20 30 40 50 60

P-PROTRUSION DISTANCE- 1/8 INCH UNITS

Fig. 9 Peak of fluorescence as a func- tion of length of rod protruding

from flashlamp enclosure. Input energy is held constant and 15 cm

of rod are pumped.

ROD PUMPED VOLUME Fig. 11 Numerical gain as a function of

flashlamp energy input for 9- inch French laser rod.

Fig. 10 Numerical gain as a function of flashlamp energy input for 4-inch

AO rod.

Fig. 12 Numerical gain as a function of flashlamp input for three types of

lamps pumping 4-inch ED-2 rod.

35
14

12

UJo

i 10 o

OLU

a.cn

UJ 6

2'3^ 4 5 .6 .7 8 9 10 WAVELENGTH (Microns)

Fig. 15 Flashlamp spectral output for two current densities. After Goncz and Newell. [8]

COmchiTS Ot4 PAPER BV CAPT C.R.JOl^ES

It MCLi, pfLopoiS-d thaZ a beAXdA incLiccution Ojj thz invn^ion £eueil coutd be. obtaA.md by movuXoKinQ

thd ] .55 vm n.adA.citLon, ncutheA than the. 1 .06 vm. In mecu,u.nj.ng the latteA, one -ci tyioubted by iupeAfLCidu-Cuicie . An cutteyt^pt had been made to momXon. the 0.&& vm and 0.91 vm nad^aJU.on, bat thg. i^gnat -en the^e coie^ wa^ g^eatty reduced by ie£{)-abion.ptA,on. The EV-4 glaa taed -in the^e te^t^ wa6 i-wt-tlafi in atl ^&4pec^ to EV-2, tncZuding ceA.iutn, except {^on the absence 0^ the Md dopant.

It woi poi.nted oat that the 10% and TBI tedact^on -in imalZ i-tgnaJL ga^n obiexved when a VAG oicilZato^ Mai employzd to d/Uve a gZaa omptidieA ove/i that ieen with a gta66 oiclLtaton. could be due to two e^jjecti, the ipectxat mtimatch (EC-2 gZoM opeAottng at 1 . 062 vm, Nd: VAG opeAating at

1 . 064& vm] , and 6atuAatU.on. The IxitteA wa4 not evident -in the^e expextmenti, . The e^{^ect on meaiuAed

gain due to ipectAat m-U'vatch haA been venJ^^^-ied both at American Optical., with A.O. gloAi, , and in

the Ph.D. thejs-t6 o{, Vuiton at RPl , uboig both AtyieJiican Optical and EV-2 glaii

.

Although not evaluated In tkli 6tudy It MOi pointed out that the VAG oiclllatofi output li llneoAly

polojLized and that the elective gain In the glaii mnpll^-teA may be reduced by b-iAe^filngence -tnduczd In the oinpltd-te/L n.od by theAnjol e(j^ecXi ne^ulttyig ^nom the intense pumping, 04 weJUi ai nej>lduaZ itKalm

.

36
Filamentary Damage in Glasses1

J. Davit

Centre de Recherches de la Compagnie Generale d ' Electr ic ite

,

Division des Applications Optiques, Marcoussis (91) - FRANCE

The diameter of the self focusing filament in glass is measured

by different means, all of which give self -cons istent results.

The filamentary damage threshold is related to a self-focusing

length. The experiments show that the filamentary damage threshold

varies with the length of the glass as indicated by the theory of

self-focusing only for lengths of glass that are smaller than the

self-focusing length.

Key Words: Damage threshold, filaments, self-focusing.

Small scale filaments appear in glass subjected to high power, Q switched laser

beams (1) . Actually this type of damage limits the breakdown threshold of the glass

when the pulse length is 2 ns (2) . A typical filament is shown in fig. 1. We have

previously described (2) such a filament as composed of a bright filament of a diameter ds^O.G pm. embedded in what appears to be a hollow cylinder of a diameter

D — 2 yum

.

We show here that the characteristic diameter of the filament is neither d nor D but a third diameter /um.

The filament in fig, 1 has been observed with a Re ichert microscope by using

transmitted and reflected light for illumination. Figure 2 shows the same filament

when only the transmitted light is utilized. Then the diameter s=;0.9 yam appears

more clearly than in fig. 1 and we note that the diameter d is now reduced to 0.3 /um.

In order to show that the characteristic diameter of the filament is s~0.9 yum, we took a picture in a plane situated at a distance b = 10 jom. behind the filament.

The point source was at a distance a = 15 mm in front of the filament. We obtain

then the diffraction pattern of an opaque strip with a Fresnel variable difference

(3) Av = 0.5 (f ig.3)

.

The size s of the strip is readily obtained by the equation:

Because a » b, the diffraction pattern does not depend on a, and this was verified. Now by substituting the values Av = 0.5, b = 10 /um and \ = 0.56 yum, the

effective wavelength of white light, we obtain a value s = 84 yum (4) .

^Work supported by Direction des Recherches et Moyens d'Essais.

1

.

Introduction

s

37
The size of the strip may also be obtained by using Cornu ' s spiral. The first

black fringe is such that v = 2,1. This corresponds to a distance of 3.85 /um

measured on fig. 3. Thus the size of the strip is s = 0.92 /um.

Finally, we took a photograph of the filament with a polarization interferometer f (5) adapted on the Reichert microscope. Then the filament is only characterized by

the diameter s which is the true diameter of the filament since the index of refract ioi inside is different from the outside. Furthermore it is seen that in the part of the

photograph on the right side of the line xy the filament has almost the same diameter |j which does not appear on fig.l.

2. Variation of the Filamentary Damage Threshold with the Glass Length

The experiments have been conducted with two laser glasses, A and C, for an excitation wavelength of 1.06 /um and a pulse length of 2 ns

.

These glasses have been selected for the experiments from the many laser glasses

we have tested because of the good reproducibility of the results obtained from one sample to another and because of the facility in testing the self-focusing theory

with them. Laser glass A is a LG 55 SCHOTT glass. Laser glass C is a MG 915 SOVIREL

glass manufactured in a continuous unit process. The peculiarity of this glass is

that the proportion of neodymium has been continuously varied during the process in

such a way that at the beginning of the process we had:

2 3 2 3 La O : 3% - Nd O : 0% and at the end of the process

2 3 2 3 La O : 0% - Nd O : 3%.

The results which we shall describe now are the same for the laser glass c with

and without Nd . This is important because we shall see that the coefficient in

the non linear addition to the refractive index must be measured with the laser glass

C without neodymium.

In order to clarify the results we have defined three thresholds:

. The input surface breakdown threshold, defined as the minimum energy density

at which a visible breakdown occurs on the input surface of the glass.

. The filamentary damage threshold, defined as the minimum energy density at

which a filament begins to appear in the bulk of the glass.

. The output surface breakdown threshold, defined as the minimum energy density

at which a visible breakdown occurs on the output surface of the glass.

3 . Results for Laser Glass C

. When the length o| the glass C is greater than 25 mm, the output surface breakdown threshold is 9 j/cm in 2 ns . It is constant with the length of the glass and

equal to the filamentary damage threshold.

. When the length of the glass C is 20 mm, the output surface breakdown threshold

is 11 j/cm^ in 2 ns . it is still equal to the filamentary damage threshold.

. When the length of the glass C is below 15 mm, the output surface breakdown

threshold is equal to the input surface breakdown threshold that is 14 j/cm in 2 ns

,

but the filamentary damage threshold is higher.

Whgn the length of the glass C is 4 mm, the filamentary damage threshold is about

55 j/cm in 2 ns

,

II

38
4. Results for Laser Glass A

. When the length of the glass A is greater than 20 mm, the output surface breakdown threshold is 17 j/cm^ in 2 ns . It is constant with the length of the glass and

equal to the filamentary damage threshold.

. When the length of the glass A is below 10 mm the output surface breakdown

threshold is equal to the input surface breakdown threshold, that is 21 j/cm^ in 2 ns

,

and the filamentary damage threshold is higher.

. When the length of the glass A is 15 mm, the output surface breakdown threshold

is either 21 j/cm^ or 17 j/cm^ . Thus the precision for the measurement of the

filamentary damage threshold of laser glass A is not as good as with laser glass C.

When the length of the glass A is 4 mm the filamentary damage threshold is about

70 j/cm^ in 2 ns

.

Interpretation of the Results by the Self-Focusing Theory

In order that the experimental results agree with the self-focusing theory, it

is important to remember, as was pointed out by Bespalov and Talanov (6), that among

the individual inhomogeneous sections in the cross section of the laser beam, there

is an optimal transverse spatial scale a for which the self-focusing proceeds at

the fastest rate. opt

Now if we consider the stationary aberrat ionless self-focusing in a medium with

+ e. e_ > 0 and if we take account of the diffraction, then the selffocusing theory indicates (7) that a beam of diameter 2a with a plane phase front

and parabolic amplitude focuses inself into a point over a length Rni*/ ' ' given by:

dif

where

;

Rnl = ^

approximation (k

2tt

X

2e2E

is the self -focus ing length in the geometrical-optics

) .

R^ = k a_ is the diffraction length of the beam.

The optimal tranverse spatial scale a is determined from the condition 5Rn£'^=0

which gives:

a ^ = 2 opt - and Z

f min = k opt

where ^ is the minimum self-focusing length. By combining these relations and

introduc ing'^the refractive index inside the beam n^ = n^ + n2E such that

"^2 = "^2 , we obtain:

f min

2TTn2E

39
It is seen that the experimental results obtained with laser glass C agree very

well with the preceding equation, since:

2 2 2 . 2 5 mm X 9 j/cm - 2 0 mm X 11 j/cm 4 mm X 55 j/cm -

• -

The precision is not so good with laser glass A, in particular because the input

surface breakdown threshold of 21 j/cm^ in 2 ns is too near the output surface breakdown threshold of 17 j/cm^ in 2 ns , which renders the measurements difficult.

6. Measurement of the n^ Coefficient for Laser Glass C

. All of the details of the experiment which allows us to evaluate this coefficient will be given elsewhere (8) . The scheme of this experiment is shown in Fig. 5.

The anisotropy is induced in the glass by the intense light wave (maximum energy

density 3 j/cm^ in 30 ns at 1,05 yum) . The 5300 A radiation blocked in the absence of

the anisotropy by the analyzer A is incident on a photomultiplier when the laser

pulse renders the glass anisotropic. The filter F passes this radiation.

The kerr constant is calculated from the experimentally determined difference of

the refractive index n]_]_ ~ = X o^opt with \q = 5300 A. If we suppose that the

contribution to n2 is due to changes in the polar izabil ity of the molecules we have

the relation:

n^ = 3 B , X

2 — opt o

Now because the laser glass has an absorption band at the wavelength of 5300 A, we are obliged to measure the n2 coefficient with the laser glass C without Nd. We

have seen previously that the filamentary damage threshold of laser glass C is

independant of the proportion of the Nd, that is the coefficient is the same.

The measurement of the kerr constant in the case of laser glass c without Nd is

Bopt = 1-1 X 10"^ esu.

Therefore we find, by postulating an electronic kerr effect:

-13

n„ = 8.7.10 esu.

7. Calculations Based on Self-Focusing Theory

. The equation for 'Z'f^^^ that we have given above and the experimental results

obtained with laser glasses A and C allow us to calculate the rx^ coefficient for

these glasses

.

7.1 Laser Glass C

40
There is about a factor 3 with the ^2 measured for this glass. We must remember

that the measurement of the n2 coefficient was made with a pulse length of 30 ns

,

while we calculate the n2 from the results obtained with a pulse length of 2 ns

.

This may explain the observed difference.

2 The critical power is obtained from the relation P^.^.^^ = o ' and we find for

the laser glass C, P^^j^ = 395 KW, of the order of the 2^

critical power obtained from the electrostr ictive ^ 2 focusing (9-10)

.

7.2 Laser Glass A

2 With this laser glass, if we choose 16 mm as a self -focus ing length and 17 j/cm

in 2 ns (E = 6.9 X 10 as a filamentary damage threshold, the same calculation

gives: n2 = 2.2 X 10 esu, not much different from laser glass A. Therefore, we cannot explain the difference in the filamentary damage thresholds of laser glasses

A and C with only the n^ parameter.

In fact it is seen that the principal difference between these glasses is that

the maximum of the optimal transverse spatial scale

^Qp-i- calculated from the selffocusing length is 75 /um for laser glass C and 60 /am for laser glass A.

It is interesting to note that many inhomogene it ies of the beam of our laser

system have a mean diameter 2a of about 100 yum.

8. Pulse Length Variation of the Filamentary Damage Threshold in the Range 2 to 4 NS

We have tested the laser glass C with a pulse length of 4 ns . In this case the

output surface breakdown threshold is equal to the filamentary damage threshold,

found to be 18 j/cm in 4 ns

.

Therefore in the range 2 to 4 ns the filamentary damage threshold is determined

by the power density of the laser beam. We recall (2) that with laser glass A the

filamentary damage threshold is much higher than the surface damage threshold, which

is another difference between these glasses.

9. Conclusion

The experiments we have described show that the filamentary damage is due to

the self-focusing of the beam. We think that the electronic kerr effect plays an important role in the contribution to the n2 coefficient. It is not quite clear

why two glasses with an n2 of the same order have so different filamentary damage

thresholds

.

It is possible that the approximations made in the case where we have applied

the self-focus ing theory are not valid above a certain diameter. For example the

beam profile may possibly deviate from parabolic and if this is true this can explain why the experimental results are not fitting the theory for a length of

the glass greater than the self-focusing length.

10. References

(1) Hercher, M., "Laser induced damage in

transparent media", J. Opt. Soc . of

America, 54_, 563(1964).

(2) Davit, J., "Damage in laser glass",

ASTM - STP 469 , 100(N.B.S. Boulder,

Colo, June 1969)

(3) Jenkins, F .A . and White, H.E.,

Fundamentals of optics , (McGraw-Hill,

Inc., New York, 1950) 2nd ed p. 373.

(4) Rigorously, as the index of refraction of the glass is 1.5, we have

b = 1.5 X 10 /u and \ = 0.56/1.5 ai which gives the same result for s.

41
(5) Francon, M., Modern applications of

Physical Optics , Interscience

Publishers,

(8) Lacour, B. and Pocholle, J. P., "Optical

Kerr constant measurement in liquids

and glasses", to be published.

(6) Bespalov, V.I. and Talanov, V.I.,

"Filamentary structure of light

beams in non linear liquids", JETPLett 3 , 307 (1966) ,

(9) Kerr, E.L., "Laser' beam self focusing

and glass damage caused by electrostrictively driven acoustic waves",

same reference as in (2)

.

(7) Akhmanov, S.A., et al, "Self focusing and diffraction of light in a non linear medium", Soviet Physics

Uspekhi. Vol 93. 609, March-April

1968

,

(10) Quelle, F.W., "Self focusing in glass",

same reference as in (2)

,

Fig. 1 A typical filament obtained in laser glass with a 2 nsec pulse, observed with a Reichert

microscope under both transmitted and reflected illumination. Reference distance = 10 (Jm in each figure.

42
Fig. 3 Image of the filament in a plane 10 \Jm behind the filament.

43
Fig. 4 Image of the filament in a polarization interferometer.

Gloss laser kDP

] /

Quorlt

i\ loser Glass C A

Fig. 5 Experimental arrangement used to determine n^.

comrns paper rv juaw vAi/u

III t'lc nntcerHiiQ papc.i, avcn.agc ci/cii-i// clcMltn vattmi c'CAe nuotcd. T/ie (ocatiz^d em^gii diini-Ltii

cit the po^nt oi^ {)iZa)ii(Lnt <,0'V)iation ma'j be much hig'kp.i than t/ie quoted vcuLuc. Tioo type^ of) zxp&'vbyie.ntal

coniiQuiat.ionii oc^e mploifed, one in icliicli the. bccun i<j(U {ocu{,pd in an eKte^naf bcunp'Ze, and one

in i^^hich a paiaiieC beam loo-.s ompfx^-tex/ in a pwvpe.d ainptA.{)ie^ ^od I'Aiic.h icai itieC.f. the expeiimzntal

ioinplle . Tlie iciu-^ti me/ic identieaL in the. tn'o caieJ>. The detailed <,ilan]entciAi' danage itKuctufie ob^eived n'ai independent of the iampie length and the di-ie.c.tion of ifiAadi.atxcn. Although occaiionatcii

a vLiible pLa.ima ("0.5 produced at the entnance iun.face of tlie iconple, no mote tlian a fem percent ofj the incident radiation Ma-i, abionbed in the plaima, due to the hhox-t dun.ation {2 nice] of the putie.

On !iigh oualitu gZaisei (qi'aiiCi A and C] , damage tli'ic-ihoid meaiuionenU afie fLcpfLoducibte to +_ 51, Mhite on qtaii of pool cp^^caC oualitii, i.e. contaA^ning itniae, a comideKable vaiA-ation in doirnge thfic6hold (Ufw icGii. Thiis Kciults f-iom tJic dibtontion of the loavefKont, n^hich pKcvcnti the fomation of

an inteme twit defined focal ipot.

davage th^ebh.oid. foi a given composition, the beit ouatitij gtaii ihoioi the toi.oei>t

To !iwnv.axize, the detailed de icUption of the filanentanu dwnage obieived in tiie scmplci , a tubc-tikc

itxuct.uie nm horned in ivhich tlie lefnacttve index laai gn.eatei tlian that of tlie iuxxoundlng glwsi btj 0.03 [in uiuts of xefiactive index], I'lith a dioiivten 0.9 pm. Tliib tube extended f-lon', one mn to 30 an

in lengtli. i'Uthln t'ae tube, intCuiiittent t^aim of babble- lihc ffiactuiei , icpafiatcd bu one vm ipacing,

locAe obieived. Tliue tnxibn tijpicatVi loeAe of one tm length. The o^gin of the. legion of incica^bed

fieffiactivc index man be due to a peimancnt change of n/iaie, as nfiopoied be Shen, on a plwtodielectiic

effect, as fie.centlij pfiopoied ha ujoKken^ at the Eell Telephone LabonatoMi in Holndel.

44
Measurement of the Nonlinear Index n2

of Glass using Picosecond Pulses

Michel A. Duguay and John W. Hansen

Bell Telephone Laboratories, Incorporated

Murray Hill, New Jersey 0797^

U.S.A.

Using picosecond pulses from a mode-locked Nd: glass laser and

the ultrafast Kerr cell apparatus we measure the nonlinear index

n2B °f BK7 and LaSF7 glass. On the assumption that the AC Kerr

effect in glass is predominantly of electronic origin we derive

the value n2 ~ 3x10" m2/v2 (2 .7x10"-'-^ esu) for the nonlinear

index n2 of BK7 glass. Laser glass is assumed to have about the same n2- At power densities -vl GW/cm^ this gives rise to refractive index increases of 'vl0~"; this is sufficient to explain the

appearance of self -focussing in glass laser rods which leads to

the formation of long fossil tracks of microscopic bubbles. In

addition, ng leads to pulse spectral broadening and gain limiting.

Key Words: AC Kerr effect in glass, frequency broadening,

light induced birefringence, nonlinear index n2, picosecond

pulses, self-focussing, stop-motion photography of light

pulses

.

1. Introduction

When a powerful laser pulse propagates through an isotropic dielectric it induces

changes in the refractive index described to first order by the equations.

nil = n^ + ng (,1)

2

n_^ = n^ + n2_L E (2)

n|| - = n2g E ' - (3)

Here, no is the usual low signal refractive index, E is the root-mean-square value of

the plane polarized optical field E*, n|| (n, ) is the refractive index seen by light

polarized parallel (normal) to E*, and n2B is the nonlinear birefringence index. In

certain materials (such as CS2 for example) the constant n2B is approximately equal to

BA, where B is the DC Kerr constant of the material, and A the measuring wavelength in vacuo (this relation does not hold in general).

The importance of the nonlinear index n2 in lasers stems from the fact that the

changes in refractive index 5n|| = n|| - no can lead to self-focussing [1,15] and

frequency broadening [2] in laser rods. The coefficient n2;o is also of special

interest because the light induced birefringence can be used in the ultrafast Kerr

cell [3] to allow the photographing of light pulses propagating in various media [4],

Figures in brackets indicate the literature references at the end of this paper.

45
2. Measurement of n^-^ in Glass

In our experiment we measured the nonlinear birefringence index ngg, and by making

an assumption about the mechanism involved, we deduce the value of n2- The experimental set-up has been described in Ref.[3]. Infrared (X = 1.06^.) pulses from a modelocked Nd: glass laser are used to induce birefringence in glass samples 2-5 cm in

length. The 1.06(1 pulses are 8 psec in duration. [2] Green light pulses derived from

them by second harmonic generation in KDP have a duration of -^-6 psec. The green pulses

are used to probe the induced birefringence. The glass sample is placed between two

crossed polarizers, and the whole arrangement acts like an ultrafast Kerr cell. [3]

The green pulses are used to measure the transmission of the ultrafast Kerr cell as a function of time.

We have measured n2B for the Schott glasses type BK7 and LaSF7. The curve for

BK7 is shown in Fig. 1. The transmission Is plotted in arbitrary units. Typical

transmission are -vO.OS^ for peak power densities ^0.5 GW/cm^ in the 1.06|a picosecond

pulses. When we replace the glass sample by a 1 cm CS2 cell typical transmissions

are '^.lO^. Since the ngg of CSg is known to be: [5]

n2g(CS2) = 2.3x10"^° m^/V^ = 2X10"-'--'- esu, • (4)

we can use the CS2 curves as a calibration in order to obtain absolute values for np„

of the glasses.

We have found this way:

n2g(BK7 glass) = (2±l)xl0'^^ m^/v^ (5)

np( LaSFT glass) = (6±2)xl0~^^ m^/V^ ' (6)

(Following Ref.[10] we use SI units. The conversion factor is 1 m /v = 0,9x10-'^ esu,

so that npg (BK7) = (2±l)xlO-13 esu and n2g(LaSF7) = 6x10-13 esu).

Also, from the fact that the curves for these two glasses have the same shape as the curve for CS2j we are able to establish an upper limit on the relaxation time t associated with n23 in glasses viz:

T(glass) < 5 psec. (7)

The very fast relaxation time of the induced birefringence and other evidence from

frequency broadening in self-focussing [6] support the thesis advanced by several

workers [7,2,6] that the mechanism at work here is the electron cloud distortion

mechanism. Another mechanism that could possibly be at work in glass in the collective

mechanism proposed by Hellwarth. [8] There is, however, very little experimental

evidence on the collective mechanism in solids, and for simplicity, we shall assume,

henceforth that the effect is purely electronic in glass. If we assume a purely

electronic mechanism for n2g, we can use the work of Buckingham et al. [9,10] to

estimate the n2g of a material from a knowledge of its refractive index. Buckingham

et al. [9,10] nave measured the birefringence induced in each molecule of a gas by a DC electric field. Each molecule possesses a hyperpolarizability coefficient 7 which

is a measure of the birefringence Induced by the field. The following formula connects

the bulk property ngg (assumed to be of purely electronic origin) with molecular 7:

(n^+2)^ IN '

! n (electronic) = 5^ V

^ .. (8) ' n n

where no is the refractive index, Eq = 8.85x10 Fd/m is the capacitivity of vacuum,

and n/V is the number of molecules per m3. For Si02, the main constituent of BK7, a

46
y 10 ^'^ C^m^J is not unreasonable. [2] With no = 1-5 at 1.06^, we find;

n2g(BK7 glass, calculated) 1.0x10"^^ m^/v^ (9)

which compares favorably with Eq.(5)' For LaSP7 we have nQ = I.89 and using the same

7 we find:

op p p n2g(LaSF7 glass, calculated) ^ 2.5x10" m /v (10)

which again compares favorably with Eq.(6). A correlation between ngo and nQcan be

clearly seen here. Since laser glass has no= 1.50, for discussions pertaining to

self-focussing and frequency broadening in laser glass, it is probably reasonable to assume

n^gClaser glass) ~ n2g(BK7 glass)

We shall assume so in the following. (Measurements of np-^ of laser glass itself are

in progress and shall be reported in a future publication.

)

Self-Focussing in Glass

In the electron cloud distortion model the relation between Snn = nn-n and

5nj_ = nj_-n is [9] "

"

5n||

5H7=+3 ^ (11)

From this and Eqs.(l)-(3) we deduce:

ng = 1.5 n^g , (12)

Assuming that np is predominantly of electronic origin in glass, we therefore have;

pp p p n2(BK7 glass) = BxlO"""^ m /V (13)

n2(LaSF7 glass) ^ 9x10"^^ m^/V^ ( lU

)

— 22 2 2 Assuming that laser glass has the value np = 3x10 m /V we can now calculate

the self-focussing length in laser rods. In the neglect of diffraction, the selffocussing length given by Kelley [11] is:

z(focus) = l^J\\ . (15)

where b is the beam parameter (the beam diameter for a beam of Gaussian profile, i.e.,

TEM mode). In mode-locked Nd:glass oscillators and 30 nsec pulse oscillatoramplifier systems, power densities P of ^1 GW/cm2 are typical. [12] The spatial power

density distribution frequently contains hot spots of ^\ mm in diameter. Assuming

ng = 3x10-22^ we then have Bnii = 1.1x10-° and;

47
Z(focus ) = 29 cm

' (16)

o for b = 1 mm and P = 1 GW/cm

In large single picosecond-pulse glass laser amplifier systems power densities of

-vl TW/cm^ have been reported, [I3] In this case we have: Sny = l,lxlO~3 and

Z(focus ) =0.91 cm

(17)

for b = 1 mm and P = 1 TW/cm

These self -focussing distances should be compared with the observations of selffocussing in laser rods for nanosecond [1,15] as well as picosecond pulses [13,6],

From Eq.(15) it is clear that for a given n2 and power density, the self-focussing

length can only be increased if more spatially uniform beams are used (i.e., larger

b's in Eq.(15)). With beams of present quality self-focussing can be expected at

power densities over 2 GW/cm .

3. Frequency Broadening

As a powerful pulse propagates through glass, it modulates the index and this,

in turn, leads to frequency modulation or spectral boradening of the pulse. The

leading edge of a pulse will be frequency down-shifted and the lagging edge up-shifted

by an amount equal to:

where 7\ is the wavelength in vacuum, 6n/5t is the rate of change of n with time

(= d(n2E )/dt), and L is the distance over which the pulse propagates without suffering severe distortion. [l4]. As a numerical example, we give: P = 10 G¥/cm^, 5n = llxlO-c

1 = 10 cm, A = 10"'^ cm, 6t = 1 psec . Then:

Av = ±1.1 THz = ±37 cm"-*- (19)

which is a considerable frequency shift. Such shifts are believed to account for the

100 cm"! spectral width of the mode-locked Nd:glass laser, and the very broad spectra

observed in self-f ocussed regions in glass. This dynamic spectral boradening is also

believed to lead to gain limiting [2] in high peak power amplifiers.

4. Ultrahigh Speed Photography of Picosecond Light Pulses

As an application of the light induced birefringence, we show in Fig. 2 photograph of a green light pulse in flight through a cell of water containing a slight

amount of milk in suspension. [4] The photograph is taken from the side by a camera

placed behind an ultrafast shutter of 10 psec framing time. [3] In this case, CSg

was used in the shutter, but in the future glass could be used for response times

faster than 2 psec (the response time [7] of the electronic effect may be as fast as 10~15 sec). The ultrafast camera could be used in studies of damage in glass. With

proper time and space resolution, laser pulses could be photographed as they are self -focussing and freqeuncy broadening. It may also be possible to photograph the

time development of regions of bubble and inclusion damage.

48
5. References

[1] Zverev, G. M. , Levchuk, E. A.,

Maldutis, E. K. , and Pashkov, V. A,,

Self-focussing of laser radiation in

active media and in non-linear

crystals. Optica i Spektroskopia

,

Vol. 27, (November 1969),pp, IO6O-IO62,

[2] Duguay, M. A., Hansen, J. W. , and

Shapiro, S. L. , Study of the Nd

glass laser radiation by means of

two-photon fluorescence, IEEE J. Quantum Electronics, Vol. QE-6 , (October 1970).

[3] Duguay, M. A. and Hansen, J. W,,

An ultrafast light gate, Appl, Phys

.

Letters, Vol. I5, (Sept. I969)

pp. 192-194.

[4] Duguay, M. A. and Hansen, J, W. , Ultrahigh speed photography of

picosecond light pulses, submitted

to Applied Physics Letters, May 28

(I97O).

[5] Paillette, M. , Mesure of I'effet

Kerr induit par une onde lumineuse

intense, Compt. Rendus Acad. Sc.

Paris, Vol. 26 2B , (Jan. I966

)

pp. 264-267.

[6] Alfano, R. R. and Shapiro, S. L.,

Observation of self-phase modulations

and small scale filaments in crystals

and glasses, Phys. Rev. Letters,

Vol. 24 (March 1970) pp. 592-594.

[7] Brewer, R. G. and Lee, C. H. , Selftrapping with picosecond light pulses,

Phys. Rev. Letters, Vol. 21, (July

1968) pp. 267-270.

