NBSIR 73-119

LASER DAMAGE IN MATERIALS

Albert Feldman, Deane Horowitz, and Roy M. Waxier

Solid State Materials Section

Inorganic Materials Division

Institute for Materials Research

National Bureau of Standards

Washington, D. C. 20234

February 1973

Sem i— Annual Technical Report

Period Covered: August 1, 1972, to January 31, 1973

ARPA Order No. 2016

Prepared for Advanced Research Projects Agency

Arlington, Virginia 22209

NBSIR 73-119

LASER DAMAGE IN MATERIALS

Albert Feldman, Deane Horowitz, and Roy M. Waxier

Solid State Materials Section

Inorganic Materials Division

Institute for Materials Research

National Bureau of Standards

Washington, D. C. 20234

February 1973

Semi-Annual Technical Report

Period Covered: August 1, 1972, to January 31, 1973

Prepared for Advanced Research Projects Agency

Arlington, Virginia 22209

ARPA Order No. 2016

U. S. DEPARTMENT OF COMMERCE, Frederick B. Dent. Secretary

NATIONAL BUREAU OF STANDARDS, Richard W. Roberts. Director

LASER DAMAGE IN MATERIALS

Albert Feldman, Deane Horowitz, and Roy M. Waxier

Solid State Materials Section

Inorganic Materials Division

Institute for Materials Research

ARPA Order No 2016

Program Code Number 3D10

Effective Date of Contract ...... January 1, 1972

Contract Expiration Date December 31, 1973

Principal Investigator Albert Feldman

(301) 921-2840

This is a progress report. The work is incomplete and is

continuing. The views and conclusions contained in this document

are those of the authors and should not be interpreted as necessarily

representing the official policies, either expressed or implied, of

the Advanced Research Projects Agency or the U. S. Government.

Parts of this report, appropriately modified, will be submitted

to a professional journal for publication.

LASER DAMAGE IN MATERIALS

Abstract

The relative contributions of the Kerr, electrostrictive , and

thermal effects to the self-focusing thresholds of borosilicate crown

glass, fused silica, and dense flint glass have been estimated from

an analysis of damage threshold data for linearly polarized and

circularly polarized radiation. The measurements were made with a

Nd: glass laser operating in the TEMOQ mode with a temporal pulse width

of 25 ns . The Kerr effect appears to be the largest effect. The

thermal effect is also significant. The electrostrictive effect is

smallest. Reasonable values of absorption coefficient are calculated

from the thermal contribution. The results are in qualitative agreement with the work of others. Self-focusing data obtained with

linearly polarized and circularly polarized radiation are presented

for yttrium aluminum garnet (YAG) and five commercial Nd: doped laser

glasses. The YAG data agree with the theory of self-focusing. Near

the threshold the laser glass data appear to indicate intrinsic

damage rather than self-focusing. Differences between the various

laser glasses are small. Self-focusing data obtained in dense flint

glass with a longer focal length lens are also presented. An electrooptic shutter actuated by a laser triggered spark gap is discussed.

Table of Contents

1 . Technical Report Summary 1

1.1 Technical Problem 1

1.2 General Methodology 1

1.3 Technical Results 2

1.4 Department of Defense Implications 3

1.5 Implications for Further Research 4

2. Technical Report 4

2.1 Self-Focusing Mechanisms in Optical Glasses. ... 4

2.1.1 Introduction 4

2.1.2 Theoretical Considerations 8

2.1.2.1 The Kerr Effect 9

2.1.2.2 Electrostrictive Self-Focusing 9

2.1.2.3 Thermal Self-Focusing 12

2.1.2.4 Combined Effect 13

2.1.3 Experimental Procedure 14

2.1.4 Results and Discussion 18

2.1.5 Conclusions 26

2.2 Self-Focusing Studies in Yttrium Aluminum Garnet

(YAG) , Dense Flint Glass (SF 55) , and Five

Commercial Nd: Doped Laser Glasses 27

2.2.1 Introduction 27

2.2.2 Self-Focusing Length Measurements 27

i
2.2.3 Results and Discussion 28

2.2.3.1 YAG 28

2.2.3.2 SF 55 Glass. 30

2.2.3.3 Five Commercial Laser Glasses 32

2.3 Laser Triggered Spark Gap and Pockels Cell .... 39

2.4 Acknowledgments 39

2.5 References 41

ii
LASER DAMAGE IN MATERIALS

1. Technical Report Summary

1 . 1 Technical Problem

The main objective of this program is the study of self-focusing

in materials used in conjunction with high-energy laser systems. These

studies are necessary because self-focusing is the main process which

leads to bulk-intrinsic damage in laser materials. The damage appears

as filamentary tracks in materials exposed to high-intensity laser radiation. Three mechanisms have been proposed to explain the damage:

electrostrictive , Kerr, and thermal self-focusing. An understanding of

the relative importance of these mechanisms is necessary if we are to

fabricate, in a systematic way, materials with high self-focusing thresholds.