[8] Hellwarth, R. W. , Quantum molecular

theory of light scattering spectra,

J. Chem. Phys.

<

.001 1 1 1 1 1 1 1 1 -20 -10 0 10 20 30 40

T/2 (psec) Fig. 1 The gate transmission is plotted vs. the time T at which the green probing pulse arrives relative to the 1.06^ pulse. The latter pulse has a peak power ~0. 5 GW/cm^ and induces birefringence in the glass

sample. The width of the curve is largely due to the 8 psec width of the

1 . 06/Ll pulse s.

[9] Buckingham, A. D. and Dunmur, D. A.,

Kerr effect in noble gases and

sulfer hexaf luoride , Trans, Faraday

Soc, Vol. 64, (1968) pp. 1776-1783.

[10] Buckingham, A. D. and Orr, B. J.,

Kerr effect in methane and its four

fluorinated derivatives, Trans,

Faraday Soc, Vol. 65, (March I969

)

pp. 673-681.

[11] Kelley, P. L. , Self-focussing of

optical beams, Phys, Rev. Letters,

Vol, 15, (Dec. 1965) pp. 1005-1008,

[12] Young, C. G. and Woodcock, R, F.,

Laser-induced damage in glass.

Damage in Laser Glass, ASTM STP 469,

American Society for Testing and

Materials (I969) pp. 86-89,

[13] Gobeli, G, W. , Bushnell, J, C,,

Peercy, P, S, and Jones, E, D.

,

Observation of neutrons produced by

laser irradiation of lithium

deuteride, Phys, Rev,, Vol. 188 , (Dec. 1969) pp, 300-302.

[l4] Joenk, R. J. and Landauer, R,,

Laser pulse distortion in a nonlinear

dielectric, Phys, Letters, Vol, 24a

(Feb. 1967) pp. 228-229,

[15] Davit, J., Filamentary damage in

glasses (paper in this issue).

Fig. 2 Stop-motion photograph of a green

light pulse propagating through a cell containing a colloidal suspension of milk particles in water. The pulse

is seen through its scattered light.

An ultrafast light gate served as a camera shutter with a framing time

of 10 psec. Glass could eventually

be used in shutters 10-100 times

faster. The pulse is travelling from

right to left. The scale is in millimete r s

.
COMMEWTS O.M PAFE'i EV liZCHEL PUGUAV

ThdfL^ ('.'04 coniid^fLable diicuM-ion on t'm quzityion o<i whicli idZfi-^ocvaing me.chaniMni i(;eA.e opzua.'tivz in the 30 nie.c tmo. 'X^q-unc. T/tcic gandnaZ agx?.ejne.nt that in the. picoizcond tone fLzg-bm, the. dominant ieiJ.- focusing mdianiMn n'o-i tJic KaK^i e^fjecf, e^t/iei (>.te.ctAoni.c, nucitaK, on. due. to moHeculoA

tibKatlon. Vn. Hc.lilman.th pointed out:, that the toit ihould be detectable fiom a detaited analiuLs of,

t'.ie !>tn.uctu>ie of Raman spectra. Although it ti ii>el!.t eitabl^iihed that theie iufficient time in 50 mec

puisei fan edectioitnctive trapping to ocean., the fact th^t obie.ive.d filaments onLii last foK tAJt^^ei tike 100 piec. 'uu.iei doubt^s that the electn.06tnj.ctA.ve mechanism ij> the only one openating. An

add-i.iU.onal comptication a-'U.se-i fn.om the fact that n'ithout extAP/ne can.e, mann 50 mec putsei contOA^n iub-nanoiecond inteiisi-tij ftuctua.t-Loni. The queit.Lon of the exact mechanLsm of ieif- focusing in the

thne neame o\ 1 to 50 nsec moi (eft ann.eioCved.

[Edtton' s no te: Due to tvve limitatiom , the foKoi'Jing comment toas submitted in uniting

bii Vn. Chanles Wang of the fon.d l^otox Companij Scientific Rcseanch Staff]

Tliis conment Invotves (J) the convention of the iuiceptibiiittj coefficients fnom HKS uniti to cgs units; [2] tlie magnitude of n^, "the coefficient of intettsittj-dependent index"; and (3) the expenimental

detenmination of thnough ovticaC KeAn effect mea^uie/nenti

.

11] The convention <toi)i MKS to cgs units is discussed in [flinck, Tenhune and i'fang, Pnoc, IEEE 54, /357

(J966)) ^ ~

x'^' [mki] -- J- X 10'^ x'^' (ci")

- 9 it is MOT 10 0,1 given bii Vuguaii.

[2] Tlie coe ff-tCACnt of the intensitn-dependent index n^ vs defined as [Ketlii, Phiis. Rev. Lettent, 1_S_, lOOS {1965]] ' " ' "~"

6H = y Ho I E|

(Wictp |E| is the ojyipZitude of the electnxc field and 6" i.i the change in the nefKact^ive index. This

coe^icAcnt is nelated to the. uAual iuscei}tihiZitn comtanti ^t^) (-^j, to, -w ,to) o4 fo.llom i'.^ang, Phiii. Rev. 152_, [1966] ) :

'

'

^n - ^ '3' (- - 1 lEl^ •

•

At fneouQ.ncie^ tmalZ companed to oik/ of the electronic nescnance fneouencie-i of the 4(/6 tejri, C/ic edectnonic contnA.bution to x'^' (-oj, ui, -u, u) f'^"- sai>ie 04 tfiot to ('^ui> a)» (o> 00' ^'^^ expenMventi of thind haninonic genena.tA.on. Thus, the electronic pant of ^'n can be accun.atelij

calculated using tJie available data of x'^' (-3io, w). T'le value of x fon EonoiUxco-te glais

IS (Wonq, Pit(/.j. Rev. B, Sept. 1970): x'^' = 1.3 x 10'^ eia. ThA.s giveA

f^n = 1.63 X 10 ^ \E\

(3) It ii I'.'cll known that reliable mea'iunements of optical Kexn. effect in solids is extxeinelu difficult,

as ojii/ birefntngence [due to local stxeis, etc.] will obdcure the mea.sune)i\ent.{, . The difference in ii^ iiieoiuAec/ bij Vavit fon glais A and glati C must thus be interpreted with caution.

50
Absorbing Centers in Laser Glasses

Herbert S. Bennett

National Bureau of Standards

Washington, D.C. 20234

Some metallic and dielectric inclusions in glass laser rods may absorb an appreciable amount of the laser radiation and thereby may produce major stresses within the glass host. The radial and tangential stress components, the stress birefringence, the optical path length change for a probing light ray passing

near the inclusion, and the "lens" effect are computed. The dependence of the maximum value of the tensile stress upon the size of the inclusion and upon the physical properties of the host is examined.

Key Words: Antimony, heat conduction, laser damage, laser glasses, platinum,

stress components, thermoelastic theory.

1. Introduction

One of the severe problems encountered in high-power-solid-state laser systems is the thermal

damage to laser rods and optical elements. One such type of damage is throught to arise from metallic

or dielectric inclusions. Such inclusions may absorb an appreciable amount of incident laser radiation

and thereby may undergo thermal expansion. This produces major stresses within the host material.

Estimating such thermal properties requires the consideration of solutions to the heat diffusion

equation and the thermal stress equations with appropriate boundary conditions. In particular, the optical path length change for a probing light ray passing near the absorbing center, the radial and tangential stress components, and the changes of the refractive index for radially polarized and tangentially polarized light due to the thermal stress field are computed. The dependence of the maximum value of the tensile stress upon the size of the inclusion and upon the physical properties

of the host is examined. The feasibility of using optical techniques to detect metallic and dielectric inclusions in laser materials before they cause damage also is studied. These computations

suggest that the use of laser pulse widths of the order of microseconds or longer may be more promising for the detection of small incipient absorbing centers than the use of nanosecond pulse

widths. In addition, the lens effect is estimated.

2. Description of the Model

The results summarized in this paper are based upon a linear theory and upon a model whose

elastic, thermal, and optical properties are constants. The values used for these properties are valid for temperatures near 300 K and for small strains. This treatment is not expected to be correct near the onset of damage. The problem is certainly a nonlinear one near the region of catastrophic damage. Whenever any of the assumptions become invalid, then the results should be viewed as suggesting trends in the behavior of the system. The inclusions which occur in laser glasses are most likely not the spheres for which the model is formulated. They could be irregularly shaped globules. Some platinum inclusions occur as hexagonal platelets. Even though the model does not take into account such geometrical aspects, one hopes that it does give a reasonable

description of the actual system. One also hopes that the manner in which it suggests one should

proceed to increase the damage threshold, though probably not quantitatively correct, is qualitatively

correct

.

A model to represent the behavior of absorbing centers in laser materials is developed. Before

the thermal properties of the absorbing center-host system can be discussed quantitatively, it is first necessary to solve the time dependent heat diffusion equation for the temperature and the thermal stress equations with appropriate boundary conditions for the stress components. This is discussed in detail in Ref. 1 and Ref. 2.

51
The model contains many physical assumptions which are necessary to render the problem solvable.

The major assumptions are summarized here.

a) The inclusion is a sphere of radius r and is always in good thermal contact with the host. The

effects of shape and orientation to the incident radiation are neglected.

b) The host material is isotropic, continuous and of infinite extent. It also is initially at an ambient temperature T and free from all stresses and strains. Because the energy content of the incident radiation is finite, the latter statement requires the temperature to be T at infinity and

all stresses and strains to vanish at infinity. The distribution and nature of microcracks and optical

imperfections are not treated in the model.

c) The linear-thermal-elastic equations are assumed to give a reasonable description of the processes which ultimately may lead to catastrophic damage. These equations are coupled equations relating the temperature and the displacement vector from which the stresses and strains are computed. They are valid only when a local temperature exists and when distances are larger than atomic dimensions

("--lO'^cm) . A relaxation time t for the definition of a local temperature T is approximately the reciprocal of a characteristic vibration frequency of the material. These relaxations times t for

Pt, Sb, A.IJ)^, and the laser glasses are about lO'^^s to IQ-l^g. Hence, the equations are physically

meaningful only when times t are much larger than 10-12s.

d) It is assumed that the radiation of heat by the center-host interface and by the heated glass

close to the absorbing center may be neglected in the thermal-elastic equations. The laser beams

studied in Ref. 1 and Ref. 2 contain energy fluxes at least 10^ times greater than the energy flux

produced by a black body at 600OC. The calculations of Ref. 1 also show that the energy flux due to thermal conduction greatly exceeds the energy flux due to radiation for times less than one second. Because the temperature is close to the ambient temperature whenever the pulse width of the laser beam

is less than a millisecond and whenever the time after cessation of the laser beam is greater than a second, the long time behavior is not in the region of practical interest for detecting damage centers before they cause damage. Hence, it is assumed that all times are less than a second.

e) The linear-thermal-elastic equations contain a coupling term and an inertia term. These two terms may be neglected whenever the three characteristic times which occur in the absorbing center-host

system satisfy a set of inequalities. These times are the following. The pulse width T of the incident radiation determines in part the rapidity of heat generation. The characteristic relaxation

time for temperature equilibration (thermal diffusion) is t^~(r2/a^), where r is the radial distance

from the center of the inclusion and is the thermal dlffusivity. The characteristic mechanical time

required for the production of stress waves is tj^~(r/v), where v is the speed of propagation of

elastic waves. Holey and Weiner have demonstrated that when ^ ^ ^ '-[4 ^^'^

""T ^

''M' ^^^^ coupling

and inertia terms are small compared to the other terms in the equations. [3] The above inequalities

are reduced to inequalities containing the pulse width T and the radial distance r;[l] namely:

T > > 2.8 x 10"^ r (s/cm) and r > > 6.7 x 10"^cm. It is assumed that these inequalities are satisfied

and thereby that the coupling and inertia terms may be neglected.

In summary, the following inequalities describe the regions for which the model is physically

meaningful

-3 -12 -12

10 s > T > 10 s, Is > t > 10 s,

r > 6.7 X 10"''cm, and r > 2.8 x lO'^ r (s/cm).

3. Results and Conclusions

The numerical results which the model developed in Ref. 1 predicts, are summarized here. Among

the many input parameters, the absorptance A(A,T) of the center-host interface is perhaps most

sensitive to the initial thermal contact and surface conditions of the inclusion and host. The wavelength is X. The numerical results are given for the case in which A(X,T) =1. This presents no additional problem because the temperature T^(r,t), the optical path length change AL for a probing

light ray passing near the inclusion, the stress components o and (J^q = CT for the spherical

coordinates r, y, and (p, and the changes in the refractive inSex due to the thermal stress field for radially polarized light An^ and for tangentially polarized light An^ are all directly proportional

to the absorptance.

The model is used to study three questions. First, how the maximum tangential-tensile stress varies as a function of the radius of the spherical inclusion for a fixed energy density E^^ and pulse

width of the laser beam T. Second, how the maximum of the tangential-tensile stress varies as a function of the thermal conductivity and the thermal expansion coefficient of the host. And third, if the maximum temperature of the inclusion is limited to a fixed value, T^ ^^q'"''^ ^ 600°C, how the parameters of the incident laser beam should be varied to increase the probability of detecting by

optical techniques a small incipient absorbing center before it causes damage. Optical techniques to detect small inclusions become more promising, the greater AL, An , and An^ are.

52
The bulk thermal, elastic, and optical properties for the laser material used in these calculations are representative of two Nd-doped laser glasses manufactured domestically. The inclusions are

Ft, Sb , and polycrystalline AI2O2 absorbing spheres.

The variation of the maximum tensile stress C (max-tensile) as a function of r for a laser

beam having an energy density = 20 (J/cm^) and a'^ulse width T = 30 ns is studied. ° When

10"^cm > r > 5 X 10~^cm, the maximum tensile stress exceeds by as much as a factor of two the theoretica? strength of the glass (6 x lO^N/m ) . The calculations show that Sb and highly absorbing

kl^^ inclusions are more likely to cause damage than Ft. The maximum tensile stresses for Sb and

AI2O2 inclusions are about 20% larger than those for Ft. It is interesting to note that one domestic manufacturer no longer uses Sb202 as a fining agent. [4]

These results demonstrate that submicron-sized inclusions have the greatest probability to cause

damage in laser glass hosts. Experimental measurements performed by industrial researchers [5] have

verified tentatively this theoretical result. Very large (r > 10"^cm) and very small (r < 5 x 10"^cm)

inclusions are not likely to produce damage.

The maximum tensile stress as a function of the thermal conductivity K, and the thermal expansion

coefficient 0^, is also studied for r^ = 5 x lO'^cm, T = 30 ns , and = 20 (J/cm^). It is found that increasing K^^ from 0.008 (W/cm°C) to 0.04 (W/cm°C) wit^ all remaining properties kept constant decreases the maximum tensile stress from about 9 x 10 (N/m ) to 4 x 10^ (N/m^). Again, all the other

properties of the host are kept the same except for the thermal expansion coefficient. The maximum

tensile stress is studied then as a function of OLx.. The maximum tensile stresses are found to have

minimum values for 10 x 10"° (1/°C) > O^^ > 8 x 10' {l/°C) . Values of 01^ outside this range yield

larger stresses. They also are slowly varying functions of the thermal expansion coefficient. In- creasing OL^ by a factor of three produces only a 10% variation in the maximum tensile stress. Hence,

the thermal conductivity influences greatly the behavior near the region of maximum tensile stress

and the thermal expansion coefficient plays only a minor role in the value of the maximum tensile

stress. Among the many possible glass laser hosts, the expansion coefficients vary by about an order

of magnitude from 10"6(l/°C)to about 10 x 10"^ (1/oC) and all the remaining bulk elastic and thermal

properties vary by only small amounts. The latter variations usually do not exceed a factor of two. Hence, extensive research on altering substantially the composition of present laser glasses to in- crease the damage threshold due to inclusions is not warranted by the predictions of this model. It suggests that probably at the best, a factor of two increase in the damage threshold due to inclusions

could be achieved.

The model also shows that the maximum value for the tensile stress does not depend upon the Young's modulus E in a straight forward manner as some researchers have suggested. The Lame constants

are the independent elasticity variables and changes should be discussed in terms of them. If it were possible to alter only the Young's modulus, then the stresses would increase in a monotonic fashion

with increasing values of E. But such changes are not possible in practice. The model predicts that glasses with higher E values are not necessarily more resistant to damage.

The optimum parameters of the incident laser beam to be used for detecting incipient damage

centers before they cause damage are examined for the case in which the maximum temperature is 600°C

at the cessation of the laser pulse. The computations indicate that pulse widths of the order of

microseconds or longer heat the center more slowly and thereby produce larger optical path length

changes for a probing light ray passing near the inclusion. For example, a Ft sphere with radius

r^ - 10"'^cm produces a path length change of about 2 x lO'^cm for T = 0 . 1/Lts and of about lO-^cm for T = 100/is . Researchers [4] using microsecond pulses and holography have detected 5 x 10" cm inclusions without its causing damage. It is not known yet whether this method can be improved

sufficiently to detect 10~^cm inclusions.

Finally, the lens effect due to heated regions of the host is estimated. Irhenever the refractive

index increases with temperature, (drij^ / and even though the inclusion does not produce

damage at its site, the heated region of the host surrounding the inclusion might focus the same laser pulse or a succeeding laser pulse which occurs after sufficiently short times and before the heated

region cools. The lens effect is estimated by considering the focal length f of a spherical lens having a radius r and mean refractive index n^. The refractive index of the host is n^^ and because

(dn^ / dT ) >0; n > PL . Some numerical examples for platinum inclusions are cited. When

r = lO-^cm, =20 (j/cm^) , and T = 30 ns , then an effective focal length due to the lens effect occurs at t ~ 3\is and is about f ~ 14cm. But the tensile stress at t = T = 30 ns exceeds the theoretical strength of the host before the lens effect becomes most important. Consider now another

example for Ft in which the maximum tensile stress is less than the theoretical breaking strength

of the glass host. When r = IQ-'^cm, = 0.33 (J/cm^) , r = 30 ns , and T (r^ ,T ) = 600°C, the effective focal length attains a value of about lO'^cm for times t~ 3s. This latter focal length is very long.

Hence, the model predicts that the lens effect arising from heated inclusions probably does not cause damage. Those cases for which the maximum tensile stress is less than the theoretical tensile

strength of the glass have minimum effective focal lengths which are much greater than the dimensions

53
of Nd-doped glass elements used in present laser systems. In those cases for which the minimum

effective focal length is comparable to the size of the host, the tensile stress exceeds the theoret

ical strength of the glass and probably causes damage before the lens effect becomes large enough to heat another inclusion or to initiate an intrinsic damage mechanism such as self-focusing.

In conclusion, the model enables one to answer qualitatively many questions concerning laser damage due to absorbing centers and concerning the detection of such centers before they cause

damage.

References

[1] Bennett, H. S., Inclusions in Laser [4] Snitzer , Elias, private communication.

Materials, to be published.

[5] Lee, Haynes , private communication.

[2] Bennett, H. S., Heat Diffusion near Absorbing Centers in Laser Materials, to be published

.

[3] Boley, B. and Weiner , J., Theory of Thermal

Stresses, (John Wiley and Sons, Inc., New •• v .1. York, 1960). _ . . .

COMvlt.VTS OiV H. dEM>JETT' S PAPER FOLLOW THOSE OF R. HOPPER'S PAPER

54
The Inclusion Problem

In Laser Glass

R. W, Hopper, C. Lee and D, R. Uhlmann

Department of Metallurgy and Materials Science Center for Materials Science and Engineering

Massachusetts Institute of Technology

Cambridge, Massachusetts

The problem of inclusion damage in laser glass is considered anew, with

attention being directed to an improved treatment of the stress around a hot inclusion particle. The existence of a layer of molten glass surrounding

such particles is suggested; and the new analysis indicates a maximum tensile

stress in the nearby cooler glass, rather than at the solid-liquid glasss

boundary. The magnitude of this tensile stress can exceed the expected

strength of the glass for a range of particle sizes under high power laser

operation, and failure is then expected to occur.

The breakdown condition is shown to depend upon the flux level and pulse

time of the laser beam, as well as the size and shape of the inclusion particles

and various material properties of the inclusion and glass. For flux levels

in the range of 1 j cm ^ns~^ and pulse times in the range of tens of ns, metal

particles as small as 1000 8 are likely to result in failure. Under most con- ditions of laser operation, non-metallic inclusions - even those containing

large concentrations of highly absorbing ions - are expected to be safe; and

under all conditions they should be appreciably less dangerous than similar metal

particles.

Key Words: Glass damage, glass lasers, heat conduction, inclusion

damage, lasers.

1. Introduction

The problem of inclusion damage - i.e., breakdown of the glass at various discrete points- has frequently limited the use of glass lasers in high power applications. The origin of this damage

has been associated with the presence in the glass of discrete second-phase inclusion particles

(1-3). In a recent paper (A), the present authors considered in some detail the origin of inclusion

damage, and concluded that such damage could be associated with the temperature rise of particles,

or surface regions of particles, relative to the surrounding glass. The particles of greatest con- cern were identified as metallic, although at very high levels ceramic Inclusions containing large

concentrations of highly-absorbing ions could likewise result in failure.

Solutions to the heat flow problems of a perfectly conducting sphere in a medium of finite con- ductivity and of the infinite composite solid were used" to represent the physical situation. These

solutions indicated that temperature of metal particles subject to a 20 1 cm"'' , 30 ns laser pulse

could exceed 10,000OK for a range of particle sizes. These high temperatures would produce stresses

in the glass adjacent to the particles which can exceed the theoretical strength of the glass, and result in failure.

The effects on the breakdown condition of the flux level, pulse time, particle size and various

material parameters, were considered. Specific applications were, however, restricted to laser

pulses of 20 j/cm-^ , 30 ns. In the present paper, we shall review the results of the previous

study and extend them to describe phenomena occurlng over a wide range of particle sizes, flux levels and pulse times. The results will be employed to delineate the ranges of particle sizes

which should be viewed as dangerous for various conditions of laser operation, and to evaluate the reliability of various methods for damage testing laser glass.

In all cases, the particles will be taken as metallic, opaque at the laser frequency, and in good thermal contact with the surrounding glass. The laser pulse will be taken as a square wave

55
of a given duration, Incident on one side of the particles, and Lambert's Cosine Law will be assumed.

Values for the assumed material parameters, which are characteristic of Pt particles in a typical Ba crown laser glass, as well as definitions of the various symbols, are summarized in the Appendix.

2. Thermal Behavior

The temperature of a metal particle and of the adjacent glass subject to a laser pulse has been

approximated by two solutions to the heat flow problem which are appropriate for different ranges of particle size relative to the pulse time.

a. R^«(D^t)'*

For particle sizes which are small with respect to the thermal diffusion distance for the particle materials (with a given pulse time), the physical situation can well be approximated by considering perfectly-conducting spherical metal particles in a medium having the thermal conductivity of

the glass. In this case, the particle temperature may be expressed (A)

where q = 3C^

^^vi' "'=[l(<l~^)] ^5 ^""^ it is assumed in obtaining the expression in this form

that q > A.^^ ^ Corresponding expressions for the cases when q = 4 and q < 4 may similarly be

obtained, and in the latter case present some interesting features (see Ref. 5).

The temperature distribution in the glass surrounding the particle can similarly be expressed:

(2)

where x is the radial distance from the periphery of the particle to the point in question.

b. (D^t)**

For particle sizes which are large with respect to the thermal diffusion distance, the physical situation can be approximated by treating the infinite composite solid with a flux, J, at the boundary. In this case, the thermal conductivities of the two materials are taken as those characteristic of the metal and glass. For this case, the temperature in the particle may be expressed:

where x^ is the distance from the boundary into the particle material, and ierfc y = -ijj—r— exp

(-y ) - y erfcy. The corresponding expression for the temperature in the glass is

56
eerie

'/z (4)

where is the distance from the particle into the glass.

The particle temperatures expected from eq(l) for various particle sizes and conditions of laser

operation are shown in Fig. 1. With increases in flux level (and hence in energy density) for a given

pulse time, the temperature increases for any given particle size, but the shape of the temperature

vs. particle size relation remains unchanged. For the assumed 30 ns pulse duration, it is seen that temperatures in the range of 10" are expected for a range of particle sizes and the range of particle sizes having temperatures above some given value is expected to increase with increasing flux

level.For a given energy density (Fig. 2), the expected behavior is more complex as the flux level

and pulse time are separately varied. The maximum in the temperature vs. particle size relation is seen to shift to larger particle sizes with increasing pulse time (as expected for increasing thermal

diffusion distances). For particle sizes much larger than the respective maxima, but still in the range where eq (1) is appropriate, the expected temeprature depends only on the energy density and hence is the same for all combinations of flux level and pulse time having a given Jt product. The

magnitude of the maxima in the temperature vs. particle size relations, and indeed the magnitude of the entire relation for particle sizes in the range of or smaller than the maxima, is expected to in- crease with decreasing pulse time (with increasing flux level).

For a given small particle size, the temperature can be higher for a short time, high flux, pulse

having a given energy density than for a longer time, smaller flux^ pulse having a larger over-all

energy density. This is illustrated by the data shown in Fig 3, where the temperature vs. particle

size relations are compared for laser pulses of 21 j cm~^, 30 ns and 150 j cm" , 1000 ns respectively.

It should be recognized, of course, that the assumption of the particles being opaque at the laser wavelength is highly suspect for particle sizes smaller than a few hundred X (the 1/e distance

for Pt, determined from measurements on thin films, is in the range of 100 R) . Further, for particle

sizes much smaller than A/10 (about 1000 8 for a Nd laser), the effective absorption cross section

of the particles, which is proportional to the spectral emlssivity in eqs (1) and (2), should no longer be taken as a constant. Rather, from the data presented in Born and Wolf (6), the effective e;^ should be taken as a linear function of which reaches the assumed constant value at about R^= X/10.

This decrease in the effective eX with decreasing particle size is associated with a decrease in the effective absorption thickness of the particle. Since the particle temperature is proportional toe^

[ see eq (1)], this size dependence of the effective e^^^ has the effect of decreasing the particle

temperature in the very small particle limit below the values estimated with a constant value of , and introduces an additional size dependence into the temperature expression for this size range. Consequently, the calculated temperatures shown in Figs. 1-3 for particle sizes smaller than 1000 8 should be reduced by a factor of R^(8)/1000.

It should further be noted that radiation heat losses from the particles have been neglected in these calculations. This assumption may be justified by noting that Pt particles would be in thermal

equilibrium with a laser beam of flux level 0.7 j cm ns ' only at temperatures about 75,000 K, or with a beam of flux level 7 j cm ns~ ' only at temperatures about 130,000 K. Since these temperatures are well above the range where damage is expected, and since radiation losses from the particles

vary as T** , such losses can well be neglected in cases of practical interest.

Temperature profiles into the glass adjacent to Pt particles of various sizes are shown in Figs.

A, 5 for various conditions of pulse time and flux level [calculated from eq (2)]. As shown there,

a volume of hot glass surrounding the inclusion particles is expected in all cases. The extent of this hot layer is generally of the order of (D t)^ , and is most significant in the case of small

particle sizes. ^

In the range of large particle sizes, where D.t< R^, the assumption of a perfectly-conducting

inclusion particle becomes inappropriate, and the alternative model of the infinite composite solid may usefully be employed. The transition form small-particle behavior described by eq (1) to largeparticle behavior, described by eq (3), should shift to larger particle sizes for pulses of longer

duration. The size range of this transition is about 1000 8 for a 0.3 ns pulse, and about 10 ]l for a 3 ps pulse.

For particle sizes. in the range where eq (3) is appropriate, the temperature at the particleglass boundary is expected to increase as 3th , and hence should be higher for high flux, short time

pulses than for small flux, long time pulses of a given energy density. The temperature decreases

57
less rapidly with distance into the particle than with distance into the glass (a difference associated

with differences in the thermal conductivity of the two materials). Examples of the surface temperatures

(at the inclusion-glass boundaries) expected for various pulse times and energy densities are shown in Fig. 6. .. ;j

3. Stresses

The view has been adopted (4) that failure of the glass will result when the tensile stress pro- duced by the heating of inclusion particles relative to the surrounding glass exceeds the intrinsic

strength of the glass. For typical glasses, this would correspond to a tensile stress of 500,000 psi or more. To introduce an element of safety into our calculations, however, we shall consider stresses exceeding 200,000 psi as dangerous and smaller stresses as safe.-'-

In estimating the maximum tensile stress in the glass, it is important under many conditions - par- ticularly when <D t - to consider explicitly the layers of molten glass adjacent to the inclusion

particles. The extent of such layers can be estimated from the temperature distributions calculated

from eq (2), using the notion that solid-like behavior may be expected when the time scale for molecular

rearrangement becomes longer than the experimental time scale. Using the Maxwell relaxation time as a measure of the rearrangement time, and taking the pulse time as a measure of the experimental scale,

the transition from liquid-like to solid-like behavior may be expected when:

;

(5a)

(5b)

where M is the appropriate modulus and n is the corresponding viscosity. Taking M as about 3 x 10" dynes cm~^, the viscosity at the liquid-solid glass boundary is estimated as about 10^ poise for a 0.3

ns pulse, 10^ poise for a 30 ns pulse and 10*' poise for a 3 U s pulse. For typical laser-base

glasses, these viscosities correspond to temperatures in the range from about 1400 to 600°C; and in the following discussion a value of 1000° C will be assumed as the temperature of the liquid-solid glass

boundary

.

In previous calculations (4), an approximate analysis was adopted in estimating the maximum tensile stresses expected for various particle sizes and conditions of laser operation. The average temperature

of the particle + liquid glass volume was evaluated by neglecting the heat external to the solid-liquid

glass boundary; and a solution was used for the problem of a sphere of size R + AR in a hole of size R

in an infinite elastic solid. This solution neglects the effect of the temperature rise in the external

glass diminishing the tensile stress component in the glass. This last could be justified, at least

approximately, by noting that the temperature in the external glass is much less than the average temperature of the particle + liquid glass volume. Finally, the heat capacities and thermal expansion coefficients of inclusion and glass were taken as equal; and a bulk modulus of the particle + liquid glass

volume intermediate between that of Pt and glass was assumed.

In the present paper, we shall adopt a less approximate treatment of the stress problem by integrating the calculated temperature distribution, given by eqs (1) and (2), out to the desired radius to obtain the average temperature of material inside that radius. This will be combined with a solution

to the thermal stress problem (7) for a material with a radial temperature distribution of arbitrary form

which includes the effect of the temperature in the glass external to the solid-liquid glass boundary.

This last effect may be visualized by recalling that a spherical hole in an infinite elastic solid will

not change in size as the body is heated, but rather a compressive tangential stress will be established

in the glass around the hole. In the present case, such a compressive stress compensates for at least

a portion of the tensile tangential stress which is produced by placing an oversized particle in the hole . . ;

Using the standard solution (7) to the thermal stress problem, the (tangential) tensile stress at a distance, r, from the center of a radial temperature distribution may be expressed:

In our previous paper (4), we considered only stresses exceeding 600,000 psi as dangerous. The

present estimate has been adopted to provide a margin of safety In the calculations and to compensate for expected increases in the spectral emissivity with temperature, which under the extreme conditions encountered in high power laser operation could significantly increase the temperatureand hence the stress - from values calculated using low temperature value for c^.

58

f
The first term corresponds to the expression obtained previously, and the second term corrects for the temperature external to r.

Evaluating this expression for various combinations of particle size and conditions of laser operation, the results shown in Figs. 7-9 are obtained. The first shows stress profiles at various distances

out from the solid-liquid glass boundary for a 5000 8 Pt particle subject to laser pulses of various

durations. As seen in the figure, the maximum tensile stress in general occurs not at the solid-liquid

glass boundary but at some distance into the glass. This results from the opposition of the two terms

in eq (6). Further, the stress immediately adjacent to the boundary can under some conditions be com- pressive in character (represented by the negative sign in Fig. 7). -2 -1 The variation of the maximum tensile stress with particle size for a 0.7 J cm ns , 30 ns pulse

is shown in Fig. 8. As seen there, the maximum tensile stress should be sufficient to result in failure

for a range of particle sizes from about 900 R to 0.9 y . The maximum stresses for various combinations

of flux level and pulse time having a given energy density are shown in Fig. 9. As shown there, the stress behavior is similar in form to the thermal behavior shown in Fig. 2 above; like the temperature,

for a small particle size the stress produced by a short time, high flux pulse of a given energy density

can be higher than that produced by a longer time, smaller flux pulse of a higher energy density.

Since each of the terms in eq (6) is proportional to the flux level, the maximum tensile stress for

a given particle size should be linear in the flux; and hence the minimum size that is dangerous should

decrease with increasing flux level, ^or example, for a 30 ns pulse time, increasing the flux level

from 0.7 to 2.1 j cm" ^ns~' decreases the minimum dangerous size from about900 X to less than 500 8.

For a given pulse time and flux level, particles smaller than this minimum size are safe because

of heat flow to the surrounding glass, while the very large particles are safe under the assumption of

perfectly-conducting particles because of their large thermal mass. For such large particles, (R^^

D.t), however, the effect of temperature gradients in the particles can be quite important; and as we

have seen, the surface temepratures of such particles can be well into the 10** K range under conditions where the average temperatures is appreciably lower. The precise magnitudes of the stress in this

case difficult to evaluate because of the shape of the isothermal contours in the particles and a general uncertainty as to the appropriate equation of state for the particle material. From observations of extensive damage when large Pt particles are intentionally introduced into the glass (3) and from esti- mates of the expected interval pressure of the particles (A), it seems apparent that such particles must

be regarded as dangerous under conditions of high power operation.

4. Change of Phase: Pressure in Particles

In the preceding calculations, as in the original work, t^e have neglected the effect of phase

changes in the particle material. In the case of fusion, this assumption would not significantly affect

the results since the heat absorbed on melting even under standard conditions corresponds to a temperature change of only about 800 K, and hence from the thermal expansion coefficient a volume change of only about 2.2%, while the volume change in fusion is about 3%.

In the case of vaporization, the considerations are more complex. First, it must be recalled that

the particles are confined by the glass, and very large superheatings above the standard boiling point

would be required to form the vapor phase (4). Further, boiling of the confined particle material can only take place to a very dense gas with a density comparable to that of the liquid; and small or negligible differences in bulk properties are therefore expected between liquid and vapor. For these reasons,

it seems sensible to neglect any absorption of heat by vaporization; and the calculations of particle

temperature and stress in the preceding sections should provide reasonable estimates of these quantities.

These suggestions are reinforced by recent work (8) which indicates that as the confined inclusion

particles are heated, they are highly unlikely to pass into a two-phase (liquid + vapor) region where

vaporization can take place. Further, the new work indicates that even if vaporization of the super- heated liquid did take place, it would only raise the pressure from the values estimated previously.

An alternate approach to estimating the tensile stresses in the glass adjacent to inclusion particles involves an estimation of the internal pressure of the particles (or of the surface regions of particles). Arguments have been advanced (4) which indicate that particle pressures within a factor or

two of the ideal gas pressures for the given temperature may be anticipated; and the magnitudes of these pressures are similar to the inclusion pressures calculated from the thermal expansion. These results were used to justify caution about the safety of large particles whose average temperatures are much

lower than their surface temperatures. From the present discussion, the high surface temperatures would

result in locally high pressures, and could well result in failure. The establishment of a precise

breakdown condition for this case involves, however, the solution of complex heat flow and stress pro- blems which lie beyond the intent of the present work. For purposes of the present work, therefore, all particles with sizes larger than the minimum dangerous size will be regarded as likely to cause failure.

59
5, Type of Inclusions

The calculations of the preceding sections were addressed to the case of Pt particles in a typical

laser glass. Similar reasoning and comparison of the thermal, optical and mechanical properties of

various likely metals suggest that similar behavior may be expected for other metallic inclusions. Differences in detail - resulting from differences in the heat capacity, thermal expansion coefficient

and spectral emissivity - may be anticipated; but the general conclusion seems clear, vis., that metallic

particles, even small metallic particles, must be regarded as dangerous in high-power laser operation.

For this reason, it seems clear that laser glasses should be prepared as free as possible from elements which are likely to form metallic inclusions. This is a decidely non-trivial task, however, since

concentrations of inclusion material in the p.p.b. range can lead to extensive damage, and since the inclusions may have their origin in the batch raw materials, including certain fining agents, or in the crucibles used to melt the glass.

Considering non-metallic inclusions, it should be noted that only those inclusions which absorb

strongly at the wavelength of the laser beam are important. At the wavelength of a Nd laser (1.06)j ), the absorption of a good glass host is in the range of a few tenths of a percent per cm.; and absorption

at any such level can be neglected in treating inclusion damge. Among ions of potential significance

for the present problem, only Fe , Ni^"^, Cu2+ and Co^'*' absorb appreciably at 1.06p . Among these,

the strongest absorber is Fe2+; and the most highly absorbing ceramic inclusion would then be one of FeO,

while a more typical iron-rich inclusion might have an Fe concentration like that of Fe2SiO^, For these

cases, the absorption coefficients would be about 0.20y ' and O.OBy * respectively. With these values,

the energy absorbed by a spherical particle may be obtained from the relation:

(7)

This expression leads to a mean particle temperature, neglecting heat flow into the glass, which

increases with decreasing particle size and reaches a limiting value in the case of very small particle

sizes. This limiting value is the same as the surface temperature of a ceramic inclusion when heat

losses to the glass are neglected:

T - -pr~ (8)

For a 20 j cm"^ pulse, this expression indicates a temperature of about 10,000'-'K for FeO and about

4000°K for Fe SiO, . Since the thermal expansivities of these and similar oxides are in the same range

as that of Pt , while their moduli are generally smaller (corresponding to a smaller stress in the glass), and since the temperatures estimated above for the most dangerous composition are no higher

than these which correspond to the dividing line between safe and dangerous behavior, and since heat

flow into the glass has been neglected and its introduction would decrease the estimated inclusion

temperature |nd the resulting stress, it is concluded that ceramic inclusions would not be dangerous at the 20 j cm level. ,

At higher power levels - as in the range of 50 j cm and above - some such ceramic Inclusions may

result in failure. The likelihood of this damage can, of course, be reduced by reducing the concentrations of the highly-absorbing transition metal irons (Fe^+, Cu^ + and Ni*+) in the melt, and by carryout the melting so as to promote complete dissolution. Beyond this, it is clear that ceramic inclusions,

even those containing large concentrations of highly absorbing ions, are far less dangerous than metallic

inclusions; and the large part of technical concern in this area should be directed to the latter.

6. Particle Shape -'

The discussion of the preceding sections has been concerned with spherical particles. In proceeding to evaluate the effect of particle shape on the conclusions, we shall consider cylinders of a given

volume having various length-to-diameter ratios. This ratio will be denoted as a, with large a values

corresponding to needles and small a values to plates. The orientation of the cylinder axis to the beam

direction will be denoted as Q ; and the projected area of the cylinder normal to the beam will be designated A g. Neglecting heat loss to the glass, the temperature of a perfectly conducting particle

characterized by an angle 9 may be written:

where V is the volume of the particle. "*

Evaluating Aq from the geometry of a cylinder, the temperature of a cylinder of orientation

relative to the temperature of an insulated sphere of the same volume, may be written:

(9)

60
This Is shovm In Fig. 10 for various length-to-dlameber ratios. As shown there, for such ratios of less than 10 to 1 (or 1 to 10), the maximum temperature of the cylinder is w;J,thin a factor of two of that of

the corresponding sphere. Only for much larger shape asymmetries does /Tg reach large values; but for such cases, the estimates of inclusion temperature based on an assumed spherical shape could be significantly in error.

Departures from spherical shape may then be important under some conditions; but in most cases the assumption of spherical particles should provide a reasonable estimate of the stress and hence of the likelihood of damage. Even in cases where large shape asymmetries are involved, the preceding analysis

should prove useful since the stress resulting from a given change in volume, and hence from a given rise

In temperature should be greatest for a sphere. Unfortunately, no data seem to be available on the distribution of particle sizes and shapes to be found in laser glasses, and nothing is kno^m about the distribution of orientations of non-spherical particles (which is expected to vary with the processing techniques used to fabricate the glass).

7. Discussion and Conclusions

The analysis and discussion of the previous sections have identified the likely sources of inclusion

damage in laser glasses, and have established conditions on particle size and material parameters which

will lead to failure of the glass. In obtaining these results, the heat flow problem has been represented

by two models: (a) the model of perfectly-conducting metal particles in good thermal contact with a medium having the thermal conductivity of a laser glass. This model should be appropriate for particles

small with respect to the thermal diffusion distance in them (R^^<D^t); and (b) the infinite composite

solid, which should provide a useful estimate of the range of temperatures expected for particles large

with respect to the thermal diffusion distance in them (R^^>D^t).

The results of the thermal analysis indicate that the temperatures of metal particles subject to high energy laser pulses can exceed 10** K for a range of particle sizes. Very small particles have lower

temperatures because of heat losses to the surrounding glass, while large particles have low average temperatures because of their thermal masses. In the latter case, the surface regions of the particles

are expected to be well in the 10 "* degree range, even when the average particle temperatures are much

lower.

In the limit of very small sizes (R.< X/10), the dependence of the effective absorption cross-section of the particles must be included, and would have the effect of decreasing the particle temperature

and resulting stress. For a Nd laser, these effects should be significant below about 1000 R in size.

Phase changes in the particle material have been neglected in the thermal calculations. In the case of melting, the heat absorption on melting would be very nearly compensated by the accompanying volume

change, with little change expected in the estimated stress. In the case of vaporization, a number of

arguments have been advanced: (1) Because of its confinement by the glass, any vaporization of the particle material would take place to a vapor which differs little from the liquid in density; and such a va- por should have bulk thermodynamic properties similar to those of the liquid; (2) extensive superheating

of the particle material would be expected before the vapor forms; (3) the pressures of the vapor would,

by a corresponding states analysis, not differ greatly from those estimated from the thermal expansion,

and by recent analysis would be higher than those calculated neglecting vaporization; and (4) vaporization is highly unlikely to occur prior to failure since the heated and confined particle material should

not pass into the two-phase P-V region where vaporization is possible.

Combining the results of the thermal analysis with the solution to the stress problem for a material

with a radial temperature gradient, it is concluded that tensile stresses exceeding the expected strengths

of glasses can be produced by high energy laser pulses. In treating the stress problem, consideration

has been given to the occurrence of molten glass layers adjacent to the particles, and to the tangential

compressive stress arising from the surrounding glass being heated.

The maximum tensile stress produced by laser heating of inclusion particles is expected not to occur

at the particle-glass interface, nor at the solid-liquid glass boundary, but rather at some distance into

the glass. This distance is of the order of a few times the glass thermal diffusion distance, (D^t)'?, from the periphery of the inclusion particle.

The temperatures of small particles (R <D^t), as well as the resulting tensile stress in t|>e gla^s,

are expected to increase linearly with the flux level. For flux levels in the range of 1 j cm ns and pulse times of tens of ns or larger, particles as small as 1000 8 are expected to cause damage. Such particles would be exceedingly difficult to detect a^ priori , since their size is small and their presence in even small concentrations can result in unacceptable damage.

61
For a given small particle size, the particle temperature and the maximum tensile stress in the glass can be higher for a short time, high flux pulse having a given energy density than for a longer

time, smaller flux pulse having a larger energy density. This behavior indicates that damage testing

a laser glass by subjecting it to a pulse of long duration can provide misleading information as to the safety of the glass under conditions of shorter pulse times. Long-time pulses are expected to cause extensive damage of the larger particles, but may provide an inadequate check on the presence of smaller

particles which are dangerous with short-time, high flux pulses. For example, a 1500 8 Pt particle subject to a 20 j cm * , 30 ns pulse would result in damage to the glass, while the same particle subject

to a 300 ns pulse vrith an energy density five times higher (100 j cm ^ ) would be safe.

The analysis has indicated that the particles of grimary concern in causing inclusion damage are metallic. At energy densities in the range of 20 j cm ceramic inclusions are expected to be safeeven those containing large concentrations of high absorbing ions. At significantly higher energy

densities, some of the latter particles may prove dangerous; but under all conditions such inclusions

should be appreciably less dangerous than corresponding metal particles.

For shape asymmetries of 10 - 1 or less, the assximption of spherical inclusion particle should

not introduce any significant error into the calculations. For larger shape asummetries, the geometrical shapes of the inclusion particles may well be significant in affecting the breakdown condition.

The other principal assumptions used in the analysis have been discussed previously (4), and indicate that the results should be good to better than order-of-magnitude accuracy; and the specification

of the break-down condition should be useful as a guide to the range of particle sizes and the conditions of laser operation which must be regarded as dangerous. The difficulty of detecting a^ priori

particles near the lower size limit for damage under high power operation leaves two apparent alternatives: (1) test individual samples of laser glass by subjecting them to pulses of somewhat higher beam

intensity than the desired operating levels; or (2) adopt more stringent procedures to avoid the possible presence of metallic inclusions. For obvious reasons, the second alternative should be preferred.

8. Acknowledgements

The authors are happy to acknowledge stimulating discussion with Dr. E. Snitzer of the American

Optical Company and Professor D. Tumbull of Harvard University. Financial support for the work was provided by the Advanced Research Projects Agency under Contract ARPA-SD-90, and by the American Optical Company, who provided one of the authors (R.W.H.) with the American Optical Fellowship in Materials

Science. This support is gratefully acknowledged.

9. References

[1] Snitzer, Glass Ind. 48, 11(1967),

[2] L.I. Van Tome, Phys. Stat, Sol, 16^, 171, (1966) .

[3] C,G. Young and R.F. Woodcock, in "Damage

in Laser Glass", ASTM STP A69 (ASTM,

Philadelphia, 1969) .

[5] H.S. Bennett, National Bureau of Standards,

to be published,

[6] M. Bom and E. Wolf: "Principles of Optics"

(Pergaraon Press, New York, 1959) •

[7] B.A. Baley and J.H. Weiner: "Theory of Thermal Stresses" (Wiley, New York, 1960).

[4] R.W. Hopper and D.R. Uhlmann, "On the Mechanism of Inclusion Damage in Laser

Glass", J. Appl, Phys., September, 1970.

[8] R.W. Hopper and D.R. Uhlmann: "On the Vaporization of Inclusions During Laser

Operation": to be published.

62
I.i =

g =

II. k = D =

P

=

C =V

R = J =

t =

a = V =

Q

=

B = G = a = V

Y

=

C =

Subscripts

inclusion

glass

Symbols

thermal conductivity

thermal diffusivity (= /C p) m

density

heat capacity per unit volume

radius of inclusion

flux level

time

spectral emissivity i melting point of inclusion

boiling point of inclusion

linear thermal expansion coefficient

Volume

heat

bulk modulus

shear modulus

stress

latent heat of melting

latent heat of evaporation

absorption coefficient

heat capacity per unit mass

Appendix

Symbols and Material Parameters Used in Text

III. Values of Parameters

k. = 0.16 cal cm ''"sec

''" °K ^

2 -1

D. = 21,5 cm sec -3

= 21.5 g cm

C .= 0.66 cal cm""^ "k""*- VI H

= T„ = 204 2°K M

T„ = 4100°K

5.9 X 10"^ °K-^

B. = 32 x 10 psi

G. = 8 X 10 psi

^ 3 -1

Lj^^= 5 X 10 cal mole

<f

1 ln~3 , -1 -1 0-1

3 X 10 cal cm sec K

-3 2 -1

3 X 10 cm sec

3 g cm

-3

C =0.9 cal cm

-3 o, -1 vg a = 9 X 10-6 o^-l

B = 6 X 10 psi

S

6 G = 4.3 X 10 psi

g^PARTICLE + LIQUID GLASS

0.031 cal g"-"- "k"-"- 3 -1 133 X 10 cal mole

15 X 10 psi

"mi 4i=

mg

0.3 cal -1 o^-l

Fig. 1 Calculated temperatures of perfectly conducting platinum particles in a glass with thermal

diffusivity, 3 x 10"^ cm^ sec"-*-, subject to 30 ns laser pulses. Various flux levels shown

in j cm" 2 ns"-'-

'

63
Fig. 3 Calculated temperatures of perfectly

conducting platinum particles in a glass with ^hermal diffusivity,

3 X 10"-^ cm sec"-'-, pulses of 21 j cm"'^, n-2 30 ns and 150 j 1000 ns. Fig. 2 Calculated temperatures of perfectly

conducting platinum particles in a glass with thermal diffusivity,

3 X 10"-^ cm sec"!, subject to laser

pulses with energy density 21 j cm"^. Various combinations of flux level and pulse time shown.

Fig. 4

DISTANCE (fil Temperature profiles into the glass

adjacent to platinum particles of

various sizes subject to 21 j cm"^,

3 ns pulse.

Fig. 5 Temperature profiles into the glass

adjacent to platinum particles of various sizes subject to a 21 j cm

300 ns pulse.

-2

PULSE TIME (NS) Fig. 6 Calculated surface temperatures of semi-infinite platinum particles in contact with semi- infinite glass slabs subject to laser pulses of various energy densities and pulse times.

64
.40 - 35

(/) a. "o 30 w B = SOLID-LIQUID GLASS BOUNDARY

DISTANCE FROM PARTICLE CENTER

Fig. 7 Stress profiles into the glass from the solid-liquid glass boundry surrounding a 5000 platinum particle subject to laser pulses of various duration.

Fig. 8

PARTICLE RADIUS (

)

Maximum tensile stress in the glass

vs. particle size for platinum

particles subject to a 21 j cm"^^

30 ns pulse.

PARTICLE RADIUS 1^1

Fig. 9 Maximum tensile stress in the glass

vs. particle size for platinum

narticles subject to 21 j cm" laser pulses of various duration. 1 = 3 ns

2 = 30 ns; 3 = 300 ns

.

65
10

(DEGREES)

Fig. 10 Ratio of the average temperature of a insulated cylinder to that of an insulated sphere of

same volume as a function of orientation various length-to-diameter ratios.

COMMENTS 0/V PAPERS BV HERBERT BEWWETT AhlV ROBERT HOPPER

HotoQiapkic invi^t^gattom, of, pcuuttculate. incJLLU>i.oiU can be ue/it/ {^nuAXf^ul, om can kuoIvq.

pa/ittctu 0(5 tht on.deA one vm <.n AiXhough thiM haj> yeX to be aciii^\jtd, abion.ptA.on o{, iadu.(xtLon ol th^e. ^nclu^ion, and conMique.nt heating o(, &uM.ounding niateAtaZ tntAoducu a theAmat

dvitontA.on pnobably obhOAvablz Mitk pfimunt hologtapiitc i^n^ittvity . fuAtheJimoKZ, -it ti not mcziioAy to obieAve tkii dtitofitton iU>tng puZie. tmgtk& ckaAacteAU>tLC Ojj d-ipoiZed opeAatLon,

5-cnce tt can be oi za^tly obieJived uaing rnWUAdcond duAaZion pwtiu. ThzKe. t6 ondoA ofi magnitude,

agtement between kolog^aplvLC obbeA'oatA.oni and theoretical, p^ed^ctioni of (^Ktnge 6lii{it^.

It wa6 atio i>aggei,ted that BAttlouiA.n icatteAtng data, taken -in conjunction Mtth the ptediction^

oi the landau-?laczek theon.y, may pn.ovide a uiefuZ technique {^on. detecting the presence o(, paAticulnte uicluiiom,

.

The theon.etA.caZ tAeatimnt ui,ed in both thete papenj, ti> invalid in the picosecond putie

nange, due to the ui,e ojj equllj.bfu.iM}] a6iuyr,ptA.oni . TuAtheMywne, MiiiZe the coiutAalnlng (,oncei: of the

iuyxnoundlng medium MeAe con^ldeAed [ai in Seitz and TuAnbulZ, i/ot. 3) no -tneAttat effects weAe

Included. The a^iuniptlon of it/ieAi equiLcbnlum acA06i the Interface a Invalid fon. tmeA Like a

nano{>econd.

A fuAtheA limitation -impoied In the calculation waj, the uie of geometnlcal cAoi,i>-i>ectlonA

nathen than the optical cAoii-iectlon6 pn.edA.cted by the Hie theony. The latteA effect It expected

to be neglA.g4.bte fon paAtictei, compcAabte to on. langen. than the Mavetength.

Vlffenent boundary conduJxoM Mere uied In the two previous papers. In Vr. Bennett's

cal.culatA.on, an adhesive boundary Mas assumed. In which the strain and the radial component of the

stress are continuous across the boundary, and no conAtralnt Is placed on the tangential stress.

In the model of Hopper and Uhlman, and assumption 1& made of a strain discontinuity at the bounduAy,

with conttnuous nontyial i,tress components

.

66
Role of Photo- Electrons in Optical Damage

R. W. Hellwarth

Department of Electrical Engineering

University of Southern California

Los Angeles, California 90007

and

Hughes Research Laboratories

Malibu, California 9026 5

Previous workers have discussed the possibility that electrons photoexcited into the conduction band of a polar crystal by a high-intensity, short

optical pulse may gain enough energy to damage the lattice by initiating an

ionizing avalanche. We discuss here other processes by which these

conduction electrons may damage the lattice even before they gain enough

energy to ionize their surroundings, specializing our calculations to the case

of sapphire and ruby. First, we show that the energy that the conduction

electrons absorb linearly from the optical beam is deposited almost

immediately in the lattice without significant heating of the electrons. At electron densities { ~ IQ-*^" cm~3) and optical intensities ( ~ 10^0 w/cm2)

likely to exist at sapphire damage thresholds, this deposited energy is found

to be of the order of what one might expect would be required to form a rupturing shock wave. We also show that the photo- excitation of both bound

and unbound impurity levels is enhanced by the presence of conduction

electrons, so markedly so for the former that the promotion of electrons

into the conduction band may be significantly "bootstrapped," thereby

increasing the optical absorption. The presence of conduction electrons and

excited impurities in the expected numbers is likely to alter the refractive

index significantly and affect thereby the focusing (self- or external) of the

beam in a complicated way. For the simplest model these nonlinear index

contributions would tend to produce repeated focal regions along the beam.

Implications of these results for raising damage thresholds are discussed.

Keywords: Crystals, electrons, optical damage, photo-absorption,

photo-conductivity, photo-electrons, polar crystals,

ruby, sapphire, self- focusing.

1. Introduction

The physical processes responsible for the bulk damage caused in various transparent crystals

by short optical pulses (causing negligible electrostriction) have not yet all been identified. Here we

argue that several processes not considered previously are likely to be important in the optical

damage of inclusion-free polar crystals, especially sapphire and ruby. For their initiation, these

processes would all seem to require on the order of 10l6 conduction electrons per cc to be present at the point of maximum optical intensity, a number widely suspected to be present in sapphire and ruby

at peak intensities ~ 10^0 w/cm^ just below damage threshold. We will argue here that such densities

of cold electrons can a) transfer damaging amounts of heat from the beam to the lattice; b) accelerate

the rates of photo- excitation of bound and free impurity electron states, thus significantly increasing

the supply of conduction electrons, possibly even in "avalanche"; and c) significantly change the local

refractive index, possibly in a way which, in conjunction with the normal nonlinear index, could cause

repeated beam focusing along its axis. In none of these processes do the electrons become hot enough

( ~ 8 eV) to ionize the lattice, in contradistinction to the process suggested by previous workers [l-4]2.

Work supported in part by the Joint Services Electronics Program (U. S. Army, Navy, and Air Force),

under Grant No. AF- AFOSR-69- 1 622A, and in part by the Advanced Research Projects Agency througl

Air Force Cambridge Research Laboratories.

'Figures in brackets indicate the literature references at the end of this paper.

67
Hence, we will refer to them as "cold" conduction electrons. How the damage processes discussed

here depend on crystal temperature, optical wavelength and pulse duration is a complex function of the

energies and wavefunctions of the states of the impurities supplying and trapping conduction electrons,

the electrons' effective mass(es), the longitudinal optical (LO) phonon structure, and the electronphonon coupling. Although only the latter two are fairly well known for ruby and sapphire, plausible

hypotheses about the former lead one to single out the processes we propose as potentially important

to damage. It would appear that reducing donor concentrations or increasing their electron binding

energies might produce more damage- r es istant crystals. However, if the conduction electron density were proportional to optical intensity (which appears not to be the case at such high intensities), it would tend to reduce self-focusing (or produce a net defocusing) and thereby lower damage thresholds.

Other conclusions and suggested experimental checks of electron processes are mentioned in the final Section. In the following Section 2 we summarize the parameters and physical regimes we encounter

in ruby and sapphire and we outline our rough criteria for when damage is expected. In Section 3 we

define the approach we take for evaluating the required parameters and discuss difficulties with

previous calculations of the conditions under which hot ionizing electrons might be produced. The

calculations of the enhancement by conduction electrons of lattice heating and photo- excitation follow

in Sections 4 and 5. Before proceeding, we first summarize our assessment of often-conflicting

reports on photoconductivity in ruby and sapphire.