1.2 General Methodology

Laboratory experiments were conducted to study the process of

self-focusing in borosilicate crown glass (BSC 517) , fused silica, dense

flint glass (SF 55) , yttrium aluminum garnet (YAG) , and five commercial

Nd: doped laser glasses. The output of a Q-switched Nd: glass laser

operating in the TEMQO mode was focused into the samples. The laser

beam was characterized fully as to pulse energy, pulse time evolution,

beam profile, and reproducibility (see section 2.1.3 of Technical Report).

Two different experiments were performed: (1) Damage thresholds were

measured for both linearly and circularly polarized radiation; (2) se'lffocusing lengths, which are related to the damage track lengths , were

measured as a function of laser beam peak power.

1
A theoretical analysis of the data was made by assuming that

the experimental damage threshold is the self-focusing threshold. The

contributions of the Kerr, electrostrictive , and thermal effects to the

intensity dependent refractive index were theoretically analyzed. The

measurement of damage thresholds for linearly and circularly polarized

radiation provided the necessary and sufficient data from which to estimate

the relative importance of each of the effects to self-focusing. The selffocusing length data were compared to the theoretically predicted values.

1 . 3 Technical Results

The ratio of damage thresholds for circular polarization to linear

polarization is found to be greater than unity in all the samples tested.

The damage is assumed to result from self-focusing. The analysis of the

data in BSC 517, fused silica, SF 55, and YAG indicates that the Kerr effect

is the largest contributor to self-focusing with a significant contribution

from the thermal effect. Electrostriction is the smallest of the effects

for the focusing beam geometry used. The latter result contradicts an

earlier report in which we neglected the thermal effect. The electrostrictive effect would be negligible for an unfocused beam. Reasonable

values of the absorption coefficient are obtained from the estimated

thermal effect.

Using a focused geometry with a 181-mm focal length lens, we

found the self-focusing length measurements in YAG and SF 55 to be in good

agreement with a theory which predicts self-focusing lengths as a function

of peak power. Using a 362-mm focal length lens in SF 55, we found that

the self-focusing lengths deviate from theory significantly.
Self-focusing length measurements were made in five laser

glasses with both linearly and circularly polarized radiation. The data

suggest that the damage threshold measured is not the self-focusing

threshold. The data deviate strongly from self-focusing theory. No

significant difference was found in the behavior of the different glasses.

The capability of our laser system has been expanded to produce

pulses with half-widths of 2.5 ns. This has been accomplished by inserting

a laser-triggered spark gap and electro-optic shutter into the beam.

Previously, the pulse width of our laser was limited to ^ 25 ns.

1.4 Department of Defense Implications

The Department of Defense has a need for high-powered solid

state laser systems. Thus it is important (1) to understand the processes

which limit the output power of such systems, (2) to obtain data which

suggest methods for increasing the power output of a given system, and

(3) to verify theories which predict the performance of such systems.

Self-focusing is the main process responsible for bulk intrinsic damage

in high-power pulsed laser systems. We have addressed ourselves to the

problem of self-focusing and have reached the following conclusions:

(1) The Kerr effect is the main process leading to self-focusing for laser

pulses with less than 25 ns width at half-maximum power. The Kerr effect

increases as the refractive index increases. The implication is that

materials with low refractive indices will have high self-focusing

thresholds. (2) The thermal effect cannot be neglected for pulse widths

> 2 5 ns. For shorter pulses the effect decreases in importance; however,

in high repetition rate systems, thermal self-focusing can be a problem

3
because of the integrating nature of the effect. Materials with lower

absorption coefficients will possess higher self-focusing thresholds.