Hochuli [5] has measured the low-frequency photoconductivity at various wavelengths and temperatures of ruby and sapphire at optical intensities I ~ 0. 2 to 5 W/cm^ and using applied voltages at frequencies zero Hz, 100 Hz, and 9. 39 GHz. He found no essential differences in results for the two

crystals. The observed conductivities (at 5 W/cm'^) were 4x10-13, 10-11, and 4. 2 X 10-8 (Om)-!,

respectively, at the above frequencies. Since all these frequencies are well below the electron collision frequency (which from the theory of Section 4 we estimate to be ~ 10^4 rps), the wide variations

in results indicate the magnitude of experimental pitfalls in any attempt to measure such low bulk

conductivities. Anomalies at the two lower frequencies probably arise from surface effects, from the

inability of electric contacts to inject charges into the crystal, and from space charge buildup. Therefore, the 9. 39 GHz value, obtained in a microwave cavity with a small electron drift excursion

amplitude (of the order of an Angstrom ), is probably the most reliable. This conductivity was linear in the optical intensity within the range of observations. Its wavelength dependence suggested that the electrons were supplied from donor levels between 0. 6 and 1. 2 eV below the conduction band, in agreement with what one would conclude by studying the normal bulk conductivity variation with

temperature at higher temperatures. The wavelength dependence also suggested more donor levels

appearing around 3 eV. Although Hochuli was able to observe a Hall voltage, it did not vary when the

light was turned on or off. The nominal Hall mobility value H- = 0. 052 cm^/V sec. derived therefrom

has nevertheless been used without question by other workers whenever a value was required in calculations. This value corresponds to a collision time t of 4 x lO"-^''' sec. , or an electron mean path

of the order lO-'l-O cm, and must be considered imphysical, corroborating the difficulty of making

electrodes on sapphire. Using the standard Frohlich theory of a conduction electron in a polar crystal

adapted to the large coupling constant of sapphire [6], one estimates t (at room temperature) to be

between lO"'-'^- ^ and lO--'-^-^ sec, depending on where the effective band mass lies between 1/10 and 10 electron masses. Assuming a free electron mass for which t = 7 x 10-15 gee (and [jl = 12 cm^/V sec), one would infer from Hochuli's microwave observations that he produced-^ 2 x 108 photo- electrons per

cc with 5 W/cm^ of broadband Hg lamp exciting intensity. We see from this that 10^6 electrons per cc would very likely be excited near damage thresholds of lOlO W/ cm'^ provided that 10l6 donor levels per

cc were occupied, a provision which is unknown.

Except possibly for the experiments of Belikova, et al . [7, 8], other reported observations of photoconductivity in ruby appear to be plagued by surface and contact effects. Belikova, et al . , observed the photoconductivity to be highly nonlinear with the (6943 A) optical intensity I for intensities near lOlO w/ cm^ [7]. One can use our value of t above with their data to estimate very crudely (since

their beam geometry was unspecified) that they were observing well over 10^^ electrons/cc at lOlO w/ cm^ (provided that the electron recombination time was short compared with the optical pulse

length). Belikova, et al . , also observed optical emission bands near 2, 2. 7, and 3 eV (they could not see below 2 eV) which are suggestive of some impurity level transitions. The foregoing is about all one can conclude about photo- electrons from existing data for ruby and sapphire.

2. Description of Electron Interactions ,

In studying the role of photo-excited electrons in crystal damage, we will constantly apply our formulae to the case of sapphire and ruby. The phonon structure of these two crystals are essentially

identical, as are the low-intensity photoconductivities. Although distinct differences in damage

behavior have been observed, the gross damage thresholds are statistically indistinguishable for sapphire and ruby. Therefore, most pertinent aspects of these two crystals can be studied together.

For brevity, we shall refer hereafter only to sapphire, but shall intend our remarks to apply also to ruby unless stated otherwise. We shall also assume throughout that the optical beam wavelength is 6943 A, that of the room temperature ruby laser.

68
A free electron gas of density 10^° cm-3 has a plasma frequency co ~ 6 x 1 0^ ^ rps that is much

lower than a) the optical beam frequency of interest v (2. 71 x 10^5 rps), b) the phonon frequencies

(~ 10^4 rps), and c) typical electronic excitation frequencies ( ~ lO^^ rps).

We shall call a conduction electron "cold" when its energy is much less than interband energies

and its wavelength is much longer than the scale of potential variations of the field lattice. Other

electrons we will refer to as "hot. " The time for cold electrons in the 1/40 to 3 volt range to equilibriate among each other by collisions at a density lO^^ cm-3 is of the order of lO'lO to 10-13 gg^ [9]^

much longer than the inverse electron-lattice collision time ( ~ lO"-'-'^ sec in ruby). Therefore, at least before any large ionizing avalanche occurs, the cold conduction electrons may be studied as independent particles, not interacting among themselves but interacting only with tiie fields and other

particles in the crystal.

When a cold electron moves in a polar crystal such as ruby or sapphire, it is often called a "polaron. " Its interactions with the crystal phonons are known to be well-described at room temperature and above by the Hamiltonian derived by Frohlich [10] and used by all previous workers in calculating electron motions leading to damage:

H, + V, (1)

where

\ = - A(t)] + (2a)

and

C, a, e k k

ik-

+ h. (2b)

Here p is the electron's momentum, and x the electron's position coordinates, aj^ is the annihilation

operation for a LO phonon of frequency Optical wavelengths are long enouglT'so that the vector

potential A(t) may be taken as a function tJf time only oscillating at a frequency v- We use dimensionless "polaron" units in which the effective band mass of the electron m-^ is unity as is Planck's constant

h- All energies are measured in units of an effective LO phonon energy h'^Q (840 cm"l or 1200° K for sapphire and ruby). Frequencies are measured in units of (= 1. 6 x lO^^ rps) so that i> - 17 for a 6943 1. beam in sapphire. Lengths are measured in units of (^/m^ '^o^^ which is 8. 5 x 10-8 cm for ruby

if we take m"b to be the free electron mass m^. Frohlich showed that in these units the coupling

coefficients are well approximated by ' '^n^ ' k"! where V is the crystal volume, a is the dimensionless polaron coupling constant (e"-*- - Sq^) (Ryd' /ft<^Q)'a • Here Ryd' is the Rydberg for an electron with mass mQ, and e and Sq are the optical and static dielectric constants (3. 1 and 10). For

m-|3 = mQ, Q ~ 3 for ruby. In ruby an electron is hot if k is of order 10 or more (in polaron units). Hot

conduction electrons have neither the simple forms of kinetic energy or lattice interaction energies

found in eq (1) but obey complex equations in which exchange must be accounted for and which have never satisfactorily been approximated in usable form for a dynamic lattice. There would seem to be

no way at present to make a reliable estimate of how strong an optical field would be required to produce enough interband electronic transitions (i. e. , lattice ionization) to cause damage.

From the discussion of the previous section, it is evident that the electrons photo- excited (below

damage thresholds) in ruby and sapphire crystals come from donor impurities to which they are bound

initially with much less energy than the valence-conduction band gap energy ( ~ 8 eV). The effects of these impurities on the supply and motions of conduction electrons, as well as on the excitation of the donors by conduction electrons, can be studied by considering the Coulomb interactions Vj. between a conduction electron at x and the i'-'^ particle of the a^h impurity having charge eq? and located at v^^.

2

e e

1, Q

(3)

where the electronic charge e is 4 in our polaron units, and is screened by the dielectric constant eg appropriate to the frequencies of motions under consideration.

To deal with the elastic scattering of the electrons, one needs only the matrix element of eq (3) diagonal in the impurity's ground state. This gives an effective classical scattering potential seen by

the conduction electron. To study inelastic scattering, we will assume that the impurities may be

described by an unperturbed Hamiltonian h^ = Y.^ with "ionized" or unbound as well as bound

electronic eigenstates. Calculations will therefore start from a total Hamiltonian H comprised of

69
Frohlich's Hamiltonian eq (1) (which describes cold electrons, phonons, and their interactions) plus

the electron impurity interactions of eq (3) and with h^- determining impurity states:

H = + h^ + + . . . (4) i

J -

I We will assume that damage to the crystal occurs when the interactions vp and vt combined

cause the conduction electrons to absorb an energy U per cubic centimeter with a short optical pulse \ that exceeds a threshold value U^. That is, we shall strive to determine at what optical beam intensity! we may expect |

U s U . (5) o ^ '

2 3 3 Present evidence indicates that is of order 10 to 10 J/cm for ruby and sapphire for 20 nsc

pulses in a beam of order one mm diameter. A shock wave of this energy surrounding the beam would

develop stresses on the order of the static yield stress [3]. Obviously a large part of understanding

optical damage in crystals entails developing an accurate theory of the amount of energy deposition

required to produce rupturing strains as a function of the amount and spatial and temporal distribution

of this deposition. However, we shall content ourselves here with the above crude estimate for Uq.

3. Approaches to the Calculation of Damage Thresholds

Previous treatments of the role of electrons in damage [1,4] started from Frohlich's Hamiltonian

eq (1) and sought to calculate the optical intensity at which electrons would gain enough energy u to excite an avalanche of interband transitions. The expected energy u of an electron in the optical field was estimated from the equation

It = - R . (6) dt fe e^

where Rfg is the average rate at which the optical field does work on the electron and Rg^ is the average rate at which the excited electron "radiates" phonons, i. e. , transfers its energy to the

lattice. Previous treatments have all taken for Rfg the usual linear conductivity loss per electron with

reasonable order of magnitude estimates from eq (1) for the optical conductivity (or "electron

collision rate"). However, they have made approximations for, or statements about, Rg^ that are not directly based on a quantum average of the appropriate operator. Wasserman [1] took for Rg^ the rate

at which an electron having a Maxwellian distribution would lose energy to a cooler lattice in the absence of the optical field (A = 0). He predicted breakdown intensities orders of magnitude above

those actually observed. Sverev, et al . [4], used for Rg^ the approximate rate at which an electron

would lose energy to the lattice starting from a momentum eigenstate |p) for which ^p^ = u also in the absence of the optical field. His predicted thresholds also exceeded observed thresholds by over two

orders of magnitude. We feel it is quite probable that a precise evaluation of the spectral energy

distribution of an electron obeying eq (1) would show that the electrons do in fact remain too cool to ionize impurities or the lattice at optical fields below damage thresholds. In the next section we show

that, indeed, collisions with phonons dominate an electron's motion. We have checked that it follows

rigorously from eq (1) that, to lowest order in the optical intensity and coupling parameter a, an

electron's expected kinetic energy is simply the sum of its coherently oscillating energy plus 3kT/2

where T is the ambient lattice temperature. The coherent energy is very much smaller than kT for

optical intensities of interest. Therefore, we now proceed to examine whether cold electrons may not mediate the deposition of damaging amounts of energy in a sapphire lattice. As we mentioned in the previous section, our approach will be to calculate the beam intensity at which the energy U deposited per unit volume in the lattice from the optical field via the electrons

exceeds a threshold value U^. If the maximum optical beam energy per unit area is S, then

U = H S (7) , " , •

' - -

! where is the absorption per unit length of an optical beam of frequency u • Following FHIP [6], we

write the quantum expectation value of the amplitude of an electron's coordinate at frequency v as Re Ee^^ V(-u ^+Xy ) when the electron is in an optical electric field Re Ee^V^. With this definition we

have ;

70

i
h = I e) Im[u^

V P

(8)

where X is the wavelength of the light in the crystal -r Ztt and t^J is the electron plasma frequency (in

units of w^). In cgs units c*jp = 4itP e^ /m-j^ with p being the numblr density of electrons.

The evaluation of K. falls naturally into two parts: first, the determination of the rate at which a single conduction electron takes energy from the field (and delivers it to the lattice) by a calculation of Xy, and second, the estimation of the number density p of these electrons. We consider these two

questions, respectively, in the following two sections.

4. Optical Response of Single Electron

We examine first an electron's optical response in the case that it is affected only by electronphonon interactions as described by Frohlich's Hamiltonian eq (1) with coupling parameters appropriate

to sapphire. We then find that, at least at room temperatures and above, collisions with impurities are relatively less important. When the electron response is linear in the applied field for a given

lattice temperature, we may use the determination of Xy by FHIP who calculated the quantum expected

value of the electron position to first order in the optical field. Their expression is exact for all temperatures at small coupling (a < 1) and gives an accurate solution even when a ~ 3 as for ruby. In

this case it shows that, for u = 1 7, both the real and imaginary parts of x^ are much less than go

that we need only calculate Imx^ to estimate the absorption constant. (The Re Xy can of course be

determined from Im Xy by Kramers - Kronig relations. )

, _ Zg-TT^P"'^^ sinh([3u/2) v_ f'^ cos(i;u) cosu du

"

3 sinh(p/2) K^J \ TJ^TJ- .„./„.,m3/2

' o

[ u + a - b cos(vu)]

Here v and w are parameters to be chosen from a variational principle, a^ = p^/4 + Rp coth(pv/2);

R= (v2 - w2) / (w2 v); and b s Rp sinh(pv/2).

In the weak coupling limit v = w = 3, R=b = 0 and a = p/2. Then the integral can be evaluated

exactly in terms of modified Bessel functions. At temperatures much lower than the Debye temperature

(P large) this result reduces to

1 Imx - 2q(u - 1)2/3 : Q < 1, p >> 1, u > 1. (10)

For a = 3 and y = 1 7, this is 8. The leading correction to eq (10) for finite temperatures multiplies it by (1 + P"^), increasing it by 30% at room temperature (p = 3. 3). When Q = 3, the variational principle gives v = 3. 4 and w = 2. 55 in the zero temperature limit [6]. Using these parameters with p = 3. 3 gives R = 0. 229, a = 1. 866 and b = 5. 53 x 10-3. We have evaluated eq (9) numerically for these parameters and have obtained Im Xu = 15. We have also evaluated eq

(9) at frequencies in the neighborhood of u =17 and found that, as in eq (8), Im Xu varies slowly with v. Therefore, electron transients associated with the rise and fall of even picosecond optical pulses are very small, and it is a good approximation in practice to assume that at any instant the electron's

motion is the same as for a purely sinusoidal field of amplitude appropriate to the intensity at that

instant. The fast response of the electron's motion, as evidenced by the nonresonant character of Xu . together with the knowledge that, at intensities of interest, the electron is gaining negligible energy

(staying "cold"), implies that the absorbed energy is being passed on essentially instantaneously to the

phonons via the coupling eq (2b). Therefore, it is valid to obtain the rate of deposition of energy in the

lattice by determining the rate at which the electrons absorb energy from the optical beam, and we

return to this problem.

When a room temperature correction is made to v and w, we guess that, as for small a, the result is raised by around 30% so that the Frohlich model may be taken to yield

Imx ~ 20 (11)

y

for a ruby laser beam driving an electron of band mass equal to a free electron mass in ruby or sapphire at room temperature. The main unc er taint v in eq (11) comes from the uncertainty in the

effective band mass m-j^. Im Xy varies roughly as m^' .

71
If the temperature goes higher thaJi the phonon energy but is still small compared with , then eq

(9) yields

Im 4q u^^^/(3p) ; Q<<l,l<<p'^<<u, (12)

showing that the heated lattice causes the electrons to absorb even more light. Note that the "Q" of the electron's oscillation, I {Z ImXy)> is of order 7 for our estimate eq (11), showing that indeed the

optical frequency is much larger than the effective electron collision frequency as we assumed.

One can see at this point that absorption by conduction electrons may cause damage, for, if the electron density were IO^d cm"-^ at an optical intensity of lOlO W/cm^ (which thg evidence outlined in Section 1 suggests as a conservative estimate), and if eq (11) were valid, then "^p ~ lO"^ and eq (8) gives n ~ 0. 012 cm"-'-. For a 30 nsc pulse this absorption would deposit 40J per cc in the lattice,

somewhat less than the value expected to cause damage. However, Belikova, et al . [7], gave

convincing evidence that the electron density is increasing very rapidly with optical intensity at these

levels, an occurrence which we expect for reasons given in the following section. Before considering

factors which affect the electron density, however, we consider contributions other than those of the linear response eq (9) to electron damping.

First, the question arises as to whether there are significant intensity-dependent corrections to the electron response at the optical frequency as represented by eq (9)- (Responses at harmonic

frequency multiples do not contribute to the average work done by the optical field on the electrons and

so we need not consider these here. ) There are two types of nonlinear corrections to eq (9): first,

those arising from the nonlinear reactions of the phonons on the electron, and, second, those arising

from the intensity-dependent deviations of the momentum distribution of electrons from a thermal

distribution. We have estimated both effects by expanding the quantum expression for the expected

electron position (and velocity) to the third order in the electric lield. We have found that both effects tend to diminish the optical absorption from its linear response value, a result expected on the physical

groixnds that electrons of high energy interact less with the optical phonons than do low-energy

electrons. For both corrections the natural dimensionless expansion parameter is (k^ ^o)^ where k^

is the wavevector of an electron having energy hv and r^ is the classical amplitude of a free electron

oscillating in the applied optical field. In our case this parameter is ~ I(W/cm ) x 10"^^. Since

optical intensities have not yet been observed to approach even IQII W/cm^ before damage, we conclude that the nonlinear corrections to eq (9) are too small to be of importance in present considerations

Next, we see why, under conditions of interest here, phonon scattering of conduction electrons

dominates scattering by ionized and un-ionized lattice impurities. For each conduction electron there

is in the lattice a heavy positive ion whose charge is shielded roughly by the static dielectric constant of the lattice (e^ ~ 10). The linear absorption by 10^^ electrons per cc in such a two- component plasma

at room temperature is ~ 10"^ per cm [11]. This is so small compared with phonon effects that one

can readily appreciate that even if lO-'-'^ per cm-^ of electrically neutral scattering centers were added

to the lattice, one would not expect them to scatter electrons as effectively as do phonons at room

temperature and above. This predominance of phonon scattering at or above room temperature has

been observed in various ways even in crystals whose electr on-phonon coupling is much smaller than in ruby and sapphire [12] . Having estimated the optical response of a single conduction electron, we now

proceed to consider how their numbers are affected by their interactions with lattice impurities.

5. Conduction Electron Interactions with Impurities

From incomplete existing absorption [13] and luminescence [8] data, it is evident that sapphire

has a complex impurity level structure with energy differences ranging up to at least 3 eV. Light of any single optical wavelength, such as 6943 A, will not be resonant with a significant fraction of the bound-bound transitions and, of course, will only excite transitions to the conduction band from bound

levels within 1. 8 eV of the band edge. K, however, the light became effective in exciting a large fraction of the bound-bound transitions, then cascade transitions of electrons into the conduction band from

levels lying more than 1. 8 eV below the band edge might dominate direct photo- excitation. We shall now show that, at conduction electron densities ~ lOlo cm"-^, the light does become so effective in exciting bound-bound transitions with which it is not resonant that cascade photo- excitation may become

important in increasing the conduction electron density near optical damage intensities. These non- resonant transitions are possible because the conduction electrons readily absorb the difference in energy u - between an absorbed photon and the energy of transition between the upper and lower

states I b) and | a). We now show that the rate RgV, for a typical impurity to make such a transition,

multiplied by a reasonable impurity density ( ~ 1 0T9 cm" 3), may exceed the total direct photoexcitation rate, and thereby initiate cascade ionization of impurities.

To calculate the rates R^b it is convenient to re- express the interaction of eq (3) as a Fourier

transform (the impurity index a is now omitted since we are considering only one impurity):

72
where vj^ is the impurity operator 4iTe V Gg k Sj expik • rj and V is a fiducial interaction volume.

The sum is confined to the bound impurity electrons as only electronic transitions will be considered.

For the transitions of interest we may take eg to be the optical dielectric constant c. With the form eq

(13) it is a straightforward matter to re-derive the quantum "Golden Rule" for calculating transition rates but with an unperturbed Hamiltonian h^ = •|(^ - Aq cosut)^ instead of -g-p . To lowest order in the electron-impurity interaction, the rate for an electron to scatter from momentum state | p) to | p + k)

while the impurity goes from | a) to ]b) is ~ ~

oo r(p - p + k; a - b) = 2tt |(b|v^|a>l^ ^

5(k^/2 + ^ • k + co^^ + ni, )

• C (k • r^)] ^ (14) n=-oo

where we have retained the terms for n-photon emission and absorption for future comparison with the n = 1 term that we are now considering. In the polaron units used here the classical electron oscillation amplitude rQ equals E/u^, where the real ar^plitude E of the optical electric field equals the amplitude in esu divided by E^ = (oj^/e) {hTn^/<^Q)2. For our parameters E equals (the field in V/cm)

(1. 24 X 10^). The Bessel function coefficients J^^ in eq (14) are the exact amplitudes for absorbing (or

emitting) n optical photons in the process. Their arguments are of order 10"^^ I(W/cm2) and so the approximation J (x) ~ (x/2)^/nI is accurate here. Consider now the rate for the impurity interacting with one electron in the optical field to make a transition from a state | a) to a state jb), for which <jo^^ < u. In terms of the rate eq (14)

""ab

" I ^^S) r(£ - p + k; a - b) (15)

p, k

where f(p) is the initial conduction electron distribution and only the n = 1 term in F is needed. To

evaluate r^^i^ it remains to estimate the dependence of the matrix elements of vj^ We shall use the "dipole approximation" in which (b| expik •

| a) ^ ik.- (b| rj|a^. For definiteness we will assume that the impurity is spherically symmetric s^ that |Sj k - (bj^'^a)] ^ = k^ -^ba where Xijg^ is the dipole matrix

element of the impurity transition. Finally, before evali:^ating eq (20), we average over all directions

of E so that the Jj^ ^ terms becomes (kE/2u)^/3. The n = 1 contribution to the sum over k in eq (15) is then

ab

where

,,-1 w 4, 2

r , = V l6Tr e*(r^/12) e'^ ^IhY. ^^P^ ^^P^ ^^^^^

K -1-p L(p) =

I dk k^'^'Vp. . (16b)

K -p m

2 1 Generally K^^ = [p + 2(u - is much larger than the magnitude of p allowed in f(p). In this case,

it is sufficiently accurate to approximate eq (16b) by

L ~ 2[2(u - CO )]4 (17) ba

and we see that the impurity excitation rate is essentially independent of the initial small conduction

electron momentum^. Since Ep f(p) - 1, this fact makes the sum in eq (I6a) trivial. The total rate

R-ab foi" an impurity to absorb a photon is r^i, times the number of conduction electrons in the interacti

volume V. It is convenient to express R^b terms of a photon absorption cross-section cj g^j-, which

equals R^b ^ (the incident photon flux). Recalling that Zv is numerically 10"! 3 I(w/cm2), we have

from eq (15) for sapphire

CT ^ ~ 7. 5 x 10"^^ I x\ e"^ - P« ' ^^^^ ab ab ' ba e

-22

in polaron units where the electron density p g is 6. 15 x 10 times the number of electrons per cc p.

73
To see the importance of the transition cross-section eq (18) relative to direct photo- exc itation, we estimate the density of impurities cm" 3 that would be required to attenuate the optical beam more

than does the direct photo- excitation process. Of course, the latter attenuation is not known, but it must be less thaji the total attenuation in sapphire, and that is less than 10"^ per cm. For argument,

suppose that direct photo- excitation causes less than 10"3 per cm optical attenuation (it probably causes much less). For our estimate, let us assume in eq (1 8) that X^^^ ~ 1 / ^^}~,, t^^b ~ ^' ^'^^ ~ 10^^ W/cm^

and P - 10^6 as in previous examples. This gives aab 10^^ cm^ so that ~ 10-^9 impurities per cc would be required to make these conduction- electron- mediated impurity transitions attenuate the optical beam by 10"^ per cm. Considering all the kinds of dislocations and foreign ions which might

take part as impurities in this process, we feel that it is not unreasonable that such an impurity

density could exist. Of course, there are so many order -of-magnitude estimates of unknown quantities

in the foregoing that the result can only be considered as suggestive of a kind of process that must be

considered as competitive with other possibilities at this time. However, the experimental observation

of a rapidly increasing dc photoconductivity near damage thresholds [7] does suggest a "bootstrap"

process such as the above by which conduction electrons can create more of their kind, even before

they become so energetic as to ionize the lattice. We have examined the enhancement of the single-photon bound-free photo- excitation transitions

that arise from eq (14), and have estimated that excitation cross-section also to be of order 10"22 cm^

under the same conditions. This is probably less than the cross- section for direct photo- excitation.

If multi-photon excitation is important in producing electrons, then the higher n terms of eq (14)

probably dominate direct absorption near damage levels. The expansion parameter in eq (14) is of order lO"-'--^ I(W/cm2), whereas it is ~ 10"-^'''

I for direct multi-photon absorption.

6. Focusing Effects

In a region of the crystal in which conduction electrons have been excited there is a change in the

refractive index 6n given by

5n - -oj^//. (19) p . , '

At a density 10^^ cm ^, electrons (with free electron band mass) have a plasma frequency of 10'''^ Hz,

which gives <^p/u ~ 0. 0023 and 6n ~ 5. 3 x 10"^. This index change is comparable to that required to self-focus a one milliradian gaussian beam. If the electron density were proportional to the optical

intensity I, and this index change were produced when I =

10_J_9 W/cm2, then the index change would

constitute a second order nonlinear index (often written n2 E'^) whose nonlinear coefficient n^ would be

-2 x 10"^ 3 esu.. This is negative and an order of magnitude larger than what one would guess is the

intrinsic nonlinear index of the bound electrons in sapphire. However, we suspect that the electron

density is increasing much more rapidly than I at high intensities [7] and so the effect of the index of eq (19) is not simple. Furthermore, impurity electrons which are excited to bound states more than v below the band edge, such as by the process discussed in the previous section, have an increased

polarizability and would tend to cancel the effect eq (19) of conduction electrons.

Suppose the net effect of impurity transitions were to produce a negative and highly nonlinear

refractive index change, as would be the case if the conduction electron effect eq (19) dominated. Then

there would be strong self-defocusing of a beam in regions of very high intensity, but only the intrinsic

self-focusing index would be operative in regions of smaller intensity. This would evidently result in successive regions of high intensity along the beam as each effect produces in turn a focusing tendency

that brings the other effect into dominance. Damage tracks in sapphire and other materials consist of

a sequence of damage bubbles that are suggestive of such a process. However, we have not calculated

the spacing of the successive high-intensity regions on the basis of some reasonable model to see whether there is any possible correspondence between these speculations ajid observation.

7. Discussion

Although there are alternate explanations for the behavior of damage tracks observed in sapphire

[14], it seems likely that self-focusing is occurring and playing a role in the damage. (It is curious

that the appearance, lengths, and positions of damage tracks differ between ruby and sapphire [14].) If self-focusing is occurring, it makes especially difficult the determination of the actual optical intensities

at which the material ruptures, and this in turn lends an extra uncertainty to the parameters we have

used in discussing the role of conduction electrons in damage. Probably the most promising way to determine more precisely what the electrons' role may be is to determine the parameters of these

conduction electrons below damage intensities. It would be especially desirable to have reliable dc

photoconductivity measurements between the intensities 5 W/cm^, the highest used by Hochuli [5], and

lOiO w/cm^, the lowest used by Belikova, et al . [7], in their measurements. With the high light

intensities available with lasers, it may now be possible to excite enough electrons to obtain a

74
meaningful Hall effect. Perhaps the time decay of photoconductivity and luminescence after an exciting

pulse could be observed and yield information on carrier lifetimes, trapping times, etc. Unfortunately,

the important and pervading parameter — the effective mass in the conduction band (and its anisotropy) —

appears to be extremely difficult to determine experimentally.

Should the photo-excited electrons be found to play significant roles in damage, such as those we

have discussed, then it maybe possible to fabricate more damage- resistant sapphire and ruby. For

example, if self-focusing is presently instrumental in damage, then it might be reduced by adding

donor impurities that produce a linear photoconductivity at high intensities and thus reduce the total nonlinear index via the index change of eq (19). On the other hand, those donors that give a highly

nonlinear photoconductivity and a sudden production of high electron densities that result in rupture by

photo-absorption may perhaps be eliminated from the crystals or compensated by other additives. In any case, it is evident that the availability of high- intensity laser sources will greatly facilitate the study of the conduction bands and impurity levels in very weakly photoconducting materials such as sapphire and ruby.

8. References

[1] A. Wasserman, "A mechanism for damage in solids by intense light," Appl. Phys. Letters

J_0, 132-133 (1967).

[Z] V. A. Pashkov and G. M. Zverev, "Destruction

of ruby and leucosapphir e crystals by strong

laser radiation," Soviet Phys. - JETP 2^, 516-

518 (1967).

[3] E. A. Sviridenkov, "Mechanism of damage of ruby by laser radiation," Soviet Phys. -Solid

State 9. 191 7-1918 (1968).

[4] G. M. Sverev, T. N. Mikhailova, V. A. Pashkov, and N. M. Solov'eva, "Mechanisms

of destruction of ruby and leucosapphir

e

crystals by powerful laser radiation, " Soviet

Phys. -JETP 26, 1053-105 7 (1 968).

[5] Urs E. Hochuli, "Photoconductivity in ruby

and sapphire, " Phys. Rev. 133A , 468-471

(1964).

[6] R. P. Feynman, R. W. Hellwarth, C. K.

Iddings, and P. M. Platzman, "Mobility of slow electrons in a polar crystal, " Phys. Rev. 127 , 1004-1017 (1962). Hereinafter referred

to as FHIP.

[7] T. P. Belikova and E. A. Sviridenkov, "Photoconductivity of ruby when strongly irradiated

by a ruby laser," JETP Letters 3_. 257-259

(1966).

[8] T. P. Belikova, A. N! Savchencko, and E. A. Sviridenkov, "Optic breakdown in ruby and

related effects," Soviet Phys. - JETP 2_7, 19-

23 (1968).

[9] L. Spitzer, Jr. , Physics of Fully Ionized

Gases (Inter scienc e Publishers, New York,

1956).

[10] H. Frohlich, "Theory of electrical breakdown

in ionic crystals, " Proc. Phys. Soc. (London)

A160 , 230-241 (1937).

[I1]V. I. Perel and G. M. Eliashberg, "Absorption

of electromagnetic waves in plasma, " Soviet

Phys. -JETP 1^, 633-637 (1962).

[12] R. H. Bube, Photoconductivity of Solids (John

Wiley and Sons, New York, I960).

[13]N. V. Beardsley, Proceedings of the Infrared

Information Symposia, Volume 1, No. 2, 47-

53 (1956).

[14]C. R. Giuliano and L. D. Hess, " Laser -induced

damage in ruby and sapphire, " in these

Proceedings.

COmENTS OM PAPER BV ROBERT HELLWARTH

Thz model- mploye.d in tkli papeJi uica ipecx^-ccoiXt/ ddvtlopzd {^on. cAyitalLLne. iotidi aoyvtcUnbig

impu/uXleyi, . Tluj, model., involving de^^inlte. unpuJvUitj tevelJ, impoied on a mtlZ- defined band i,tAaatuA&,

dou not apply to qIomu -in -uU pKUznt {^om.

75
Damage Threshold Studies in Ruby and Sapphire^

C.R. Giuliano and L.D. Hess

Hughes Research Laboratories

Malibu, California 90265

In this presentation a mode-controlled giant pulse ruby

laser oscillator and amplifier are described. The oscillator

employs a temperature-controlled resonant reflector, a dye Qswitch, and a 2 mm aperture to assure single mode operation.

The results of damage threshold measurements on a few ruby and

sapphire samples are discussed. Scanning electron micrographs

of surface damage, and photomicrographs of bulk and surface

damage are presented. The dependence of damage threshold on Ti02

doping and optical pumping is discussed, and some marked differences in the damage phenomenon between ruby and sapphire are . pointed out.

Key Words: Bulk damage, damage thresholds, lasers, mode

control, optical pumping, r\iby, sapphire, surface damage.

1. Introduction

In this presentation we wish to describe some experimental work that has been

carried out as part of a continuing program to study laser induced damage in solids.

We will first describe the apparatus used in the damage experiments. We will then

discuss some of the gross physical characteristics of both surface and bulk damage

.

We will present data on damage thresholds for a number of different samples, and

discuss the effects on the damage threshold of adding titanium dioxide to ruby and

sapphire

.

Finally, we will present the results of experiments in which we optically pump

the samples while irradiating them with the laser.

2 Since the earliest observations of laser- induced surface [1] and bullj [2] damage

there has been a large volume of published work [3-10] covering many aspects of this

phenomenon in a variety of solid materials . Many mechanisms have been proposed and

discussed, and considerable threshold data have been reported; despite this intensive

effort, a number of questions remain to be answered. Our approach is to use a laser

whose output properties are well characterized and monitored, so that any fluctuations in the data must be attributed to something other than fluctuations in the source

.

2 . Experimental Apparatus

The experimental setup is shown in Fig. 1. The oscillator employs a 4 in. long

X 1/4 in. diameter ruby pumped by two linear lamps in a double elliptical pump cavity.

The ruby crystal is water-cooled by a closed-cycle refrigeration system maintained at

0°C. The high reflectivity mirror is coated with a 99+% reflectivity high field

damage coating from Perkin Elmer Corporation. Q-switching is accomplished with a solution of cryptocyanine in methanol in a 1 mm path length cell whose transmission

is 30% at 6943 A.

''"This work was supported by the Advanced Research Projects Agency under Contract No.

F19628-69-C-0277 with Air Force Cambridge Research Laboratories.

2 Figures in brackets indicate the literature references at the end of this paper.

76
The temperature controlled (34°C) resonant reflector that was designed to optii mize longitudinal mode control consists of two quartz etalons and a quartz spacer

whose combined effect is to enhance cavity modes separated by 2 cm"! and to discrimi-

' nate against intermediate modes.

!

I Portions of the laser beam are split off in various ways (see Fig. 1) , so that

i the power output, near- and far-field patterns, and Fabry-Perot patterns can be monitored for each shot. This is accomplished in the following way. Light reflecting

from wedged beamsplitter Vlj^ gives two diverging beams; one of them hits the magnesium

oxide diffuser, where the scattered light is monitored by a biplanar photodiode used

as our power monitor. The second beam from W]_ hits ground glass screen G, where it

is photographed through lens L and the 1 m focal length camera focused at infinity.

This gives a magnified {'^ 5x) near-field picture. Another portion of the light is

I removed by beamsplitter B^^ and hits mirror M2 , which can be placed in or out of

'1 position depending on the use of the alignment laser. From M2 the light either goes

f to the Fabry-Perot interferometer or can be partially reflected from wedged beamsplitter W2 , where it results in a pair of far-field patterns. A 0.6 neutral density

filter is placed near the focal plane of the camera so that the far-field pattern and

the Fabry-Perot pattern can be seen at two different exposures. The two Glan prisms

are used as a variable attenuator after the amplifier. Beamsplitter B2 samples the

light to photodiode No. 2, which monitors the power incident upon the focusing lens,

[' which was designed for minimum spherical aberration (Special Optics) . Photodiode

No. 3 monitors the light after the sample. The signals from the two detectors are integrated and displayed on a dual beam oscilloscope. . The water cooled amplifier ruby is 6 in. long x 0.5 in. diameter, with one end

wedged relative to the other by about 0.5°. The input end of the amplifier rod is

antireflection coated to minimize the chances of oscillation within the amplifier

itself. The ruby rod is closely coupled to a helical flashlamp, which is pumped with

a power supply capable of delivering 8 kJ in a 3 msec pulse. The power supply

employs a pulse shaping network of 20 sections, each section pumping for 150 ysec.

The maximum gain obtained with the amplifier is about 10 dB

.

Figure 2 shows an example of what we see with our monitoring camera, and Fig. 3 shows a time trace of the laser output taken with photodiode No. 1 and displayed on

j the Tektronix 519 oscilloscope. Figure 3(a) shows the smooth temporal shape seen

I about 95% of the time, while Fig. 3(b) is an extreme example of multimode oscillation.

' In this case two modes are oscillating with a frequency separation of 750 MHz. This

frequency corresponds to the spacing between the end of the ruby and the resonant re-

; fleeter. The overlapping spectral ranges of the Fabry-Perot interferometer and the

519 oscilloscope insure that the oscillation of anything other than a single longi-

\ tudinal mode will be detected.

The characteristics of the laser are summarized in Table 1.

Table 1. Characteristics of ruby laser.

Energy Output^ 12 - 15 mJ (+15%)

Pulse Length 20 nsec

Peak Power 0 . 6 - 0 . 8 MW

Beam Radius (1/e for E field)

1 mm (±10%)

Beam Divergence 0.6 ± 0.1 mrad (full angle)

Calculated Beam Divergence 0.44 mrad (full angle)

^Our energy monitor was checked against three different

"calibrated" detectors; the error quoted (±15%) reflects

the disagreement of the standards.

77
3. Gross Characteristics of Damage

We now wish to point out some of the qualitative features of the damage we have

observed in ruby and sapphire, and point out the various differences seen in bulk and

surface damage.

When we place these samples in the beam we often see some plasma formation at the

entrance and exit surfaces; this is shown in Fig. 4(a) . In this shot no internal

damage was formed, but a small pit was visible at the exit surface. We wish to emphasize here that exit surface damage is the first to appear in most of our measurements

and that the threshold for exit surface damage is about an order of magnitude lower

than that for bulk damage. We also notice that the plasma formed at the exit surface

is often irregular, sometimes with a pointed appearance in the direction of light

propagation; the plasma formed at the entrance surface is more rounded in appearance.

Figure 4 (b) shows a photograph of another sample in which internal as well as exit surface damage was formed. Here we see a damage track beginning about a third of the way

in from the entrance surface. Notice also the flaring out of the beam past the damage

track. This blowing up of the beam could be caused by a scattering of light from the

damage sites or perhaps by self-focusing and subsequent diffraction. If we assume

that the fanning out of the beam is caused by diffraction from a self -focused spot, we

can determine roughly the spot size by measuring the angle of the fanned out part of

the beam. A crude measurement gives 7 x 10"^ rad for the half-angle , which corresponds

to a self -focused spot whose diameter is 6.3 ym. This is not an unrealistically small

spot size for self-focusing, and thus the flared out beam could arise from that. On

the other hand, we notice that the flared out part of the beam is not very uniform in

that the center part has much more light than the outer portions. This would suggest

scattering from the damage sites in which a small part of the beam is deflected while

most of it continues along the same path.

3.1 Surface Damage

The difference in the qualitative features of entrance and exit surfaces will be

discussed briefly in this section. Figure 5 shows photographs of both the entrance

and exit faces of a ruby rod subjected to varying amounts of laser radiation. Note the

difference in the kind of damage seen. The exit surface generally shows definite

crater formation, while a relatively small amount of material is lost from the entrance

surface. ,. ^ The influence of entrance surface damage on the apparent threshold for bulk

damage has come to our attention recently in this work. It is possible that one reason for the large fluctuation in the bulk damage threshold is the generation of damage

at the entrance surface and subsequent scattering of light from this damage site (or

absorption by the plasma) , which could result in a much lower power density in the

interior of the sample than expected. It has been observed that once this entrance

surface damage has been formed it is very difficult, if not impossible, to create bulk

damage with subsequent shots in the same place. For example, when the same region of

the sample is repeatedly irradiated with the laser, each time with increasing power,

the bulk damage threshold often cannot be reached; however, the damage on both surfaces

generally increases from shot to shot. The problem of surface damage varies considerably from sample to sample and from place to place in a given sample. No substantial

difference in this behavior is seen when the surfaces are cleaned with hot nitric acid

and rinsed thoroughly with deionized water. (Generally all surfaces are cleaned with

ethyl alcohol .

)

The photographs in Fig. 5 illustrate that there is a spatial correspondence

between the entrance and exit surfaces. As an example of the variation in results for

different parts of the sample, let us compare the different regions marked on the

photographs. In region A, for example, both entrance and exit damage are observed in

a location subjected to several shots from the laser. This region was not damaged

internally, even though the power incident on the sample far exceeded that for which

internal damage was created in other regions (e.g., region B) . Region B is one in

which both internal damage and exit surface damage were generated (in this case with

one shot), with barely noticeable entrance surface damage. Region C shows a location

subjected to a single shot of less than half the total energy as in B. In this case

no internal damage was formed but the exit crater is considerably larger than that

seen in B. Figure 6 shows entrance and exit surfaces of another sample, where we again see the qualitative features of the different kinds of damage formed. Note

the general anticorrelation between the extent of entrance and exit damage as exemplified in Regions A and B. In one case (A) we see exit damage with little or no en- trance damage, and in the other we see just the opposite.

78
j Next let us compare the entrance and exit surface damage at somewhat higher mag-

' nification. Figure 7 shows a magnified view of one of the damage sites seen on the

entrance surface of the sample shown in Fig. 6. The feature we wish to point out here

is the crazed appearance of the surface. There appears to be a general direction to

the crazing on the surface that is the same for all the damage sites examined on that

crystal. Other crystals also show this type of linear crazing, but it is not seen on

i all the samples examined. Figure 8 shows magnified views of exit surface damage.

, Note that the exit surface damage consists of pitting or crater formation, as well as the crazing similar to that seen on the entrance surface.

We have used a scanning electron microscope to examine the damage pits formed at

: the exit surface of a ruby sample. The particular sample is a 1/4 in. diameter x 3 in.

' long rod. Figure 9 shows several views of the surface damage under different magnifications. The first photograph (Fig. 9(a)) shows the rod under 23x magnification. The

' damaged areas were caused by three different shots of the laser; the one small pit at

the lower left was caused by one shot, the cluster at the lower right by another, and

the large craters at the top by a third. Further magnification of the last two regions

is seen in the other electron micrographs in the figure. Figures 9(c) and (d) show

j the large crater at the top magnified 610x and VOOOx, respectively. Figures 9(e) and

jl (f) show one of the multiple pits on the lower right magnified 660x and 6600x, respectively. Electron micrographs of the undamaged surface at 7000x magnification show es- sentially a smooth surface (Fig. 9(b)). The magnified view of the large crater in

Figs. 9(c) and (d) shows what appears to be a molten region around the hole, while

' the views of the pitted area (Figs . 9 (e) and (f ) ) appear more as multiple fractures

than a melting phenomenon.

3.2 Bulk Damage

* During these studies we have noticed a difference between the qualitative features

of the bulk damage in ruby, compared with sapphire. This is illustrated in Figs. 10

J and 11. In Fig. 10 we see some typical damage tracks seen in a ruby sample. These

ij tracks appear to be a series of bubbles or small fractured regions of variable spacj ing; they are more densely packed at the beginning of the track and spread out toward

i| the end, so that in some cases there is an appreciable gap between damage sites in a

I given damage track. The beginning of the track generally shows a more densely damaged

ij region that is usually much wider than the rest of the track. In contrast, the bulk

I damage in sapphire appears to be qualitatively different. In Fig. 11 we see an example of typical damage tracks observed in sapphire. These are generally more con- tinuous (fewer interruptions) than those seen in ruby, and often contain a "hollow"

Ij core with fractured regions at the periphery (see Fig. 11(a)).

In this particular sample there were a few irregular tracks such as that shown

j in Fig. 11(b) . It is curious to note that these tracks occurred when there was appre-

! ciable temporal modulation on the laser pulse. When these measurements were made there

was an unusually high percentage of modulated shots . It was noted that the irregular

' damage occurred only on those shots when the pulse was modulated (about six tiiaes)

.

We offer no interpretation to this observation, but merely point it out as a curious

occurrence.

'!

'

, This section may be summarized with the following statements concerning the qualitative features of the damage in ruby and sapphire.

I There are three distinctly different types of damage: bulk, entrance surface, and

I, exit surface damage. The surface damage appears to be similar in both ruby and sapji phire, while the bulk damage differs as described above.

I Entrance and exit surface damage are similar in two respects and differ in a third.

; They are similar in that plasmas occur at both surfaces and both show some crazing at

I the damage site. They differ in that a fracture crater occurs on the exit and not on the entrance surface. We suspect that the crazing is connected with and perhaps caused

by the plasma that is seen at both surfaces, whereas the crater, which is unique to

the exit surface, is generated by a phenomenon that takes place in the bulk of the

material and manifests itself at the surface.

The threshold for exit surface damage is about an order of magnitude lower than

that for bulk damage. It is more difficult to make a definitive statement concerning

the relative thresholds for entrance surface damage and internal damage . The ease of

plasma formation at the entrance appears to be a function of undetermined surface

79
parameters, the most likely of which are adsorbed substances and surface finish.

Therefore, the state of the entrance surface definitely determines what occurs inside

the crystal and at the exit surface. In the extreme case all of the light could be

dissipated in the entrance plasma.

Finally, let us assume that a hypothetical sample is subjected to a series of

shots with increasing energy, each time striking a different spot, and assume that

the power density is uniform over the length of the sample. We will first observe

exit surface damage at some threshold. As the energy is increased, the extent of the

exit surface damage will increase to give a larger crater than on the previous shot.

At an order of magnitude higher input we reach the threshold for bulk damage, at

which point a short damage track will appear; at the same time, we will probably ob- serve a decrease in the size of the exit pit relative to what it was just below bulk

damage threshold. As we increase the energy further we will generally observe more extensive internal damage and perhaps begin to see some entrance surface damage,

depending on the condition of the entrance surface. At still higher incident energy

the extent of entrance surface damage (or absorption by the plasma) can be so great

that it precludes the formation of bulk damage.

4. Damage Threshold Experiments - . ,-

In this section we present the results of damage threshold experiments for internal damage in a number of different materials from various sources. In all the cases presented the data represent a large number of shots for a given sample. There

was a large amount of scatter in the data, as mentioned earlier; we believe this re- sults in part from the varying amount of plasma formed at the entrance surface. It is

also reasonable to believe that there is an intrinsic variation in damage threshold

from place to place in the same sample. As a result, th'ere is a range of incident

energies over which one may or may not see internal damage, depending on the particular location in the crystal. For example, at a particular location in the sample no damage is seen at a given incident energy, while extensive damage may be seen in

another part of the sample for a lower energy in another shot. The data presented

in Fig. 12 reflect this fact. The dashed line corresponds to a range of power densities where damage was not observed at some locations in a given sample and is terminated on the high end by the highest power for which internal damage was not created.

The solid line corresponds to input energies where damage was observed at some locations in the same sample and is terminated on the low end by the smallest input

energy for which damage was observed. For example, let us examine the data presented

for Cz Ruby L104 in Fig. 12. The dashed line shows that certain regions of the

sample were subjected to power densities up to 7.1 GW/cm^ without damage. The solid

line shows that damage was observed in some other parts of the sample at input power

densities as low as 6.3 GW/cm^ . Thus, the amount of overlap gives a measure of

the definability of damage threshold for a given sample.

The power densities in Fig. 12 are calculated power densities at the beam waist,

lyiode propagation equations described previously [11] were used to compute beam radius

and divergence at various locations. The energy incident on the focusing lens first

is measured by photodiode No. 2 (Fig. 1) . This is converted to power by dividing by

the appropriate pulse width (FWHM) as determined by the Tektronix 519 oscillograms.

The power density at the lens is computed by dividing this power by the area of the

beam at the lens. This gives a spatial average for the power density or energy density

The energy density at the peak of the gaussian distribution is twice the spatial

average. The power density at the focus of the lens is obtained by computing the

beam size at the focus.

3 It xs definitely known that a substantial plasma will form on a dirty entrance surface. In addition, in our limited observations it appears that those crystals with

more surface scratches are more easily damaged at the entrance surface.

The gaussian beam radius oj is defined as the radius for which the electric field

reaches 1/e of its peak value. This is the radius for which the intensity or the

energy density reaches l/e^ of its peak value. If we define a beam area A = ttw^ and divide this into the total energy ^tot' have a kind of average energy density

It is easy to show that the energy density at the peak of the gaussian distribution

2E-j-Q|-/Trto . In most of the reports in the literature the power densities or energy densities refer to a kind of average. That is, the total energy is divided

by the "beam size" determined by some means or other. This method is convenient

when the spatial power distribution is not known.

80
We wish to emphasize that these power and energy densities are based on the following assumptions : (1) The spatial profile of the output is gaussian with a 1 mm

radius (1/e radius for the electric field.) (2) The spreading of the beam is by diffraction only, and the beam suffers no distortion, focusing, or defocusing in passing

through the ruby amplifier. (3) The diffraction limited spot size is reached at the

focal plane of the focusing lens. The degree to which these assumptions reflect the

reality of the physical situation can only be estimated at present, pending further

measurements. Measurements of the near field spot size at the oscillator output mirror give a 1 mm radius for the 1/e points of the electric field (assuming a gaussian

distribution) . This was done both by photographing a pair of spots on a ground glass screen with a known attenuation difference and by measuring the sizes of burn patterns on Polaroid film, with the relative energies of successive shots known. The

measurements by both techniques agree to better than 15%. Measurements of the farfield divergence of the oscillator give values that are higher than that expected for

a gaussian, although the measurements are not highly accurate. We obtain 0.6 ± 0.1

mrad (full angle) from relative spot size measurements in the focal plane of the

1 m focal length camera. The calculated beam divergence gives 0.44 mrad (9 -= (2 A) / (ttWq) ; full angle); this is appreciably lower than that observed but is almost

within the uncertainty of measurement. Even though we are well below the saturation

flux for the amplifier (4J/cm2 compared with 15 J/cm^)^ the uncertainty in the effect on the beam properties of the amplifier is probably the largest and most difficult to estimate.

5. Dependence of Damage Threshold on Added TiO^

Recent work of Nath and Walda [12] reported a striking increase (40x) in the

damage threshold in sapphire when small amounts (20 to 100 ppm) of Ti02 were added.

We decided to check these results and extend them to ruby as well. We purchased

Verneuil ruby and sapphire samples from the same source used by the above workers

(Djeva in Switzerland via Adolf Meller Co.), both undoped and doped with nominally

30 ppm Ti02 . The threshold for internal damage was measured, and the results were

found to be essentially opposite those reported previously. Table 2 shows the re- sults of these measurements. The numbers in the table are given in pairs. As discussed in connection with the data in Fig. 12, the numbers reflect the variation of

threshold from place to place in the sample. Of the two numbers quoted, that on the

left is the highest value for which damage was not observed in the sample, and that

on the right is the lowest value for which damage was found in the same sample. We

see from Table 2 that the thresholds for the titanium doped samples are at least an order of magnitude lowerS than those for undoped samples. The reason for this discrepancy with the results of Nath and Walda is not known. In addition, contrary to

the results of Nath and Walda, we found that the ultraviolet absorption edge for

the Ti02 doped samples occurred at a shorter wavelength than that for the undoped

sapphire (2600 versus 2300 A)

.

Table 2. Effect of TiO_ doping on damage threshold.

Power Density for Internal

Damage , GW/cm^

Without TiO^ With 30 ppm TiO^

Verneuil Ruby

Verneuil Sapphire

5.4, 9.9

12.1, 9.4

0.94, 0.70

0.36, 0.52

Because of these discrepancies it is reasonable to suspect that we may in fact

have different material from that studied by Nath and Walda.

'These titanium doped samples are examples of ruby and sapphire for which the bulk

damage threshold is so low that surface damage does not form.

81
6 . Optical Pumping Experiments

During this reporting period we have carried out a few experiments in which we optically pumped the samples while subjecting them to the laser radiation. The ex- periments were carried out on two ruby samples and one sapphire sample.

The samples were pumped with a power supply similar to that used for pumping the

amplifier flashlamp. In these experiments we pumped at two different levels (1200 J

and 3700 J) into the flashlamp (model FX60 by E.G.&G). As in the previous experiments

we fired a number of shots (generally 10 to 20) at each pumping level for a given

sample . , The results of the threshold versus pumping experiments are shown in Fig. 13.

Here the results are depicted in a manner similar to that of Fig. 12, where the dashed

line refers to the powers where no damage was seen in some parts of the crystal and

the solid line to powers where damage was seen in other parts. The scatter in the

data is relatively high, but nevertheless we can confidently say that there is no appreciable lowering of the threshold with optical pumping and, if anything, there may

be a slight increase.

One reason for the scatter in this case is the use of a shorter focal length lens

than has been generally used (19 cm compared with 48 cm) . We used this lens because

the output from our system was somewhat lower than previously and we were not quite

able to reach damage threshold with the long focal length lens. A more extensive

plasma was formed at the entrance surface at times when the 19 cm lens was used, and an appreciable fraction of the light undoubtedly was absorbed by the plasma.

We observed another interesting phenomenon in these pumping experiments related to

the location of the damage in the crystal as a function of pumping. In ruby that is

not externally pumped, we see damage tracks whose beginning is usually uniquely located in the sample. That is, for a number of shots at different powers we find that

the damage tracks begin at roughly the same distance from the entrance surface. The

length of a given track generally will be longer for higher power.

When the ruby samples are optically pumped, we see damage tracks that begin

at an appreciably different location "downstream" from the tracks for the unpumped

sample. Harder pumping shifts the tracks even more. Results for a sequence of

nonpumping, pumping, nonpumping, pumping are reproducible, showing that the phenomenon

is reversible. . The results of these experiments are shown in Fig. 14 , where the location of the

beginning of the damage track is plotted as a function of energy discharged into the

flash lamp. The lengths of the bars on the plot reflect the variation in position

from shot to shot of the beginning of the damage track.

This effect of apparent defocusing of the light cannot be explained as a sort of

thermal focusing due to the optical pumping; it is much too large for tha;t. For

example, if we were to assume that the ruby has somehow become a negative lens, we might ask what the effective focal length would be. Taking into account the distance

of the entrance surface of the ruby from the lens and assuming that the shift in the

location of the damage track corresponds to a shift in focus, we compute that the

ruby would have to act as a negative lens of ^^^20 cm focal length, which corresponds

to a radius of curvature of the end of the rod of "^1 cm. Alternatively, we can compute the apparent change in refractive index with pumping to account for the shift in the position of the damage track. The relative shift

in the distance from the entrance surface to the focus is directly proportional to

the relative change in refractive index. This then corresponds to an apparent index

change of 40 to 50%, a very large effect!

It is difficult to account for this effect by postulating any change in the

linear refractive index. A decrease in nonlinear index that somehow depends on the

degree of optical pumping is a possible explanation, but this should result in a higher damage threshold for pumping than for nonpumping. This may be the case, but

there is too much scatter in the data to confirm this (Fig. 13) . We also mentioned

that in the pumping experiments there was a substantial amount of plasma formation

at the entrance surface. It is conceivable that optical pumping of the surface plasma

could lead to some defocusing effect. It is clear that more experiments in this

area are needed, especially with regard to the relative damage thresholds.

82
A correlation for sapphire similar to those seen for ruby in Fig. 14 does not

exist. The location of the beginning of the damage tracks in unpumped sapphire varies

over a much wider range, depending on the incident energy from the laser, and any effect of optical pumping is obscured by this variation.

When the incident laser power is close to threshold the damage is found farther

"downstream"; as the incident energy increases, the location of the beginning of the

track moves "upstream" toward the source. [8] This is illustrated in Fig. 15, where

we plot the distance of the beginning of the damage tracks from the entrance surface

versus laser power incident on the focusing lens.

7. Conclusion

Qualitative features of surface damage are shown to be quite different for exit

and entrance surfaces. The difference between laser-induced internal damage in ruby

and sapphire, both in the gross and more subtle aspects, is pointed out both in ac- tual appearance of the damage tracks and in the dependence of the location of the

tracks on input laser energy and optical pumping. Perhaps these differences can be

attributed solely to the presence of chromium ions in ruby. At any rate, the effect

of chromium concentration on these phenomena should be studied. Further studies on these materials are in progress.

8. Refere

[1] Giuliano, C.R., "Laser-induced

damage to transparent dielectric

materials," Appl . Phys . Letters 5,

137-139 (1964 )

.

[2] Hercher, M., "Laser induced damage

in transparent media," Opt. Soc. Am.

5±, 563 (1964)

.

[3] Belikova, T.P. and Sviridenkov, E.A.,

"Effect of a focused ruby laser beam

on ruby," JETP Letters 1, 171-172

(1965) .

[4] Ashkinadze, B.M., Vladimirov,

V.I., Likhachev, V.A., Ryvkin, S.M.,

Salmanov, V.M., and Yaroshetskii

,

I.D., "Breakdown in transparent dielectrics caused by intense laser

radiation, " Soviet Physics — JETP

23_, 788-797 (1966) .

[5] Pashkov, V.A. and Zverev, G.M.,

"Destruction of ruby and leucosapphire crystals by strong laser

radiation," Soviet Physics - JETP

2± 516-518 (1967)

.

[6] Belikova, T.P., Savchenko, A.N.,

and Sviridenkov, E.A., "Optic breakdown in ruby and related effects,"

Soviet Physics - JETP, 27^ 19-23

(1968) .

[7[ Zverev, G.M., Mikhailova, T.N.,

Pashkov, V.A. , and Solov'eva, N.M.,

"Mechanism of destruction of ruby

and sapphire crystals by powerful

laser radiation," Soviet Physics —

JETP 26, 1053-1057 (1968) .

[8] Zverev, G.M. , Maldutis, E.K., and

Pashkov, V.A., "Development of

self-focusing filaments in solid

dielectrics," JETP Letters 9_, 61-63

(1969)

.

[9] Dupont , H., Donzel, A., and Ernest,

J., "On laser-induced breakdown and

fracture in glasses," Appl. Phys.

Letters 11, 271-272 (1967) .

[10] ASTM Special Technical Publication

4 69 "Symposium on Damage in Laser

Glass," 1969, and references therein.

[11] Giuliano, C.R., Hellwarth, R.W.,

Hess, L.D., and Rickel, G.R.,

"Damage Threshold Studies in Laser

Crystals," Semiannual Report No. 1 (January 1970) - ARPA Order No. 14 34.

[12] Nath, G., and Walda, G., "Strong

reduction of laser produced damage

in sapphire and ruby by doping with

Ti02," Z. Naturforsch. 23a , 624-625

(1968)

.

9. Acknowledgments

We wish to acknowledge the many enlightening discussions with V. Evtuhov and R.W.

Hellwarth, helpful comments and suggestions of E.S. Bliss and CM. Stickley, and

the skilled technical assistance of G.R. Rickel.

83
ALIGNMENT LASER

M|DRUBY AND ' 2mm FLASH LAMP RESONANT

APERTURE r" 1 REFLECTOR

I Mg RUBY

AMPLIFIER

HRLI28-IRI PHOTODIODE NO. 3 'Q? MgO

LENS

'PHOTODIODE NO 2

CAMERA

AUTOCOLLIMATING TELESCOPE

Fig. 1 Schematic representation of experimental apparatus.

... . J

Fig. 3 Tektronix 510 oscilloscope traces of laser output with 20 nsec/div sweep

rate, (a) Smooth pulse observed

~9 5% of the time, (b) Modulated

pulse (~750 MHz).