(3) Electrostriction appears to be unimportant as an effect leading to selffocusing for unfocused laser beams. (4) The current theory of self-focusing,

which predicts self-focusing lengths as a function of peak power, is not

always in agreement with experiment. (5) YAG has a lower self-focusing

threshold than the five commercial laser glasses examined in this study.

1 . 5 Implications for Further Research

A more detailed analysis of the self-focusing data for YAG and

the five laser glasses is planned. Damage threshold and self-focusing

measurements are to be extended to crystalline materials, used as modulators,

such as deuterated potassium dihydrogen phosphate (KD*P) , lithium niobate

(LiNb0

3

) , and calcite (CaC0

3

) . We also plan to measure self-focusing thresholds in materials with low refractive indices (LiF, NaF) . These are

expected to possess high self-focusing thresholda.

2 . Technical Report

2 . 1 Self-Focusing Mechanisms in Optical Glasses

2.1.1 Introduction

The output of high-powered laser systems is limited by the damage

occurring in components exposed to the intense electromagnetic radiation.

Self-focusing fl] is the main process leading to bulk intrinsic damage

in the components of Q-switched solid state laser systems. An understanding of the mechanisms underlying self-focusing is necessary if we

are ever to fabricate in a systematic manner materials with high self-
focusing thresholds. For example, it has been proposed that electrostrictive effects can be largely eliminated by the production of

materials with extremely small electrostrictive coefficients [2]

.

The mechanism responsible for the self-focusing of laser beams

with pulse widths of ^ 25 ns has not been uniquely identified. Three

mechanisms have been proposed to explain the effect: electrostriction

[3-7], Kerr effect [3-5,8], and thermal self-focusing [9-12]. Up to

the present time insufficient data exists to judge the comparative

importance of the proposed mechanisms. Self-focusing in liquids is

known to be caused by the Kerr effect because of the large contribution

of freely rotatable molecules or ions to the nonlinear index coefficient

n

2

« Because solids lack freely rotatable molecules, it was thought that

electrostriction [3-5] was the dominant mechanism. Duguay and Hansen

have calculated the nonlinear index of refraction due to the Kerr

effect n^ (K) from measurements of induced birefringence in borosilicate

crown glass using picosecond pulses [13,14] . They find that the value

obtained is of sufficient magnitude to cause self-focusing and are of

the opinion that the Kerr effect is the predominant mechanism for all

pulse widths.

E. L. Kerr [7] has developed the theory of electrostrictive

self-focusing to explain the data of Steinberg [15] , who used 55-ns

pulses from a ruby laser to measure damage thresholds in several optical

glasses. Kerr is of the view that electrostriction is the principal

self -focusing mechanism for pulse widths £ 10 ns. For pulses less than

5
10 ns, on the other hand, the electrostrictive mechanism has insufficient

time to take effect, and thus will decrease in magnitude as the pulse

length decreases.

For glasses such as we are considering, thermal self-focusing

was not thought to be important. Quelle [12], in a sample calculation,

showed that the threshold for thermal self-focusing would be two orders

of magnitude greater than for electrostriction. However, other authors

[16] indicated that the thermal effect would be of comparable magnitude.

In this paper we present a semiquantitative estimate of the

relative contributions of the Kerr, electrostrictive, and thermal effects

to self-focusing in borosilicate crown glass (BSC 517) , fused silica,

and dense flint glass (SF 55) from measurements of self-focusing

thresholds for circular and linear polarization [17,18]. We believe

this to be the first attempt to take into account all three effects.

The method was suggested in an earlier letter [17] in which we showed

that the damage threshold for circular polarization was higher

than for linear polarization. In the letter, we had deduced the

relative contributions of the Kerr effect and electrostriction to selffocusing assuming the thermal effect could be neglected. In this work

we find a significant thermal contribution. The Kerr effect appears to

be the largest of the effects. Electrostriction is found to be the

smallest, in disagreement with E. L. Kerr. Kerr used the Clausius-Mosotti

(Lorentz-Lorenz) relations to calculate the electrostrictive index change

in order to explain self-focusing on the basis of electrostriction alone,

6
whereas we have calculated the electrostrictive index change using the

experimentally determined stress-optic coefficients. The change of

refractive index with density calculated with the Clausius-Mosotti relation

agrees poorly with experiment when applied to solids [19]

.

In Section 2.1.2 we discuss the theoretical framework upon which our

estimates are based. We include an analysis of electrostrictive strains

and of thermally induced strains that takes into account the constraining

effect of the medium surrounding the irradiated portion of the sample.