Fig. 2 Typical photo monitoring FabryPerot interferogram, near-field,

and far-field beam patterns. The

difference in optical density between

the two halves of the picture is N. D, 0.6. The free spectral range

of the interferometer is 1. 6 cm~l.

84
A

B

Fig. 4 Photographs of ruby samples being subjected to laser radiation. The light is traveling

from left to right. Note surface plasma formation, (a) No internal damage,

(b) Internal damage plus flaring of beam.

85
^- ...

* •

' - #

ENTRANCE EXIT Fig. 5 Exit (right) ana entrance (left) surfaces of damaged ruby sample (1/4 in. square) after a number of shots. The

regions A, B, and C are relevant to the discussion in the text.

'4 * • •

• V »

ENTRANCE EXIT

Fig. 6 Exit (right) and entrance (left) surfaces

of damaged ruby sample (3/8 in. square). The regions A and B are discussed in the text.

0.1 mm

j

1

1

",1

Fig. 7 Magnified view of entrance surface damanee asuch as that seen in Figs. 5 and 6.

A B

Fig. 8. Photomicrographs of exit surface damage pits and crazing. (a) End view, (b) Side view.

86
A

Fig. 9 Electron micrographs of exit surface damage at different magnifications, (a) End of ruby rod - Marker length - 400 jum. (b) Undamaged surface - Marker length - 1.4 Mm.

(c) Region A - Marker length - 16 fim. (d) Region A - Marker length - 1.8 ^m.

(e) Region B - Marker length - 15 iim. (f) Region B - Marker length -1.5 ^m.

87
Fie. 10 Photomicrograph of damage tracks in -r-~- ,1 -r->u ^- l, r j 4. i

• * 6 f 6 Fig. 11 Photomicrograph of damage tracks in ruby (see text for discussion). 1 t r j- \ ' ' sapphire (see text for discussion).

^ I I I I I I

I

1 Cz SAPPHIRE LI22

( I9cnn LENS)

I

I VERNEUIL SAPPHIRE

( 19 cm LENS)

I

I VERNEUIL RUBY MII9

I

I Cz RUBY AlOO

_l Cz RUBY CI24

_l Cz RUBY LI05

( 19 cm LENS )

Cz RUBY LI05

I Cz RUBY LI04

0 2 4 6 8 10 12 14 16 18 20 22 POWER DENSITY , GW/cm^

AT BEAM WAIST (48.3 cm LENS EXCEPT AS NOTED ) (SPATIAL AVERAGE ) Fig. 12 Bulk damage thresholds for a number

of ruby and sapphire samples. The

power density and energy density

scales are spatial averages . The

power and energy densities at the peak of the gaussian distribution are

twice the spatial averages (see text). The dashed line corresponds to powers where damage was not observed; the solid line to powers where

damage was observed for a number of shots in different regions of the same

sample. Sample sources: AlOO - Airtron; L104, L105, L122 - Union

Carbide; CI 24 - Crystal Optics;

M118, M119 - Meller.

1 1 1

1 1 1 1 1 1 1 RUBY L 103

1 _l UNPUMPED

1200 J

'

1

1 3700J

1

Cz RUBY L 105

1 UNPUMPED

1

' I200J

1

1 3700 J

Cz SAPPHIRE Lies

1

_l UNPUMPED

1 1200 J

1 _^ 3700 J

1 1 1 1 1 1 1 1 1 1 0 02 0.4 0 6 08 1.0 1.2 14 16 1.8 2 0 RELATIVE POWER

Fig. 13 Relative bulk damage threshold as a function of optical pumping for dif- ferent samples. The thresholds are normalized to unity for each sample

(unpumped). Dashed line - no damage; solid line - damage.

88
01234 PUMPING ENERGY, KJ 01234 LASER POWER , MW

Fig. 14 Location of beginning of damage Fig. 15 Location of beginning of damage

tracks from entrance surface versus tracks from entrance surface versus

optical pumping energy for ruby laser power incident on 19 cm lens

samples. L103 - 0. 03% Cr+^, for Cz sapphire sample L122.

L105 - 0. 05% Cr"*"^.

COMMENTS ON PAPER BV CONCETTO GIUILIANO

tation uioA not available..

Sa^ale^ ^<lkz obtained iKom manu^acJtuA^n^ in tk^ UnU^d Statu, Japan, and EiOiope, and mzH^

onltMlT^SiTapp^^iU Juhout t^QaKd to g^o^tii duitctlon. Ho t^Qn^i^canZ dzpzndmct oi dmage

£iMd on th^ ^04 dlt^cted. The mby and ^apphixe tampla. u^ed we^e g/ioi.n the

£g axS oi the bZl at 60° to the opUc a^ . In mo,t te^t^ , the InM la^e^ Ught^a,

onAoQonal to the planz

Z Z oi thz c-axli. No poloAlzaUon dependence oi the damage tiiKe^hold could be defected, due to the con^ldejiable icatteA oi the data points.

In ievcMol photoQULphi oi the damaged iuA^ace, icm^-paxalZel UneA wexe ieen to be 6upcfUjnpoied

on thz cxazed iuAiace. In general, the^e Unu MeAe peApend^caloA to the plane oi the c-axAJ^ oi the

c^y6tal, and MCAe aUo oKientcd poAaUcl to the electnlc ileZd vecXoK oi the ^nc<-dent Ught. It woi

noted that thu^ i^tAactixxe li ^ImiJiaA In appeafiance to theAmal eXching.

Although thexe It, home uncertainty in the inteApfietation oi iocu^ed-beam damage l&velA , the

^ /LQ^ulti quoted in thli, papex conxe^pond to enexgy deniiticA In tiie bulk, matexial oi 200 joules I cm in

10 mec puUe, which i^ an onden oi magnitude gxeatex tiian bulk damage levcU pxeviouity fieponted in

the titexatuxe ion. both Uexneuil and Czochnaldki mbiej>.

The occwxxence oi pitting on the exit iace^ oi iample^, with dimenhiom much mallex than the

beam diameter, iuggeJtthe poiiibiltty oi iiXament iomatton witliin tiie matexial. li iuch iiZament

ionmation did occur, it. wa6 not accompanied by caJxustAopfiic damage to tiie bulk matexial at enexgy

levelji at which exit iuxiace pitting wai obiexved. In those cases in which extemive cxatexlng

occuAxed on the exit suxiace in a single shot, thexe was evidence oi botii ilow oi matexial and imctuxe.

Ton the smalZex cxatexs, no detexmination oi the pncsence oi ilow was caxxied out.

data taken in sapphixe exhibited a gncatex vaxiation in damage thxe^hold than tiiat taken in nuby.

Vn. Guenthex nemaxked tiiat 0° sappjiixe shows a considexable lowex damage threshold than 60' sappliixe,

inom results obtained u^ing sapphire resonators. This could result irom diHexencc-i in the growtSx processes ior the. two orientations. The damage observed in resonators made oi 0° sapphixe appeared to

be iilamentaxy in nature, extending completely through the iuJil thickness oi the resonator.

89
Laser -Induced Damage to Nonlinear Crystalline Materials*t

Michael Bass

Raytheon Research Division

28 Seyon St. Waltham, Massachusetts 02154

The parameters necessary to specify surface damage to nonlinear crystals are described

and the power densities descriptive of the damage process are defined. The definition of the occurrence of surface damage is discussed and preliminary experimental results given for LiNb03,

Ba2NaNb50]^5 and several other materials irradiated by a Q-switched Nd:YAG laser. These results

obtained using TEMqq and "multimode" lasers are analyzed and used to provide the basis for planning

future experiments.

Key Words : Damage Threshold, Nonlinear Optics, Optical Damage , Q-Switched

Laser, Second Harmonic, Generation I

1. Introduction

The essential component in many modulators and Q switches, and in all frequency doublers

and parametric oscillators, is an optically nonlinear crystal. Unfortunately, the nonlinear materials

having the largest nonlinearities (i.e. , linear electro-optic coefficients, second harmonic generation (SHG) coefficients, etc.) are also those most easily damaged by intense laser beams. Even the slightest damage, which can occur on the surfaces or in the volume of the material, can render the crystal useless. Damage to optically nonlinear materials is thus a major limitation in the design of high power lasers and optical devices.

Most reports which describe new optically nonlinear materials mention the occurrence of index-of-refraction gradients when high-average-power visible light passes through the crystal. In LiNb03 this type of damage is thought to be caused by the presence of crystalline imperfections,

possibly oxygen vacancies, which trap electrons. Visible light frees these electrons, which then move away from the imperfection. The resulting internal electric fields cause index-of-refraction

gradients throughout the crystal, by means of the linear electro-optic effect. Thus a coherent process such as phase -matched SHG will be severely limited. However, since heating the crystal

permits the electrons to return to their initial sites, this type of damage is reversible.

On the other hand, when the light intensity incident on the crystal is high enough, irreversible damage occurs. Because of residual absorption, very high average power beams can heat the material to the point where thermal-stress-induced fracture occurs. The present discussion, however, is concerned with damage caused by very high-peak-power pulses of light to crystals which do

not absorb at the optical wavelength. When exposed to such pulses, the crystal's surfaces may be- come pitted and charred, and/or the interior may become cracked or filled with bubbles. This

catastrophic damage can be corrected only by repolishing the surfaces or by replacing an internally

damaged crystal. Since inmost operational configurations surface damage usually occurs in nonlinear

materials at lower power densities than volume damage, itis the first type of damage to be considered.

2. Parameters Necessary to Characterize Surface Damage

Since the operational characteristics of all lasers and laser systems vary widely, it is necessary to describe the light pulse responsible for the damage in question. In this manner, meaningful comparisons can be made between different materials and the results of different workers.

The relevant properties of light pulses are listed in Table 1. The pulse energy must be given in joules rather than some arbitrary relative unit which is meaningful only to the investigator who defines it. It is adequate to give the power density in standard units (MW/cm2) if one also gives the pulse duration and area irradiated. Moreover, the definition of pulse duration (FWHP or the time

interval between 10 percent and 90 percent of the total energy, etc. ) must be given to permit the pulse power to be computed. Finally, because the pattern of damage pits and the estimate of the power density depend on the mode pattern and size of the beam incident on the crystal surface, these

too are essential.

Initially supported in part by the Electronics Research Center under NASA Contract NAS12-2155.

t The research reported in this paper is presently being sponsored in part by the Air Force

Cambridge Research Laboratories, Office of Aerospace Research, under Contract F19628-70-C0223, but the report does not necessarily reflect endorsement by the sponsor.

90
I It is, of course, necessary to specify the state of the surface by giving the parameters

i listed in Table II. Since contaminants such as polishing compounds and finger grease can lead to spurious conclusions, comments about the cleaning procedure are necessary. In addition, such

crystalline properties as hardness or hygroscopic nature are necessary to describe the character

: of the surface studied.

Having specified the light pulse and the crystal surface, it is now possible to identify the power densities which describe the interaction leading to surface damage. It is intuitively obvious

(that for very small power densities, no damage occurs. The highest power density of the particular

[ pulse which will never damage the surface is defined as Pqq . It should be noted that, if a system

j employing this pulse and this crystal surface is to operate successfully and reliably, then the power

[density on the surface must always be less than Pqo • It is also obvious that a single pulse at some

high power density will damage the surface. We therefore define the lowest power density which will

i damage the surface in a single pulse as P j^. Note that by definition

If Pqq # P i, then for power densities between P ^ and P i the number of pulses required

j to damage the surface, N, will depend on the power density. The form of this relationship is

\ potentially very useful in helping one to understand the mechanism of surface damage.

j For a particular light pulse the surface damage properties of a crystal's surface can be

,| characterized by P , P-|^, and the relationship between N and P for P^^ < P < P]^. Since

jl damage-free operanon results if P < Pqo. the value of P oo in, say, MW/cm^, can be called the

ij crystal's resistance to surface damage. Comparing operational limits of various materials thus

involves determining the values of P;^^

3. Defining the Occurrence of Damage

1 Before damage, the crystal surface, under high magnification, is clean and as free of scratches and pits as possible. When a pulse of light of intensity > P-|^, impinges on a crystalline

'l surface, a spark is emitted as shown in Fig. 1; one or more pits, depending on the transverse mode

ij pattern of the light, are left in the surface. For values of P in the range Poo£ P £ Pi. pits can

' be seen when the surface is viewed with the unaided eye, only after a number of pulses and generally

:i only after a visible spark has been seen. Thus we can say that a surface has been damaged when,

jl after irradiation, one or more pits in the area irradiated can be seen with the naked eye. The

i! possibility exists that very tiny pits do occur before they are visible to the naked eye; this will be

studied further in future experiments. However, even using magnifications up to ~200X, such

"mini-pits" could not be detected before there were pits which one could see or before a spark was

observed. Therefore, since the present definition is a reliable criterion and is functionally easy

I to apply, it is used in the experiments described below. There is, however, the reservation that

jl future experiments may prove this definition incorrect; in that event the results given at this time

might have to be suitably modified.

I 4. The Present State of Surface Damage Data

for Optically Nonlinear Materials

There is a paucity of data on this subject. Our experience with the problem extends back

about three or four years, to the first LiNbOg Pockets cells we used in Nd:YAG laser Q-switches.

Since this material is not hygroscopic, is harder than KDP, and has large linear electro-optic

coefficients, LiNbOg is an attractive alternate to KDP in Pockets cell applications. However, as

I the operating level of a 5 mm Nd:YAG rod in a cavity using two flat mirrors is increased to obtain

! "multimode, " 10 nsec pulses of 20 millijoules or more, one or both of the surfaces of the LiNbOg

crystal become pitted in a pattern characteristic of the most intense regions in the laser beam.

An example of this is shown in Fig. 2. This limits the use of LiNbOg Q-switches to low -power

devices; KDP must be used in high-power units.

About one and a half years ago, while designing and building a frequency doubler to operate on pulses with 1. 06 ;u power densities which could be as high as 10 MW/cm^, it became necessary

for us to characterize the doubler crystal's damage resistance as well as its potential as a doubler.

At the same time, we discovered the nonlinear properties of certain dye crystals; moreover, we

found that some of them showed very high resistance to damage by 1. 06 yu pulses. This property

makes these crystals potentially effective doubters of high -peak -power pulses.

On the basis of nonlinear properties alone, we narrowed the choice of doubler material to "hot-LiNbOg" or Ba2NaNb50]^ c , assuming both could be obtained in high-optical-quality pieces.

Today LilOs would also be included. The experiment sketched in Fig. 3a was used to study the resistance of these materials to surface damage. During these first experiments, we used "multimode" beams, cared little for the orientation of the crystalline axes with respect to the light polarization, and used pulses which varied from ~10to30nsec, depending on operating conditions. The

91
pulse energy was varied by varying the laser input energy. We were, however, careful to obtain

similar surface quality in all crystals (at least X /4 flat over the small regions irradiated), treat them equally (except for those which were hydroscopic), use a low pulse repetition frequency (i. e. , ppm), and to employ two observers to obtain two independent sets of data. The damage pattern

caused by a focused "multimode" laser on a LiNbOs surface is shown in Fig. 4. The list of surface damage resistance in Table III was obtained in this initial phase of the work. Clearly the table is incomplete, it represents damage from a "multimode" beam and does not reveal any of the functional dependence of the number of pulses required to damage the surface on

the power density. On the other hand, such a list as this is indicative of the differences in resistance

to surface damage among nonlinear materials. In addition, since the surface quality of KDP, which

has the highest resistance to surface damage, was not as good as that of LiNb03, this compilation

also shows that the differences are caused by the material and not the surface finish. As we were interested in "hot" LiNb03 and Ba2NaNb50i5, detailed studies of these two materials were initiated. However, since we had no piece of "hot LiNb03" which we could sacrifice

to damage studies, LiNb03 was used. * We used samples which were cleaned and polished flat to \ /4 to obtain the results shown in Fig. 5. The straight-line relation between log N and log P for Pq© < P < P]^ shows that for irradiation by pulses such as those which we used, the number of pulses required to damage a surface

and the power density are related by an inverse power law. The functional form of N(P) is shown

in Fig. 6. Since the laser output was varied by varying the flashlamp input in these early experiments, it is possible that the laser mode varied in a systematic manner, resulting in these particular

relationships. However, the LiNb03 damage data described below, which was obtained using a TEMqo mode laser, also shows a power law relationship for intermediate values of P though the value of m is different.

The values of P , P]^ and m depend on the beam's transverse mode or, in other words, on

the transverse intensity distribution. Using the setup sketched in Fig. 3b where the laser was restricted to the TEMqq mode and the power density could be varied without altering either the pulse

duration or the polarization state, we found that the value of P oo for LiNb03 is ~ 350 MW/cm^

as compared to 6 MW/cm^ for a "multimode" pulse.** In this case, P]^ s 1600 MW/cm2. The

damage pit on LiNb03 obtained in a single pulse of 1. 06 in a TEMqo mpde of P ^ 1600 MW/cm^ is shown in Fig. 7. This pit is ~ 2t7 X 10-2 nim in diameter and ~ 2100 A deep. The volume of the

pit depends on the power density in a manner which is presently under investigation.

Figure 8 shows the measured relationship between N and P for LiNb03 when irradiated by

the pulsed, Q-switched TEMqo mode, Nd:YAG laser shown in Fig. 3b. The pulse duration was

15 nsec (FWHP) and it was focused to a nearly circular spot of diameter < 3 X 10^2 mm. The

crystal surface was polished flat to X /lO and its smoothness figure was (0, 0). It was uncoated

and cleaned with lens tissue and methanol after each damage spot occurred. During these experiments the crystal was oriented so that the b axis was normal to the surface and the light polarization

parallel to the crystal's a axis. Note the similarity in the functional relationships between N and P

obtained in the "multimode" and TEMqo mode experiments.

Determination of the area irradiated proved to be the major source of error in the measured

power densities. Several measurements of this quantity were obtained by direct measurement of the area burned by the focused laser beam on the surface of several different materials (stainless steel,

anodized aluminum, etc. ). The area was also calculated from the beam diameter incident on the objective lens and the effective f number. These various determinations agreed reasonably well

with one another, but in order to be conservative and underestimate the power density, we selected

the largest value of the area obtained.

The difference between the values of Pqo and using TEMqq mode and "multimode" beams

can be understood by considering that the peak power density in a "multimode" beam (i. e. , in each

"hot spot") can be many times the value estimated from the pulse energy, its duration and the total irradiated area. In each hot spot, power densities as high as in a TEMqq mode are possible (see

Fig. 4 ) if at least 75 percent of the "multimode" energy is evenly distributed among the several hot

spots. On the other hand, we do not at this time have an adequate explanation of the power law

relationship obtained with both types of irradiation. It is possible, however, that the different slopes I in Figs. 5a and 8 represent differences due to the orientation of the crystal.

This was a LINOBATE crystal obtained from Crystal Technology, Inc. Since damage to properties may be related to the crystal preparation procedures samples from other producers will

be studied in future work.

Note that this is the average power density of the focused TEMqq mode beam. At the center the peak power density is at least 2X the given value.

92
All the preceding measurements were performed at a pulse -repetition frequency of 1 pps, at room temperature, and in air. No noticeable difference was detected in Pqo for LiiNrb03 when the crystal was heated to 200° C or when the ambient atmosphere was N2, Ar or vacuum.

5. Some Analysis and Future Plans

We see from the preceding results that the occurrence of surface damage in nonlinear materials has a well-defined threshold; in terms of incident power density, the threshold for surface

damage is Poo • The damage process at power densities above P^ appears to involve a localized

change on the surface. It might be that microscopic damage spots occur, then grow with successive

pulses until they become visible. However, the change in the surface, whatever it may be, accumulates until the last pulse of light strikes the area and causes a breakdown (at this point we usually see

a spark) and damage becomes visible to the eye. Determining the nature of the change and how and

why it accumulates are major objectives of future damage studies. It is also important to determine

the generality of the behavior shown in Figs. 5 and 8 and the effect of environmental conditions and

sample treatment on P , and P^, and m for various materials.

The comparative data on surface damage reveal that the material, and not the surface treat- ment alone, accounts for the differences recorded. The KDP offers outstanding evidence of this; it cannot be polished finer than X /4 and smoother than (10, 20) but the resistance to damage is the highest yet measured. Improvement in surface quality alone then could improve a given material's

resistance to surface damage, but it will not eliminate the differences between materials.

Since the surface -quality question inevitably arises, we recently began to examine the imperfection density per unit area of various crystalline surfaces using large angle X-ray scattering.

Even the smallest crystalline misorientation, and any cracks, scratches, or other imperfections,

I show up as areas of different scattering intensity in this type of measurement. Figure 9 shows these

I Berg-Barrett X-ray topographs of the polished surface of both a LiNbOs and a KDP crystal. This

! procedure enables one to locate surface imperfections and to try to correlate damage pits with these

' locations. The density of these imperfections per unit area might also be correlated with damage

threshold. We shall continue these X-ray measurements in order to explore these possibilities and

to provide the requisite data about surface quality.

Future work to determine the causes of surface damage includes:

1) Studies of the dependence of P^^ , F^, and the relationship between N and P on the laser

1 wavelength, pulse duration, temporal properties, repetition rate, and transverse mode pattern. The

dependence on crystal orientation, temperature, and environment must also be included.

2) Examination of the surface after each pulse using high magnification microscopes and /or

interferometric techniques (possibly holographic correlation methods) and

3) Measurement of changes in the electronic character of the surface.

Various Nd, ruby, and dye lasers and appropriate second harmonics will be used as the sources in these experiments. The data will be analyzed and correlated, if possible, with other

i crystalline properties such as the location of the band edge, ir absorption bands, and hardness.

"1 In this respect, the dye crystals should prove interesting since they will permit us to attempt to relate damage properties to very small changes in chemical composition.

We have, in a manner of speaking, only scratched the surface of this problem. To date we

have been able to place limits on the performance of a few materials under certain specific types of irradiation. These measurements for the several most important crystals provide useful design

data for high power optical devices e/nploying nonlinear materials. In addition, we hope, through

the experiments outlined above, to be able to understand the damage mechanism and perhaps discover

procedures to overcome the problem.

6. Acknowledgements

The author wishes to thank D. Bua for his invaluable experimental assistance and

Dr. R. Mozzi for the Berg-Barrett X-ray topographs.

I*

93
Fig. 1 Spark Emitted by a LiNb03 Crystal when

Irradiated by an Intense 1.06^ Laser

Beam

Fig. 2 Damaged LiNb03 Pockels Cell

3^

PULSED Q-SWITCHED LENS /' SAMPLE ON X,Y,Z STAGE NdiYAG LASER 1

I 06^ BLOCKING FILTER

OBSERVER; 2 USED

EXPERIMENTAL SETUP, INITIAL PHASE

EYEPIECE PULSED, Q-SWITCHED FIXED NdYAG LASER POLARIZER

-^OBSERVER ; 2 IN USE

-I.06/J. BLOCKING FILTER

-DIELECTRIC COATED BEAMSPLITTER

I ^ 100% R AT 1.06/1 AT 45° i^OTATABLE POLARIZER ^Y^—lOX OBJECTIVE

crbll——SAMPLE ON X,Y,Z STAGE

EXPERIMENTAL SETUP •, PRESENT PHASE

Fig. 3 Setup for Surface Damage Experiments

Fig. 4 Surface Damage on LiNbOs Due to One

Pulse from a Multimode Q-Switched

Nd:YAG Laser. Average power density

~250 MW/cm^; dark field illumination.

1000

Z 100 -

1000

2 100

Power density (MW/cm )

(a)

1000

10 100

Power density (MW/cm^)

(b)

Fig. 5 Measured N= N(P) using Multimode,

Pulsed, Q- Switched Nd:YAG Laser

1000

94
O FOR P< P<D N— CO

FOR P,^ < P < P, N a P""^ AND N > I WHERE m»0.8 FOR Li Nb O3

AND ms.1,3 FOR Ba,NaNhO„

FOR P = P|

N = I

Fig. 6 Functional Form of N(P) for LiNb03

and Ba2NaNb50i5 with Multimode

l-06^( Irradiation

2 m.m

LiNbO,

0. 1 mm

Fig. 7 Surface Damage on LiNb03 Due to One

Pulse from a TEMqq Mode, Q -Switched

Nd:YAG Laser. Average power density

~1600 MW/ cm^; bright field illumination.

ipOOr R„=350

100

10 -

Fig. 9

KDP

Berg-Barrett Surface Reflection X -Ray

Topographs of Polished Crystalline

Surfaces

1,000 10000

Fig. 8

POWER DENSITY (MW/cm^) Measured N= N(P) Using TEMqo Mode

Pulsed, Q-Switched Nd:YAG Laser

95
Table I Parameters Necessary to Characterize Table II Parameters Necessary to Characterize

a Pulse of Laser Light a Crystalline Surface

1 WAVELENGTH , X , AND SPECTRAL WIDTH, A X

2 ENERGY IN JOULES

3 PULSE DURATION

4 TRANSVERSE MODE PATTERN

5 LONGITUDINAL MODE CONTENT

6 BEAM'S TRANSVERSE DIMENSION AT THE SURFACE

7 POSITION OF FOCAL POINT IF ANY OR THE SEAM WAIST

8 POLARIZATION STATE

9 PULSE REPETITION RATE

1 NAME OF THE CRYSTAL

2 CLEAVED OR POLISHED SURFACE

3 FLATNESS

4 SMOOTHNESS

5 CLEANLINESS

6 ORIENTATION WITH RESPECT TO CRYSTALLOGRAPHIC AXES AND LIGHT BEAM k AND E VECTORS

7 TEMPERATURE

8. ATMOSPHERE ABOVE SURFACE

Table III Resistance to Surface Damage for

Several Nonlinear Materials

p (ML)

cm 2

' POTASSIUM DIHYDROGEN PHOSPHATE (KDP) >400

AMMONIUM DIHYDROGEN PHOSPHATE (ADP) >400

7- DIETHYLAMINO- 4- METHYLCOUMARIN 400

COUMARIN 10

BQj NaNbjOij 10 LiNbOj 6

COmEMTS ON PAPER BV MICHAEL BASS

A dejj^tix^e on^zt o/j damage wcu, alwayi, notud in thjj, mnk. k(^tzx. a loAgt numb&A o(, ihoti, without

v-Uible. dantagz, t^ie. iimultamoLii occiwimco. o(, vi^ibZz and audible, plaima (,oHmatlon and a damaQZ pit

MOA doXdctzd. TheAe woi no dzpmdmct ol the. damage tkn.e^hold on cxyitaJL tempeKatiinej, , up to lOO'C,

oh. otmoipheAic enviJionment {incZading aoi, angon, nitAogen, and vacuum] . Ktt te^ti wejie cannied out at a nepetltLon Kate 0(5 one pal^e peJi iecond. It u)ai> a^iumed that no electronic e{i{^ect6 [photozlectAom] could accumulate oveA pexiodi, one iec. Special, phecautiom weAe taken in the handling

o{^ hyg/LOicopic cAyitali [KDP, kVP] but they wexe exposed in a manneJi iijmilajL to the otheA matzxiaJLi,

.

In moit te^tM, the incident la6eA beam Mai {^ocuied on the entAance {^ace 0(5 the iample. When the beam

Mai, {jOcuied above on. beZow the entAance ^ace, extt iuA{,ace damage waA obieAved {^iAit. In Lithium

niobate, it appeoAi that theAZ ii a meoiuAable dependence of, Ro on the {^ocaZ length, although thii

fiziult ii not completely veAi^ied.

Att 0|) thej>e meaiuAementi weAe made u^ing a {^ocuied laien. beam of, good uytif^onmiXy ( TEM^^

mode] . VfL. GuentiieA pointed out that caAe muit be excActied in extAapolating (,ocuAe.d-be.am valuer

{^OA. damage thAe^holdi to geomeXnlej, [an.eai] loAgeA dimemiom.

In mea^uAementi peA(,onmed at Sylvania, neponted by Vi. Fountain, a cAyital of, lithium niobate

lAJoi immeAied in Vow Coining 200 (,luid, and innadtated with an interne dtveAging beam cteated by

docuiing the. incA.de.nt VAG laieA beam above the cnyital with a 20 cm ^ocal length lem . In all caiei>

,

damage wai ieen at the exit {^ace o^ the cAyital. When the. cnyital woA immeAied in the Vow {^luid, the thASMhold ion. plasma {^omation i^ reduced by a {,acton. o^ thn.ee. In addition, i{, the cAiyital 0() tithium niobate ij> not present, breakdown Li not obieAved in the. Vow ^lutd. The in{,eAence ii made

that, an acouitical e^ect playi a role in the plaima (^onmation. An additional result reported by

Vr. Fountain ii, that i^ one placet, quartz in optical contact with the iuA(,ace o^ the cryital, the

damage thre.ihold increaiej, by a (^actor o{^ {^our.

Vr. Giuliano commented that in experimenti he had carried out, the ipzctrum of^ the plaima {^orme.d at the iuA{,ace various matcriali woi characteAtitic oi the. mateAial itielf,, and independent o^ the. atmoipheric environment.