We also calculate the expected ratios of self-focusing threshold for circular and linear polarization for each of the effects acting alone.

In Section 2.1.3 we discuss the experimental procedure and the

data we use in our calculations. We have obtained the data by

focusing into the samples the output of a Q-switched Nd: glass laser

(t = 25 ns) operating in the TEM00 mode. These data are thought to be

more indicative of the self-focusing threshold than earlier measurements

[17] because a longer focal length lens was used. Zverev and Pashkov

[16] have pointed out the importance of using a long focal length lens

for measuring self-focusing thresholds.

In Section 2.1.4 we calculate the total nonlinear index n„ from the

2 threshold data and the contribution of electrostriction n^ (ES) , the

Kerr effect n^ (K) , and the thermal effect n^(T) to n^. The integrating

nature of the thermal effect is taken into account in these calculations.

The numbers obtained for n^ are in good agreement with values calculated

by Owyoung et al. [20] from elliptical polarization rotation measurements.

We also estimate the absorption coefficients necessary to account for

n_ (T) and obtain reasonable values.

7
2.1.2 Theoretical Considerations

Self-focusing of laser radiation occurs when the focusing effect

due to the intensity-dependent refractive index exceeds the spreading

of the beam by diffraction. The refractive index of the medium can be

expressed in the form

n = n + n.E

2

(1) O 2. where E is the RMS electric field obtained from an average over several

optical cycles. The second order nonlinear index is a function of

time unless it derives from mechanisms that instantaneously follow the

temporal shape of the laser pulse. For the experimental conditions in

this paper, both the Kerr and the electrostrictive effects are

instantaneous, but the thermal effect is never instantaneous. Thus,

in general, a critical power for self-focusing will not exist. For a

2 2 given pulse shape, E = E f(t), we can write Eq. (1) in the form

o

fin = n_(t) E

2

, (2)

2. O

2 2 2

where E

q

is the peak value of E , and the time dependence of E is

incorporated into (t) . At a time t = t , fin will have a maximum value.

2 At a critical value of E , self-focusing will take place and we can

o obtain an expression for the critical peak pulse power P necessary to

cause self-focusing . It must be emphasized that the maximum index

change will not occur at the peak of the pulse. The expression for P

that we use has been derived for beams with a Gaussian profile [7,16,21] :

P = X 2 c/(32 tt 2 n ) (3)

where X is the wavelength of the laser radiation in air, c is the

velocity of light, and n has been redefined to equal n

2 (t^) . Equation

(3) is also equal to P in the work of Dawes and Marburger [22].

8
2.1.2.1. The Kerr Effect

In this work we assume that the Kerr effect arises from nonlinearities in the electronic polarizabilities and that orientational

effects can be ignored. Recent experimental work [20] suggests this

is indeed the case. Thus the Kerr effect would be instantaneous up

to optical frequencies.

For an isotropic material the nonlinear polarization is given by

[23]

PMT = 3 c ri -_(E'E)E; (4) NL 1122

°1122 * S a constant ' !f we insert the field for a linearly polarized

wave

E » E [cos(wt-kz), o, 0l (5) o and a circularly polarized wave of equal intensity

E = E [cos(iot-kz) , sin(wt-kz), 0]//2 (6) o into Eq. (4) and calculate the Fourier component of P at

NXj

frequency w, we obtain a ratio of 1.5 for n (Kj/nJ^K). Throughout this

paper primed symbols refer to circular polarization, and unprimed

symbols to linear polarization. Third harmonic contributions can be

ignored because the phase matching condition is not met.

2.1.2.2. Electrostrictive Self-Focusing

Electrostrictive self-focusing is due to refractive index changes

caused by strains induced by the strong electric fields present in

high-powered laser radiation. E. L. Kerr has treated the full dynamical

problem of electrostrictive self-focusing [7] . He has shown that the

electrostrictive response will depend on the parameter X = aQ

/vx

,

9
where a

Q

is the 1/e intensity point radius of a Gaussian beam at the

focus of a lens in the absence of self-focusing, v is the longitudinal

sound velocity in the medium, and x is the temporal pulse width of the

laser beam at half the maximum power. Kerr has shown that for X < 1,

the electrostrictive strain has time to develop fully and hence n^(ES)

can be calculated from the steady state. For our experimental conditions,

3 3 a = 14.7 ym, t = 25 ns , and v varies from 3 x 10 m/s to 6 x 10 m/s

,

oyielding X = 0.1 to 0.2. The electrostriction can follow the

pulse shape and hence the instantaneous approximation is valid.