96
Raman Scattering in Microscopically Damaged Quartz* 12 3 David F. Edwards , C. Y. She , J. D. Masso , Y. D. Harker'^and H. C. Schade2

Quantum Electronics Laboratory

Colorado State University

Fort Collins, Colorado 80521

Raman scattering is being used to study microscopic damage in crystalline quartz.

Three experiments have been performed to date. The Raman spectrum of undamaged quartz

was measured to serve as a standard from which the criteria for microscopic damage may

be defined. A controlled defect experiment was next in which was measured the effect

of an applied uniaxial stress on the Raman spectrum. A modif ied-valence force model

was developed to calculate the stress dependence of the Raman shift for the A-j^-vibrations. The agreement between the observed and calculated values is satisfactory.

Quartz samples were damaged by a Q-switched ruby laser and changes in the Raman spec- trum were observed and are reported here.

Key Words: Applied stress, laser damage, linewidth, microscopic damage, pre- catastrophic damage, quartz, Raman scattering.

This is a report of work we have been doing in the Quantum Electronics Laboratory of Colorado State University. We have been studying laser produced microscopic damage in crystalline materials and glasses. [1]5 By microscopic damage, we mean damage that is not visable under ordinary visual examination. Microscopic damage also could go by the name of precatastrophic or fatigue damage that accumulates from shot-to-shot until some threshold is reached and then cracks or "bubbles" appear within the crystal.

The primary objective of this research has been to make an experimental and theoretical investigation into the criteria governing the onset of damage and of the associated mechanism or mechanisms by

which the damage is produced by laser radiation in transparent solids. We are using light scattering as the diagnostic tool since the type of defect or inhomogeneity that we are searching for has the dimension of the order of the wavelengths of light.

Quantitative Raman scattering is being used as the diagnostic tool for our experiments, that is, not only do we measure the line position but we also measure the linewidth and the line intensity. The

binding or interatomic forces in solids are dependent on the electronic structure surrounding the atoms. The application of a uniaxial stress, a temperature change, or an intense laser pulse might be expected

to change the structure in a crystal and thereby alter the interatomic forces. This alteration might

be indicated either by the production of a Local-phonon mode, or by a change in the characteristic fre- quency of a vibrational mode, a change in the phonon lifetime and thus a change in linewidth, or the induced electronic polarizability might be effected causing a change in the line intensity. Each of these effects (i.e., the Raman line position, width, and intensity) were measured for various Raman

lines in quartz in an attempt to measure the effects of microscopic damage. Quartz was selected because

it is a crystalline material and has physical properties similar to those of glass. Investigations

similar to those reported here for quartz have also been made on sapphire and ruby but will not be

reported here.

This work was sponsored in part by a contract with the Air Force Cambridge Research Laboratories,

Office of Aerospace Research, USAF.

2 Electrical Engineering and Physics Departments.

2 Physics Department.

^ Present address American Optical Company, Keene, N.H.

^ Present address Idaho Nuclear Corp., Idaho Falls, Idaho. Figures in brackets indicate the literature references at the end of this paper.

97
We have performed three experiments; the first was to determine the quantitative Raman spectra of undamaged quartz, the second was a controlled defect experiment, and the third was to examine laserproduced damage.

In the first experiment a detailed measurement was made of the quantitative Raman spectra of un- damaged quartz. We carefully measured the line position, linewidth, and line intensity of each of the Raman-active vibrational modes in the quartz sample. The quantitative spectra of undamaged quartz

serve as a standard from which the criteria for microscopic damage may be defined. The samples were of natural and artifically grown material and from our measurements no differentiation could be made as to the source of the material. From these experiments the components of the Raman scattering tensor were evaluated and the effects of the long-range electric-dipole forces were determined. The details of this

work are reported elsewhere. [2]

The next experiment was to measure the change in the Raman spectra produced by a controlled defect

or inhomogeneity. [3] Starting with an undamaged quartz sample, it was placed between the jaws of an hydraulic press and pressure was applied; the quantitative Raman spectra was measured as a function of the applied uniaxial stress. We measured the line position, linewidth, and line intensity for some of the strong Raman-active vibrations. Given in Fig. 1 is a plot of the experimental data showing the shift in phonon frequency as a function of applied stress for three of the four A-j^- or symmetic vibrations. The 207-cm~l vibration is the soft mode of quartz and is associated with the a-B phase transition. The 466-cm~l line is the most intense vibration. It should be noted that the 352-cm~-'- line is essentially stress independent. In Fig. 2 are given the experimental data of the changes in the linewidth (FWHM) of the same three Aj^-vibrations . Here one can see that the linewidth of the 466-cm~l line

is only slightly affected by the applied stress while the linewidth of the 207-cm~l soft mode has the greatest stress dependence. A calculation was made of the stress dependence of the line position for the

4 Aj^-vibrations . The valence-force model of Kleinman and Spitzer [4] was modified to include the ef- fects of an anharmonic potential and an applied stress. Using this model the microscopic or internal

strains produced by the atomic displacements necessary to minimize the deformation energy were calculated following the procedure of Born and Huang. [5] The resulting stress-dependent potential, including

the anharmonic contributions, was calculated in terms of the normal-mode coordinates of the A^-modes

given by Kleinman and Spitzer. The chances in the normal-mode frequencies produced by this stress de- pendent potential were evaluated using first-order perturbation theory and the results are given in Table I. The details of these calculations can be found elsewhere. [6] Within the accuracy of the calculations and measurements the agreement between the predicted values and the measured values is quite

good. The stress dependence of the line position of the lOSl-cm"-'- line was not measured because it was

too weak, however, we did calculate a negative slope. One should notice that for these four Aj^-vibrations, (symmetric vibrations) the stress dependence is not monotonic as measured and predicted. Also

given in the table are the slopes as measured by Asell and Nico [7] for applied hydrostatic pressures. One can see that within the large error that they quote our measurements are in very good agreement.

Table 1. Comparison of the calculated and observed values of the slope of the frequency shift- stress dependence for the A]^-modes in quartz. , =: . - :_

Mode _^

(cm ) (Slope) ^

, calc.

cm -^/kbar (Slope)

_•] , obs . cm -"-/kbar (Slope) cm 1/kbar

207

352

466

,33

,02

,13

1.28 ± .06

-0.05 ± .06

0.44 ± .12

1.6 to 2.1

-0.2 to + 0.3

-0.2 to 0.4

(a) Asell and Nicol, reference [7] hydrostatic pressure.

The effects of the applied stress on the line position and width are similar to that observed for decreasing sample temperature. The increase in frequency as the sample is compressed is what might be

expected since the atoms become more closely packed making it more difficult for each atom to move.

For no change in sample temperature, the increase in phonon frequency would lower the associated phonon

population number. Since the phonon life-time depends on the number of phonons available for the multiphonon interactions, a general reduction in phonon population numbers would result in lengthened phonon

life-times and consequently narrowed Raman lines. In addition and perhaps more important than the popu98
lation effect, the phonon lifetimes are also influenced by different multi-phonon interactions resulting

from the strain. [8]

Shown in Fig. 3 are spectra of the stress dependence of the line shape for the 128-cm ^ E-vibration.

Although this line was not used for the studies reported here the stress dependence is typical for the other vibrations. Here is a slight dependence on stress can be seen for the line position, however, the change in linewidth is not discernible from the raw data. Upon deconvolution of this raw data with the instrument function the brodening effects of the spectrometer can be subtracted. When this is done one

can easily see not only the change in line position under the applied stress but also the change in width such as given in Figs. 1 and 2.

In the third experiment the change in the Raman spectra was measured in a quartz sample before and after irradiation with a commercial Q-switched ruby laser pulse structured with multi-transverse modes.

Starting with an undamaged sample the Raman spectra was carefully measured in the region of the 207-cm~

modes. The sample was then placed in the beam of a pulsed laser having a peak power of the order of 1 MW unfocused, and a power density of about 100 MW/cm for a focused beam. No microscopic or visable

damage was observed within the sample after the laser pulse. The sample was then placed in the spectro- meter and again the Raman spectra was measured for these two lines. This experiment was repeated for various peak powers and power densities for the pulsed laser. Shown in Fig. A is a schematic diagram

for one of the samples measured. This particular sample contained a seed vein and the relative orientations of the incident radiation and polarization directions are indicated. For this particular measurement a small pit or crater was produced on the exit face of the sample. The Raman spectrum in the re- gion of the 466-cm~l line is shown in Fig. 5. At the bottom is shown the Raman spectrum for an un- damaged sample indicating the strong 466-cm~l line with a peak intensity of about 7,000 counts and a FWHM line width of 6. A ± 0.1 cm~l. For the damaged sample containing the seed vein the spectrum is that shown in the middle. Here one sees not only the A66-cm~l line with a peak intensity of about A, 000 counts and a line width of 6.7 ± 0.1 cm"-*-, but also new lines at SAO-cm"-'- and 579-cm~l. In order to check whether these new lines are due to laser-damage or due to the seed, a sample containing no seed vein previously damaged for our preliminary study [1] was examined in the same spectral region and re- sults were shown at the top. Here new lines at SAO-cm"-'- and 579-cm~l are observed indicating that the

540-cm~-'- and 579-cm~''- lines are probably due to the defects or local phonon modes induced by the laserdamage .

Our immediate goals are to continue this study to try to determine the effects of polarization and direction of propagation of the damaging laser beam on the change in linewidth of the existing lines as well as the creation of new lines. The transverse dimensions of the damaged region are being determined

by measuring the Raman spectra of the sample at different distances from the position where the damaging

laser was incident.

Two different Q-switched ruby lasers are being used for damaging the quartz samples. For one laser

no attempt has been made to eliminate hot spots in the beam. The other laser has been carefully con- structed such that no hot spots exist in the beam; the output is a TEMqq mode with a Gaussian shape.

Preliminary results indicate that for the laser pulse having the hot spots the average power density necessary for producing damage is significantly lower than that required for the TEMqo pulse. Also the crater produced by the two lasers are noticably different. This work is continuing.

The authors wish to acknowledge the assistance of Dr. G. McAllister and Mr. V. Draggoa for their

assistance in helping us perform some of these experiments.

References

[1] Edwards, D. F. , Barker, Y. D. , Masso , J. D., and She, C. Y., "Diagnostics and Evidence of Pre-catastropic Damage in Transparent Solids,"

ASTM STPA69, 1969, p. 128.

[2] Masso, J. D., She, C. Y., and Edwards, D. F.

,

"Effects of Inherent Electric and Anisotropic

Forces on Raman Spectra in a-Quartz," Physical Review B, May 15, 1970; She, C. Y., Masso,

J. D., and Edwards, D. F. , "Raman Scattering

by Polarization Waves in Uniaxial Crystals,"

Journal of the Physics and Chemistry of Solids, submitted for publication; Masso, J. D., "Raman Scattering in a-Quartz," Ph.D. Thesis, Colorado State University, March,

1970, unpublished.

[A] Kleinman, D. A., and Spitzer, W. G. , "Theory

of the Optical Properties of Quartz in the Infrared," Physical Review, Vol. 125, 1962,

p. 16.

[5] Born, M. and Huang, K. , "Dynamical Theory of Crystal Lattices," Clarendon Press, Oxford,

195A.

[6] Harker, Y.D., "Effect of Uniaxial Stress on

the Vibrational Modes in Quartz," Ph.D. thesis, Colorado State University, December,

1969, unpublished.

99
[3J Barker, Y. D., She, C. Y., and Edwards, D. F., "Stress-dependent Raman Frequency and Linewidth

in a-Quartz," Applied Physics Letters, Vol. 15,

1969, p. 272; "Effect of Uniaxial Stress on the Vibrational Modes in Quartz," AFCRL-69-0445

,

October, 1969, "Raman Spectra of a-Quartz Under Uniaxial Stress," Journal of Applied Physics, submitted for publication.

\

stress ( JO' dynes/cm^ )

Fig. 1 Shift in phonon frequency as a function of applied stress for three

A. -vibrat ions

.

[7] Asell, J. F., Nicol, M. , "Raman Spectrum of a- Quartz at High Pressures , "Journal of Chemical

Physics, Vol. 49, 1968, p. S395.

[8] Cowley, R. A., "Phonons in Perfect Lattices

and in Lattices with Point Imperfections,"

edited by R. W. H. Stevenson, Plenum Press, New York, 1966.

stress { 10* dynes /cm^ )

Fig. 2 change in fullwidth-half maximum as a function of applied stress.

100
I'S Ok QUARTZ y(2^)x

Fig. 5 Raman spectrum in the region of the 466-cm line for undamageri and laser damaged quartz

samples

.

101
Exoelectron Emission from Optical Surfaces

P. Braunlich

Bendix Research Laboratories

Southfield, Michigan 48075

The first exoelectron images obtained from dielectric materials are reported. Possible applications of the new technique in characterizing a surface with respect to laser damage are discussed.

Key Words: Electron emission, work functions, electron imaging,

glass surface damage.

1. Discussion

Laser surface damage is a serious problem wherever high power laser beams are used. Optical

materials such as glass, sapphire, ruby, single crystals of alkali halides, etc., and non-linear

optical crystals such as lithium nlobate, barium sodium niobate, lead molybdate, etc., are damaged

at various densities. Surface damage usually occurs at lower power densities than damage of the bulk.

The mechanism for this surface damage is presently not well understood . [l] One fact, however,

appears to be established: the condition of the surface is the most Important factor in determining

the surface damage threshold of a particular material. In most cases, an increase in photoemission

of electrons seems to preceed surface damage.[2] All the materials mentioned above have a wide bandgap

Multi-photon absorption of electrons from the valence band or from defect levels below the Fermi level ! is therefore the obvious mechanism of generating photoelectrons at typical laser wavelengths. In the i case of single-photon absorption, photoemission from defect levels plays only a minor role. The j quantum efficiency in this case is typically three orders of magnitude smaller than the efficiency of

emitting electrons that originate in the valence band. [3] Because the minimum energy required to emit

an electron from a defect level is smaller than the energy required to emit electrons from the valence I band, electrons from defect levels become important contributors to multi-photon photoemission and can

even dominate the total emitted current. Defect levels can also influence photoemission indirectly

through the production of band bending. [3] The type of bending that takes place is determined by the

position of the Fermi level In the bulk of the material and by the energy available in the surface.

It may increase or decrease the minimum energy required for an electron to escape across the work

function barrier at the surface.

Obviously, information on the defect levels, the surface states, and the potential barrier of

the solid-gas Interface is needed in order to estimate the vulnerability of the entire surface or of ! only certain "weak" areas to high intensity light fluxes. Detailed studies of photoconductivity

appear to be the natural source for this information. Unfortunately, the experiments that have to be performed are fairly Involved. Multi-photon photoemission requires intense light sources, and surface

damage is again likely to occur. Single-photon photoemission, on the other hand, requires light sources emitting in the vacuum uv. This requirement causes detection problems, because most electron

detectors (e.g., open electron multipliers) are also photoemltters in the vacuum uv, thereby con- tributing sizable background problems. Furthermore, the quantum efficiency of photoemission of

electrons from defect levels is so small that the investigation of this contribution to the photoeffect is fairly difficult. Thus, a more direct experimental approach to the problem is clearly

desirable. In this paper we suggest using the technique known as exoelectron emission (EEE)f4] to study the various aspects of laser surface damage.

i After having been exposed to ionizing radiation, many dielectric materials emit electrons from ' their surfaces. The initial emission decays after a certain time; however, further heating of the compound causes additional electrons to be emitted (EEE) . Usually emission peaks at various temperatures are observed, which are characteristic of a specific material and its surface condition.

Figure^l shows a typical EEE curve obtained with LiF that had been exposed to 10 rad ;3-rays of a i Sr^O-Y source prior to heating. [5] ,1

Figures in brackets Indicate the literature references at the end of this paper.

102
The mechanism of EEE is believed to be the escape of electrons from traps in the surface across

I the work-function barrier. The traps are formed by crystal defects, adsorbed layers of impurities,

etc. The EEE curve of some compounds is remarkably similar to the so-called thermoluminescence glow

I curve; in these cases, electron traps in the bulk of the sample appear to be the origin of the emitted

' electrons. The mechanism by which the electrons are released or expelled through the surface is not clearly understood.

j The connection between surface damage threshold and EEE seems obvious: the condition of the surface layers is the determining factor for both. Furthermore, the defect level structure and the

, work function are important in explaining both phenomena.

I For the study of EEE, relatively simple experimental techniques are needed. The detection of

' exoelectrons requires a sensitive counter without a window. Gas-flow Geiger counters, "point counters"

I and proportional counters are frequently employed. [5] For studies on a surface in high or ultra-high

!j vacuum, "open" electron multipliers are used. [4] Our preliminary experiments on ED-2 laser glass

J showed that Bendix Channeltrons° in various configurations are ideal detectors for exoelectrons.

Their input aperture can be selected for diameters from 0,001 inch to over 1 inch. It is therefore

f possible to either scan the surface of the sample or collect the electrons emitted from the entire

j surface. The quantum efficiency for electrons is close to 100% and typical gains are 10 to 10^. An

|! example of such a device is shown in Fig. 2. Yet another Channeltron device, the microchannel plate,

I even permits imaging of the sample via the emitted exoelectrons. With this device, we have been able

I to demonstrate EEE-imaging for the first time.

The microchannel plate is a bundle of closely packed Channeltron multipliers having a limiting

resolution of 0.002 inch (see Fig. 3). Its physical dimensions are typically about 1 inch diameter

and 0.080 inch thickness. Electrons emitted from various points on the surface of the specimen are collected by the bundle and multiplied. The electron beams emerging from the channels are accelerated

in a dc electric field and then made visible with the aid of a phosphor screen. The gain of these

bundles is presently about 10-^. Other similar devices are available that have gains up to 10^. The

'j dark current is very low and was never found to distrub the imaging in any way. In order to demonj strate the principle of exoelectron imaging, we have performed some preliminary experiments on cleaved

I samples of LiF single crystals which were subjected to various surface treatments. The images obtained

I may be interpreted as maps that display the features of the work function, of the defect level distribution, and of certain macroscopic defects across the surface.

I A typical EEE image is shown in Fig. 4. A 10 mm x 10 mm sample of 1 mm thickness was cleaved

1 from a high-quality pure LiF single crystal. It exhibited two pronounced cleavage steps (35/i and 50/i height) across its center. In order to fill the electron traps, the sample was exposed to X-rays

(50 kV, 15 mA, tungsten anode) for four hours. After that, one half of the crystal was etched for one minute in a 3% HF solution, which causes only slightly visible changes in the appearance of the surface. The etching demonstrated that different surface treatments distinctly influence EEE images.

With the aid of two steel brackets, the sample was then mounted on a beatable copper block inside a vacuum chamber. For good thermal contact, an Al^O^-compound having a low vapor pressure was applied

between the copper block and the crystal. The Channeltron bundle was placed 5 mm in front of the crystal and parallel to its surface. The temperature was then raised within a few minutes to about

200 C. During the appearance of the 150°C peak (see Fig. 1), time exposures of the image displayed

on the phosphor screen were recorded with a camera.

The EEE images obtained exhibit a complex structure. At this point, we shall not attempt to interpret this structure other than pointing out that the exoelectron emission from the etched part appears to be distinctly different from that of the rest of the surface. The cleavage steps are clearly visible. Since many other features could not be related to any visible structure of the crystal surface, it seems that not only macroscopic defects, but also other defects and "invisible"

property differences of various parts of the surface influence exoelectron emission.

It is hoped that EEE techniques will provide a tool for studying certain surface properties of dielectric solids, as well as the much needed means for characterizing and predicting the quality of optical surfaces with respect to their laser damage threshold.

2. Acknowledgment

The author greatly appreciates the assistance of W. Colson and R. Hall in performing the experiments

.

103
References

Damage in Laser Glass, ASTM Special Publication, 469, 1969.

4. Scharmann, A.^ article in "Festkorperprobleme

VI" (Vieweg und Sohn, Braunschweig, 1966).

Glass, A. J. and Guenther, A. H., Review in Damage in Laser Glass, ASTM Special Publication, 469, 1969.

5. Attix, F. H., private communication (1970).

Larch, S., ed . , Photoelectronic Materials and

Devices, van Norstrand, N.Y., 1965.

150"

^LiF EE RESPONSE

TEMPERATURE

1/205°

\zhO° THERMIONIC EMISSION

330" \^

// N0-OOSEEE\ // RESPONSE V ^

Y 1 / 1 1 1 _ - -"^T^ 1 Fig. 3 Channeltron Arrays.

EL4PSE0 TIME AFTER REACHING 50°C (SECI

Typical FEE count-rate versus heatinj

time for a 10 mg LiF sample (powder)

measured with a methane gas flow counter after exposure of the sample

to 10 rad B-rays from a ^x^^ -X^^ source. (The author is indebted to

Dr. F. Attix for making the figure

available for this publication.)

Channeltron® electron multiplier.

Fig. 4 EEE-image of a LiF crystal. The

schematic shows how the sample was mounted on the copper block. The

left half of the crystal was etched

in a 3% HF solution after the X-ray

exposure. This part appears brighter

(see especially upper left corner).

104
Appendix I

Pulse Duration Dependence of Laser Damage Mechanisms

E. S. Bliss

Air Force Cambridge Research Laboratories

Bedford, Mass. 01730

A number of mechanisms for laser damage in transparent dielectrics are examined

for pulse duration dependence and the results are compared with experimental measurements when possible. The differences in dependence on pulse duration and other

variables from one mechanism to another suggest that different mechanisms may

initiate damage in different parameter ranges. Experimental identification of these

mechanisms will be aided by measuring the pulse duration dependence of the damage

threshold.

Key Words: Conduction electrons, dielectric breakdown, inclusions,

laser damage, laser glass, ruby, self-focusing.

1. Introduction

It has become clear that damage thresholds under both ruby and glass laser radiation are influ- enced by a large number of variables. For example, temperature t-'- J pulse duration [2], optical

pumping conditions^, beam diameter [3], beam focusing [3], laser frequency [1], and details of material growth and preparation [4, 5] all appear to be significant in particular instances of laser

damage. This multiplicity of variables often makes it difficult or impossible both to compare

various experimental findings with each other and to understand their relation to a particular damag

theory or to an operational laser system. A plot of damage threshold versus pulse duration from

data available in the literature, for example, reveals considerable scatter. This probably results . from significant variations in other important parameters from one experimental arrangement to another.

Various theoretical efforts have been directed toward detailed studies of individual damage

mechanisms, but only rarely has an attempt been made to explicitly predict how the damage threshold might vary over a wide range of a given system or material parameter. The purpose of this paper is to indicate what pulse duration dependence is expected for a number of laser damage mechanisms. Information about dependence on other important variables is essential in some cases and

is included for completeness. When possible these predictions are compared with experimental

measurements. However, only a few workers are known to have measured damage thresholds as

a function of pulse duration [1, 2, 6, ?]. Consideration is limited to internal damage resulting from

pulsed radiation.

Figures in brackets indicate the literature references at the end of this paper. Compare references 1 and 2

105
2. Possible Damage Mechanisms j Damage from laser radiation always occurs because sufficient energy has been absorbed to drive some kind of failure mechanism, but the ways in which laser energy can be absorbed and lead to damage are numerous. Some of them require imperfections in the material or depend on properties

which are subject to control during the growing or melting process. Others are a result of more

intrinsic properties and constitute fundamental limitations on the performance of the material.

2. 1 Absorption by Inclusions or Bulk Absorption

Inclusions may be highly absorbing at the laser frequency. They can, therefore, cause several

local heating effects leading to damage by thermal expansion, melting of the surrounding material,

or other means [6, 8]. For purposes of this analysis damage is assumed to result from the stress associated with thermal expansion.

2 During a very short pulse of duration At, or for a large inclusion of radius R (such that R / At

D| > Dji. where D^ and Dj^ are the thermal diffusivities of the inclusion and host matrix respectively)

the inclusion surface is heated to a depth of roughly {D^ At)^^^, but very little heat is conducted into the surrounding material [9]. The laser energy density J^j (energy per unit cross-sectional area)

required to produce a damaging stress S in the host at the surface of the inclusion due to expansion

of the heated outer shell is approximately

cS - (C. k^ D. S/i3. e M) (At)^^^. ^_ (1) d 1 h 1 1 A

Here C is the heat capacity per unit volume, k is the volume compressibility, j3 is the volume

expansion coefficient, and e^ is the spectral emissivity of the inclusion at the laser wavelength. It is assumed that meaningful average values of these material properties can be used over the large

temperature range involved and that heats of fusion and vaporization can be neglected to a first approximation. In addition, radiative heat transfer is taken as small compared to conductive

transfer [8] in this and all following cases. The use of M is necessary to correct for the modified

effective cross-section of sub-wave length inclusions [10]. Its value is approximately unity for R> X/20 and 20 R/X for R < X/20.

Depending on the relative values of Dj and Dj^ there may be a range of pulse duration and inclusion

size (Dj^ ~ R^/At » D^) for which essentially the whole inclusion is heated during At while conduction

into the host matrix is still negligible. In this case the threshold for damage due to stress from

expansion of the inc lusion is given by . y .p '

.

= (4 C. kj^ S/3^. e^ M)R. (2)

Finally for long pulses or very small inclusions (D- > Dj^ » R^/At) a considerable volume of the surrounding material is heated by conduction during At, and both the inclusion and the host matrix

will undergo thermal expansion. In the absence of a significant difference in the expansion coefficients of the inclusion and host materials, attainment of a large temperature gradient in the host

is now necessary to cause damage [ll]. More specifically, the difference between the strain at some

distance r due to the heating of the host material in the volume (4/3)77 r^ and the strain which would

have occured at r solely due to the local temperature change AT must cause a stress equal to the breaking strength S of the host. This requirement can be expressed by

(A T A T), (3)

106
where the mean temperature change AT^ is defined by

ATm

= f'^AT (u) u^du. (4)

J. 3 >Jo

Treating the inclusion as a continuous spherical surface source generating heat at a constant rate during the pulse [12], the minimum laser energy density required to cause damage is found to be on

the order of

(lOCj^ S/i3j^e^ M) (At/R), ' . . (5)

The derivation of eq. (5) ignores the fact that in this small inclusion limit the host may be

heated to the extent that it can flow and become immune to fracture damage even at distances large

compared to R. If such flow occurs in the short time of the laser pulse duration, then to cause

fracturing the breaking strength S must be exceeded at the liquid-solid boundary, and this requires

a higher laser energy density. Although this may be an important consideration for numerical calculations [13], it is not expected to change the dependence of eq. (5) on At and R.

Equations (1), (Z), and (5) give the dependence of damage threshold on inclusion radius and pulse

duration for three limiting cases. Note that has a minimum as a function of R. The pulse duration dependence is summarized in figure 1 and compared with experimental data for two different

glasses, one which is known to contain platinum inclusions and one which is presumed to by virtue

of its having been melted in a platinum crucible. If the inclusions are more accurately described

as disks than as spheres, as is suspected in ruby [8], and if the face of the disk is illuminated

rather than the edge, then the same R and At dependences are expected provided the R in M and in eq. (5) is taken as the disk's radius and the R in eq. (2) as its thickness.

Bulk absorption resulting, for example, from impurities or color centers can also cause laser

damage either by simple heating to a temperature which permanently alters the optical properties

of the material or by fracture of the region surrounding the beam by thermal expansion [9]. When

thermal conduction out of an illuminated path of radius r^ is negligible (r^^ / At » D), the laser

energy densities required to cause a temperature change AT in the beam or a stress S at its boundary

are respectively,

tS^ = C A T/a (6) d

and

(S, = CkS/8a, (7) d

where a is the bulk absorption coefficient and the other symbols are as defined after eq. (1). When

conduction is limited by the finite radial dimension R^ of the sample instead of by thermal diffusivity,

eq. (6) must be multiplied by Rg^/r^ , and eq. (7) does not apply at all since there will be no unhealed material to be strained.

2 2 When conduction becomes important (r^ /At « D < Rg /At), the illuminated region can be treated

as a continuous line source [12] supplying heat to the surrounding volume. Then the energy densities required to cause a damaging temperature change AT or a thermal stress S in the vicinity of the beam are respectively,

[4 GDAT/a In (4D At/r^ )] [At/r^ ] (8) d b b

107
and

5^ (4 CkDS/|3a) (At/r^^). (9)

The derivation of eq. (9) follows the same arguments as those presented for eqs. (3) through (5).

It is possible, of course, that processes other than ordinary bulk absorption contribute to general

heating of the irradiated volume at laser intensity levels. The absorption coefficient Ci should be

understood to include all mechanisms for which the heat deposited is directly proportional to the local

laser energy density. Experimental data at a pulse duration of one millisecond is available for glass

intentionally doped with iron [9]. In figure 2 the dependence of the bulk absorption damage threshold on At and r as given by eqs, (6) through (9) is fit to a data point for a = 10~^ cm"''-.

2. 2. Conduction Electron Absorption

It may be possible for an electron in the conduction band of a material to be accelerated by the laser field to an energy greater than the band gap [!]• Each such electron would then be capable of exciting another electron into the conduction band by impact ionization, leading to an exponential

increase in the number of conduction electrons N.

N = N 2 , (10) o

where t' is the time required to accelerate an electron to the energy of the conduction band. Inter- action of the growing number of electrons with the lattice could cause electron avalanche breakdown.

Conduction electrons absorb photons from the laser field only in conjunction with impurity and

phonon scattering However, scattering also extracts energy from the electrons; so the first requirement which must be met to create an electron avalanche is that the electric field be strong

enough to cause a net increase of electron energy in time until the band gap energy is reached. This

requirement determines a minimum value of electric field E^^j^^^ and an associated laser power

density (power per unit cross-sectional area) at which electron avalanche will occur [1,14]. Since

the phonon density decreases at lower temperatures, will increase with decreasing temperature

as long as phonon scattering predominates. At low enough temperatures, however, P^ will reach a temperature independent limit set by impurity scattering.

A second requirement for the electron avalanche to lead to actual breakdown is that the field be

strong enough to cause the creation of a sufficient number of electrons during the pulse. Considering

the problem classically and assuming collision losses to be negligible, the time derivative of electron

energy can be written as [1,15]

dS /dt = f (5 )E ^

, (11) e e o

where f (t?^) is some function of S . The time t is then given by

2 r> Cr,.,.n-1

t = e" f [f (<5)]' d<?, ' (12) O

where S is the energy needed to raise an electron to the conduction band. Substituting t from eq.

(12) into'^eq. (1 time At gives

c

(12) into eq. (10) and solving for the energy density required to produce Nj^ conduction electrons in a do°^ E^ At « In (Nbo/N ). (13)

108
Since both requirements noted above must be met, and provided that the necessary number of elec- trons is independent of At, the dependence of on pulse duration changes from linear with At

for long pulses to independent of At for short pulses.

In the preceding paragraphs it has been tacitly assumed that the lifetime of electrons in the conduction band T„ is long compared to t , the time between generations in the electron avalanche. If T /t is less than about five, however, the avalanche process is slowed and a somewhat greater

energy density is required to cause damage at a given pulse duration, When Tg/t is less than two,

avalanche development is impossible. Taking this into account and noting the variation of t' with E

as given by eq. (12), one concludes that at most the effect of a short Tg is to make the transition

between the two forms of At dependence more gradual and to shift the constant power threshold for long pulses from the one determined by E^^^ to a higher nearly constant power required to keep

Tg/t greater than two. A complicating factor which has not been treated here is the possibility of raising electrons to intermediate states short of the conduction band [16].

Some difference of opinion exists over whether electron avalanche breakdown actually occurs Recent calculations [17] of energy transfer rates from an optical field to a conduction electron and

from an electron to the lattice via longitudinal phonon scattering, suggest that an electron avalanche

is unlikely in ruby or sapphire because the electron energy rises only slightly in transfering energy

from the optical field to the lattice. These calculations were made to lowest order in optical intensity and electron-phonon coupling, and it is possible that higher order solutions will lead to different

I conclusions. In the meantime, however, the effects of low energy conduction electrons should be

considered.

The transfer of energy from a field E with wavelength X to electrons of effective mass m-":= couple

; to longitudinal optical phonons may be characterized by an optical absorption coefficient [17]

!l Q!= (16 77^ N e^ y) /(Xm=;< E^ ), (14)

1 o

where N is the conduction electron density and y, the rate at which the field does work on an electron

is proportional to . One possibility is that a substantial number of electrons are excited early in the laser pulse from impurity levels close to the conduction band. If N remains roughly constant

for the rest of the pulse, then these electrons simply contribute to the bulk absorption described

in eqs. (6) through (9).

At the high intensity levels which can be reached in lasers, conduction electrons may also be

created by the simultaneous absorption of several photons [18,19]- Various schemes have been

proposed for two-, three-, and four-photon absorption in ruby [15,19-23] and four-photon absorption (of ruby radiation) in glass [24]. Since the probability for n-photon absorption increases with

decreasing n, anything which affects the number of photons required to get electrons into the conduction band will influence the probability of the multiphoton process. Clearly the photon frequency

is an important parameter. In addition, elevating electrons to excited states by optical pumping or

altering the energy level structure by addition of impurities [4] may affect the importance of multiphoton absorption.

The probability of n-photon ionization depends on the electric field strength through a factor

E^n, so N E^n ^t. If Q: of eq. (14) is averaged over the pulse duration At and substituted in either

eq. (6) or eq. (7), the dependence of the damage threshold on pulse duration is given by

At

(n-l)/(n+l)

2 subject to the condition r / At » D as noted before eq. (6).

In figure 3 the pulse duration dependence predicted for the electron avalanche breakdown threshold is fit to a group of experimental points thought to represent avalanche damage [l]. A curve for damage by low energy conduction electrons created through multiphoton absorption is also given,

although no related data is available.

109
2. 3. Stimulated Brillouin Scattering

Under certain conditions it is possible to combine the electrostrictive generation of an acoustic wave by the interaction of two electromagnetic waves (EMW) with the generation of an EMW by the Bragg diffraction of an initial EMW from an acoustic wave. This leads to stimulated Brillouin

scattering (SBS), an internal feedback mechanism for amplifying an acoustic wave (oJa > k^) and a secondary EMW (w^, k ) at the expense of an input laser beam (W^ , k^) [25]. At high enough power ' levels damage may occur from the mechanical stresses associated with the acoustic wave [26]. The

stress arising from heating due to damping of the acoustic wave is negligible by comparison [27].

Depending on the pulse duration, transient or steady state SBS theories may be appropriate [28,

29]. In either case the acoustic power level reached by the end of the pulse will depend on the length

of the interaction region, the mechanical parameters of the material (such as acoustic attenuation and

elastic constants), the electromagnetic parameters (such as permeability, permitivity, and index of refraction), and the Pockel's elasto-optic constants which couple mechanical and optical phenomena

in the material. In addition, the pulse duration At is of primary importance since a finite time,

dependent on the laser power density P(j.{,> is required to generate an acoustic power P^j^g.- Experimental evidence of this delay in acoustic generation has been found in quartz [27], glass [30], and

CS2 [31].

For pulses too short to establish steady state SBS and in the limit of an infinite interaction

length [28]

P, °= At P^ \ . •,. , . (16) da ds

and [28, 32]

P^^ o: exp [(AP^^At)^/^] = exp (A^^' sj'^). : (17)

Here A is determined by material parameters. Comibining eqs. (16) and (17) leads to ' . BP

^dt tin(-^)]^ ; (18)

where B depends on the material and the laser frequency. Since the breaking strength of the material

corresponds to a particular value of P^g^> the laser energy density required for damage will increase

as At is reduced

The use of eq. (17) assumes that P^^ does not reach a limiting value in the time At. There may

be an intermediate range of At for which P^^ does reach its limiting value but for which eq. (16) is still correct [28]. In that case

Pda " ^dl - ^dl (19)

so that the laser energy density required for damage is independent of At. Finally, for long enough

At, steady state SBS can be achieved. Then P^^ increases exponentially with P^^^ [29, 32] (until

P<^g approaches P^^) and P^^ is proportional to the product of P^jg and [27]. Thus for long At,

damage occurs at a constant power level and S^i ^ At. The At dependence of the threshold for damage by SBS is illustrated in figure 4.

110
For a non-lasing sample irradiated by coUimated laser light, the peak SBS acoustic intensity- occurs at the entrance end of the sample [33], suggesting that damage caused by SBS should be found

very near the entrance face. That the damage is not found at this location in a particular experiment

does not provide sufficient basis for eliminating SBS as a possible damage mechanism, however,

since a focused probe beam or the self-focusing mechanisms described in the next section may cause

the peak acoustic intensity to be generated further from the surface

2. 4. Self-Focusing

All of the mechanisms discussed to this point are more likely to lead to damage for a given At

if the laser energy density is increased. Thus any degree of self-focusing, i. e. any reduction of the laser beam diameter below the value predicted from the optical properties of the unirradiated material, is potentially important in the creation of laser damage. Such a reduction can result from any

process which leads to an increase of the index of refraction with increasing light intensity. In solids

where gross molecular motion is frozen out, possible self-focusing mechanisms include electrostriction [3, 34], electronic distortion [35-37] or molecular librations [38], and absorptive heating

[391

Electrostriction is a likely mechanism for self-focusing in transparent dielectrice under Qswitched and long pulse laser irradiation [3], The net electrostrictive force at any point in a material is proportional to the gradient of the square of the electric field. Thus a radially symmetric

beam whose intensity decreases smoothly with distance from the axis ^ causes a radially symmetric

compression and an associated change in the refractive index which leads to self-focusing. Since

the process is a dynamic one, the compression takes the form of a radially propagating acoustic wave with velocity v . For a given initial beam radius r, , a minimum time T = r. /v is required

' a " b b a . for the acoustic wave to propagate across the beam. In a single pass through a lossless medium

and for At »T, self-focusing will overcome normal diffraction spreading from a collimated beam at the self-trapping threshold given by

(?, = g (n At/rl , (20)

Q 1 o b

where C-j^ depends on the elastic properties of the material, g is a function of the original refractive

index n^, and X is the laser wavelength in vacuum.

For At « T the acoustic wave does not have time to develop fully, and trapping requires an in- creased energy density given by

. - C,g (n )X^/At. (21) a ^ o

Equations (20) and (21) predict a constant total power threshold [34] for At »t and an energy density

threshold varying inversely with At for At « T. To illustrate this behavior, curves based on cal- culations for ruby laser radiation in BK-7 glass [40] are plotted as solid lines in figure 5 along with

a data point for damage accompanied by self-focusing from a 40ij, initial beam radius [41]. The

exact agreement between this measurement and the calculations is probably fortuitous since the damage level should exceed the trapping threshold in order to reduce the beam cross-section significantly

The beam must also travel a finite distance in the material for self-focusing to have a notable

effect An approximate focusing length can be defined by equating the optical path length (n^ + An)L£ along the beam axis with the path length n^ (L^^ +^h^^^^ from the beam perimeter to the axis,

where An is the change in refractive index on axis [42]. Using appropriate limiting forms for An

[40] and requiring to equal the sample length L, gives

Large local intensity variations over the beam cross-section can cause localized self-focusing

resulting in the formation of multiple filaments

111
2,2 - - - • °= At/L (22) d b ^

'

for At »T and

0= rj^/ {1} At) (23) d D

for At «T. When a sample is irradiated by a sharply focused beam, the length which is useful for development of self-focusing is less than L. In the extreme case the sample length loses all significance because the energy density is high only over a short distance near the focused minimum.

The dashed electrostriction curves in figure 5 have been located on the energy density axis by

fitting eq (22) to damage measurements [41] made in BK-7 with a 125j:xbeam. At about this beam

size the damage threshold was observed to begin rising with increasing beam radius. Since significant focusing will not occur unless the requirements of both eqs. (20 and (21) and those of eq. (22)

and (23) are met, the threshold for damage initiated by electrostrictive self focusing has a minimum

as a function of both r and At. It should be emphasized that the increase in trapping threshold for short pulses does not occur because of a reduced acoustic response, but rather because of the time

(T = r^^/ v^) required for that response to fully develop. In other words, even extremely short pulses can be focused by this mechanism if they are preceded by other pulses which initiate acoustic lens

formation. A mode-locked laser produces just such a pulse train.

Other self-focusing processes with much shorter relaxation times contribute a quadratic term

to the refractive index n, even for a single pulse with duration on the order of picoseconds. These

include electronic distortion [ 35-37] and molecular libration [38]. Setting the approximate focusing

length as defined before eq. (22) equal to the Raleigh range for a beam of initial radius r^, gives an order of magnitude result for the trapping threshold

2 „ 3 , ,2

(X C/I6ir n ) (At/r ), (24) b

2 where n = n^ + n^ . Also, following the same arguments for the effect of sample length as were

given for electrostrictive focusing leads to the further requirement,

(?, ^ (cn^/ 16 77 n^) (rj At/L^). " (25) a o Z b

-13 4 Using n^ = 2x10 esu [36], plots of eqs. (24) and (25) for ruby radiation in glass have been

added to figure 5 for representative values of beam radius. Again the trapping threshold is indicated

by solid lines and the energy requirement resulting from a finite (10 cm) sample length by dashed

curves. It is clear that the electronic distortion or molecular libration mechanisms dominate for very short pulses, while electrostriction becomes competitive for Q- switched or longer duration

pulses. In any case the energy density required for significant focusing has a minimum as a function

of initial beam radius, and for mechanisms with relaxation times shorter than the pulse duration the location of this minimum is found by equating eqs. (24) and (25). The result is

r . (X L/n TT)^^^ • ... (26) mm o

independent of n^ and At.

4 This is approximately the value measured for 1. 06fi radiation in fused silica.

112
When dn/dT is positive, heating by absorption at the laser frequency will also contribute to self- focusing. Even materials whose total derivative is found to be negative by a steady state measurement, can exhibit thermal self-focusing for pulses sufficiently short (At «T) that the effective value

of dn/dT is just the positive partial derivative at constant density [39]. Moreover, since unheated

material surrounding a laser irradiated area will limit thermally induced density changes, it may

be possible to obtain thermal self-focusing for longer pulses as well [43],

The approximate threshold for significant thermal self-focusing is given by the larger of eqs.

(Z4) and (25) with n^^ taken as

n. = (dn/dT) „ {a cn At/87r C), 0?^ (27) 2 eff o ^'»-J ^

'

2 , provided only that At « ^^/D so that the heat lost from the beam path during the pulse is negligible.

As with the other mechanisms the threshold has a minimum as a function of initial beam radius, but thermal self-focusing is unique in that no pulse duration d ependence is expected [42] provided At is much less than both t and r^/D. Some tentative experimental evidence exists to confirm such a lack of At dependence for self-focusing of short pulses [?].

The importance of this mechanism relative to those plotted in figure 5 can be judged by comparing values of n For (Sn/aT). = 5x10"^ [44], a = 0. 25%cm"^ At = 10"^ sec, and C = 0. 9 cal/

cm - °K, the n^ for thermal self-focusing is approximately 0, 6xlO"''-'^ esu. This is somewhat less than the n^ previously noted for an electronic distortion type of focusing. However, a rather small

increase^ m absorption would make the two comparable at this pulse duration. So, although for very

short pulses thermal self-focusing is expected to be negligible compared to other mechanisms, it must be regarded as potentially important when At approaches 100 nanoseconds or when absorption

at the laser frequency is high.

Thermal effects also occur due to other radiation sources such as flash lamps [45], These are

not considered here.

3, Conclusions

Pulse duration is an important parameter for each of the mechanisms discussed in the preceding

pages. As shown in the equations of Section 2 and in figures 1 through 5, the form of the time dependence varies from one mechanism to another. This raises the possibility that for a given material different mechanisms are responsible for initiating damage in different ranges of pulse duration

and suggests that experimental identification of damage mechanisms can be greatly aided by measuring the pulse duration dependence of the damaging energy density. The incident beam radius has

also been demonstrated to be an important parameter, particularly for self -focusing mechanisms,

which also are effected by sample length. Since most mechanisms are expected to cause damage

at energy densities independent of beam radius and sample length, variation of these parameters

can be useful both in determining whether self-focusing is involved in a particular laser damage

problem and in designing systems less susceptible to such damage.

Having explicitly shown the importance of the above parameters and alluded to the significance

of others such as temperature, optical pumping conditions, beam focusing, and laser frequency, it is appropriate to emphasize the need to carefully control and specify these parameters in any damage

experiment. Hopefully such experiments combined with further theoretical efforts will lead to un- ambiguous identification of limiting damage mechanisms over the useful range of laser system

parameters. Progress in preventing damage can then be expected through discrimination against

the mechanisms involved.

4, Acknowledgements

Discussions with C. M. Stickley, R. A. Bradbury, E. L. Kerr, C. R. Giuliano, R. W. Hellwarth,

and many others with whom I have enjoyed less extensive contact are gratefully acknowledged.

113
5. Symbols Used in The Text

Subscripts

a = acoustic

h = host

i = inclusion

1 = laser

s - secondary

Symbols

OL = bulk absorption coefficient

j3 = thermal volume expansion coefficient

C = heat capacity per unit volume

c = velocity of light in vacuum D = thermal diffusivity

E = instantaneous electric field strength

= electric field amplitude

e = charge on an electron

e^ = spectral emissivity at the laser wavelength

= band gap energy

(Sj = energy density (energy per unit c ros s - sec tional area)

= electron energy

k = volume compressibility

k = wave vector L - sample length

Lf = focusing length

X

- wavelength in vacuum M = multiplication factor to correct particle cross-section for Mie effect m* = electron effective mass N = conduction electron number density

= value of N required for breakdown

n = number of photons absorbed in n-photon ionization n = refractive index

n^ = original refractive index

n2 = coefficient for quadratic term in expression for n An = change in n

P(j = power density (power per unit cross-sectional area)

R = inclusion radius

R = sample radius

s ^

r = distance from center of inclusion

r^ = beam radius

S = breaking strength, damaging stress T = temperature

t = time

t = time required to accelerate an electron to the energy of the conduction band

At = pulse duration

T = time required for acoustic wave to propagate across the beam

Tg = conduction electron lifetime

V = velocity

CO = angular velocity (frequency times Itt)

6. References

[1] G. M. Zverev, T. N. Mikhailova, V. A. Pashkov, and N. M. Soloveva, Soviet Phys. - JETP 26, 1053 (1968).

Final Report (1968)

[4] G. Nath and G. Walda, Z. Naturforsch,

23a , 624 (1968).

[5] J. Davit, J. Appl. Phys. ^i- ^052 (1968)

[2] P. V. Avizonis and T. Farrington, Appl.

Phys. Letters 7, 205 (1965).

[3] E. L. Kerr, ONR Contract N00014-67-C-0468,

114
[6] C. G. Young and R. F. Woodcock in Damage

in Laser Glass ASTM STP 469 , ed. A. J. Glass, A. H. Guenther, C. M. Stickley, and

J. D. Myers (American Society for Testing

and Materials, Philadelphia, 1969).

[7] J. Davit in Damage in Laser Glass ASTM

STP 469 , ed A. J. Glass, A. H. Guenther,

C. M. Stickley, and J. D. Myers (American

Society for Testing and Materials, Philadelphia, 1969).

18] F. R. Charvat, G. A. Keig, O. H. Nestor,

P. E. Otten, and J. C. Smith, Government

Contract NONR-4132(00), Annual Technical

Summary Report (1967).

[9] R. D. Maurer, W. W. Lester, and M. E. Vance, Government Contract N00014-66-

C0159, Final Technical Report (1967).

[10] M. Born and E Wolf, Principle s of Optics

(Pergamon Press, Oxford, 1965), 3rd

Revised ed. , p663.

[11] L. M. K. Boelter, V. H. Cherry, H. A. Johnson, and R. C. Martinelli, Heat

Transfer Notes (McGraw-Hill Book Co. , N. Y. , 1965), p630.

[12] H. S. Carsl aw and J. C. Jaeger, Conduction

of Heat in Solids (Oxford University Press,

London, 1959), 2nd edition.

[13] R. W. Hopper and D, R, Uhlmann, submitted

to Journal of Applied Physics.

[14] A. Wasse rman, Appl. Phys. Letters 10, 132

(1967) . ~

[15] E. A. Sviridenkov, Soviet Phys. - Solid State

9, 1917 (1968).

[16] Y. P. Raizer, Soviet Phys. - Usp. _8, 650

(1966).

[17] C. R. Giuliano, R. W. Hellwarth, L. D. Hess,

and G. R. Rickel, Government Contract

F19628-69-C-0277, Semi-annual Report No.

1 (1970).

[18] L. V. Keldysh, Soviet Phys. - JETP 20_, 1307 (1965).

[19] F. V. Bunkin and A, M, Prok.horov, Soviet

Phys. - JETP 21_, 725 (1965).

[20] V. A. Pashkov and G. M. Zverev, Soviet

Phys. - JETP 24, 516 (1967).

[21] T. P. Belikova, A. N. Savchenko, and E. A. Sviridenkov, Soviet Phys. - JETP 27_, 19 (1968) . [22] T. P. Belikova and E. A. Sviridenkov, JETP

Letters 3, 257 (1966).

[23] T. P. Belikova and E. A. Sviridenkov, JETP

Letters 1, 171 (1965).

[24] B. S. Sharma and K. E. Rieckhoff, Can. J. Phys. 45, 3781 (1967).

[25] R. Y. Chiao, E. Garmire, and C. H. Townes,

Proc. of the Enrico Fermi Int'l School of Physics , Course XXXI, ed. P. A. Miles

(Academic Press, N. Y. , 1964).

[26] R. Y. Chiao, C. H. Townes, and B. P. Stoicheff, Phys. Rev. Letters 12, 592 (1964).

[27] C. L. Tang, AF Contract AF19(628)-5677,

Final Report (1968).

[28] N. M. Kroll, J. Appl. Phys. 36_, 34 (1965).

[29] J. Walder and C. L. Tang, Phys. Rev. 155, 318 (1967).

[30] L. D. Khazov and A. N. Shestov, Optics and

Spectroscopy XXV, 248 (1968).

[3l] D. von der Linde, M. Maier, and W. Kaiser,

Phys. Rev. 178_, 11 (1969). [32] E. F. Hagenlocker, R. W. Minck, and W. G. Rado, Phys. Rev. 154, 226 (1967). [33] J. Walder and C. L. Tang, Phys. Rev. Letters 19, 623 (1967). [34] R. Y. Chiao, E. Carmine, and C. H. Townes,

Phys. Rev. Letters 13, 479 (1964).

[35] R. G. Brewer and C. H. Lee, Phys. Rev. Letters 21, 267 (1968). [36] M. A. Duguay and J. W. Hansen, Spring

Meeting of the Optical Society of Am. (1970). [37] R. R. Alfano and S. L. Shapiro, Phys. Rev. Letters 24, 592 (1970). [38] R. Polloni, C. A. Sacchi, and O. Svelto,

Phys. Rev. Letters 23, 690 (1969).

[39] R. L. Carman, A. Mooradian, P. L. Kelley,

and A. Tufts, Appl. Phys. Letters 14, 136

(1969).

[40] E. L. Kerr, to be published in IEEE J. of Quantum Electronics (August 1970).

[41] .G. N. Steinberg and E. L. Kerr, unpublished. [42] F. W. Quelle in Damage in Laser Glass

ASTM STP 469 , ed A. J. "Glass, A. H. Guenther, C. M. Stickley, and J. D. Myers

(American Society for Testing and Materials, Philadelphia, 1969).

[43] G. M. Zverev, E. A. Levchuk, E. K. Maldutis, and V. A. Pashkov, JETP Letters 11, 108 (1970).

[44] E . Snitzer, private communication (June

1970).

115
[45] R. L. Townsend, CM. Stickley, and A. D. Maio, Appl. Phys. Letters 7, 94 (1965).

10 10 10 10

PULSE DURATION (sec)

Fig. 1 Threshold for damage due to absorption by platinum inclusions in glass. The pulse

duration and inclusion radius dependence of eqs. (1), (2), and (5) have been fit to data

from reference [2] {indicated by A) for glass known to contain Pt inclusions and data

from reference [6] (indicated by O) for glass presumed to contain Pt inclusions. The

inclusion radius R and a scale factor for energy density were treated as free parameters

and varied to obtain the best fit while requiring the break points in the curves to be at pulse durations of R^/Dp^ and R^/^gj^^gg. The resulting inclusion sizes are indicated.

The dashed curves and R values in parentheses illustrate the theoretical dependence on R for the glass in reference [6].

10° -

CO 10'

> 4 o 10 z

JL _1_ .-4 10 10 I 10

PULSE DURATION (sec) .-10 8 10 10 10

PULSE DURATION (sec)

Fig. 2 Threshold for damage by bulk absorption for three beam radii in glass

with an absorption coefficient of 0. 1 cm"^. The pulse duration dependence of eqs. (6) through (9) is fit to data from reference [9] taken with

millisecond pulses. The break points occur at At = rb/°glass'

logarithmic dependence on At/r^ in eq. (8) is neglected.

Fig. 3 Threshold for damage due to electron

avalanche breakdown in ruby (solid

line) and to low energy conduction

electrons created by three photon

ionization (dashed line). The constant power density requirement

noted after eq. (10) and the constant energy density requirement of eq.

(13) are fit to data from reference

[1] for electron avalanche damage.

The position of the dashed curve

illustrating eq. (15) has been chosen

arbitrarily since no data are

available

.

116
-8 -4 10 ' 10 " 10 " 10

PULSE DURATION (sec

Fig. 4 Predicted pulse duration dependence of the threshold for damage due to stimulated

Brillouin scattering. The energy scale is estimated from quartz and glass data in A. I. Ritus and A, A, Manenkov, JETP Letters 6_, 349 (1967) and from quartz

calculations in reference [26]. The time scale is estimated from quartz data in reference [29]. The exact form of the dashed part of the curve cannot be determined

without knowing B in eq. (18).

PULSE DURATION (sec)

Fig. 5 Self -trapping of ruby radiation in glass for several beam radii by electrostriction and

by mechanisms with a refractive index change which is quadratic in the electric field. The solid electrostriction curves, which indicate the trapping threshold, result from

fitting eq. (20) to calculations in reference [40] and are compared with a data point

(A) from reference [41] for a 40u beam. The dashed electrostriction curves, which

indicate the additional requirement imposed by a 10 cm sample length, result from a

fit of eq. (22) to a damage measurement in reference [41] with a 125/i beam (O). The

other solid curves are a plot of the trapping threshold predicted by eq. (24) for n^ = 2xl0"13 esu. while the other dashed curves are a plot of the sample length

restriction given by eq. (25) for a 10 cm sample.

117
Appendix II

Participants''"

E. D. Baird, Lawrence Radiation Lab., Livermore, California 94550

M. Bass, Raytheon Co., Waltham, Massachusetts 02154

R. W. Beck, Owens-Illinois Inc., Toledo, Ohio 43607

H, Bennett, National Bureau of Standards, Washington, D.C. 20234

R. J. Bieringer, Owens-Illinois Inc., Toledo, Ohio 43607

E, S. Bliss, A.F. Cambridge Research Lab., Bedford, Massachusetts 01730

N. L. Boling, Owens-Illinois Inc., Toledo, Ohio 43607

J. Davit, Campagnie Generale D' Electricite , 92 -Marcousses , France

M. A. Duguay, Bell Telephone Labs, Murray Hill, New Jersey 07974

D. F. Edwards, Colorado State Univ., Fort Collins, Colorado 80521

S. J. Ekstrom, Lawrence Radiation Lab., Livermore, California 94550

A. Feldman, National Bureau of Standards, Washington, D.C. 20234

A. D. French, General Electric, Syracuse, New York 13201

D. H, Gill, Los Alamos Scienti f ic Lab .

, Los Alamos, New Mexico 87544

C. R. Giuliano, Hughes Research Labs, Malibu, California 90265

A. J. Glass, Wayne State Univ., Detroit, Michigan 48202

A. H. Guenther, Kirtland A.F.B., New Mexico 87117

R. Hellwarth, Hughes Research Labs, Malibu, California 90265

L. T. James, Lawrence Radiation Lab, Livermore, California 94550

P. M. Johnson, Lawrence Radiation Lab., Livermore, California 94550

C. R. Jones, Kirtland A.F.B., New Mexico 87117

Y. Ksander, Institute for Defense Analyses, Arlington, Virginia 20022

H. Lee, Owens-Illinois Inc., Toledo, Ohio 43607

J. R. Lenhoff, A.F. Cambridge Research Lab., Bedford, Massachusetts 01730

P. Mace, Los Alamos Scientific Lab., Los Alamos, New Mexico 87544

J. D. Myers, Owens-Illinois Inc., Toledo, Ohio 43607

C. A. Pitha, A.F. Cambridge Research Lab., Bedford, Massachusetts 01730

R. C. Puttbach, Litton Industries, Morris Plains, New Jersey 07950

L. R. Rothrock, Union Carbide Crystals, San Diego, California 92123

R. R. Rudder, Kirtland A.F.B., New Mexico 87117

P. M. Rushworth, Martin Marietta Corp., Orlando, Florida 32805

Approximately 100 others who did not formally register, attended selected sessions.

118
T. Saito, Kirtland A.F.B. , New Mexico 87117

C. Y. She, Colorado State Univ., Fort Collins, Colorado 80521

L. D. Smith, Harshaw Chemical Co., Solon, Ohio 44139

E. Snitzer, American Optical Co., Southbridge, Massachusetts 01550

J. B. Sonderman, Lawrence Radiation Lab., Livermore, California 94550

K, Steinbruegge, Westinghouse, Pittsburgh, Pennsylvania 15235

C. M. Stickley, A.F. Cambridge Research Lab., Bedford, Massachusetts 01730

C. C. Wang, Ford Scientific Lab., Dearborn, Michigan 48121

E. J. Woodbury, Hughes Aircraft Co., Culver City, California 90230

R. F. Woodcock, American Optical Corp., Sorthbridge, Massachusetts 01550

A. W. Young, Rank Precision Industries, Inc., Des Plaines, Illinois 60018

C. G. Young, American Optical Corp., Southbridge, Massachusetts 01550

119

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