Kerr, in treating the problem of electrostrictive self-focusing, has

ignored the tensorial nature of the effect because of the complexity

of solving vectorial differential equations. In view of the

steady state nature of the problem as applied to our work, we treat the

effect as a statics problem and therefore we can take into account

the tensorial properties of electrostriction. We calculate n

2 (ES) and

n

2 (ES) for a material containing a uniform electric field in a

cylindrical region and zero electric field outside this region. A

rigorous calculation would be more complex due to the Gaussian spatial

variation of the laser field. However, the solution we obtain is

rigorously correct on the axis of the laser beam.

The strain induced in the cylindrical region due to the intense

electric field is given by [24]

E,, = y. ,E.E./2 + S. . P (7)

kl ljkl i j klmn mn

where y is the electrostriction tensor, S is the elastic compliance

10
(8)

tensor, and P is the stress tensor. The stress comes from the constraining effect of the field free region. From a set of thermodynamical

Maxwell's equations, we can show that [25-27]

Y ijkl ~ K imK jnSnnkl^^

where < is the dielectric tensor and q is the stress-optic tensor.

The change in dielectric tensor with strain is given by

AIk"

1

] . . > p. ... e. . ; (9)

lj ljkl kl

t p is the elasto-optic tensor. In order to calculate n

2 (ES) and n

2 (ES),

we must first calculate the electrostrictive strains

e° = y . ...E.E./2 (10)

kl 13 kl l j

For an isotropic material the net strain becomes [28]

e n

= [2(e°

1 + e°2

) + (3 - 4v) (e^ - e°

2 )]/[8(l ~ v) ] ' (lla)

£ 22 = [2(£

11

+ e 22 } ~

(3 " 4v)(e

ii " e 22 )1/t8(1 " V)1? Ulb)

e 33 - 0 (HO

where v is the Poisson ratio. These strain components are inserted

into Eq. (9) and the final result is:

n

2 (ES) - n^q^ + q12

+ 2vq

12 ) (p^ + p

12 >/[64 (1 - v) ] (12)

n

2 (ES) = n^(qn - q12 >(P n - P12 ) (3 " 4v >/t 128 ^"v) ^ + n

2

(ES) (13)

Equation (12) is identically equal to Kerr's [7] steady state limit.

11
2.1.2.3. Thermal Self-Focusing

Thermal self-focusing results from positive refractive index

changes caused by absorptive heating of a sample exposed to high-energy

laser radiation. For an isotropic material the change of index with

temperature is _

, _ n (1 + v) (p + p ) £ 35. = _ _° 11 12 . (14) dT V 3T ; 12(1 - v) ' 1 1 P

£ is the volume coefficient of expansion. We assume that heat diffusion

does not occur during the passage of the laser pulse. The thermal effect

differs from the two previous effects in that it depends upon the

integrated energy of the pulse.

The first term in Eq. (14) , the change of index with temperature

at constant density, follows the instantaneous temperature. The

change in temperature is governed by electron-phonon relaxation times

which are fast compared to 25 ns. The term is positive in most

glasses

.

The second term in Eq. (14) is the change in index with temperature

due to thermoelastic strains. It is derived with the same boundary

conditions used to compute the electrostrictive strain. A similar term

has been derived by Zverev et al. [29], who have pointed out that, due

to the constraining stresses, thermal self-focusing can take place

even though the conventional value of dn/dT < 0. The response time of

the thermoelastic strain term is equal to the response time of electrostriction. Since X < 1 it will also respond to the temperature

12
instantaneously. The change of index due to the thermal effect is [9]

otcn dn

{n(t) -EcJ3r Eo/

t

f(t

i )ati

(15)

where a is the absorption coefficient, c is the velocity of light,

C

p

is the specific heat at constant pressure, and p is the density.

We assume that the absorption coefficient is small so that the laser

beam undergoes insignificant attenuation while passing through the

sample. From Eqs. (3) and (15) we see that the thermal self-focusing

threshold will vary inversely with the pulse width for a given peak

power. There will be no polarization effects for isotropic materials,

i.e. , n

2 (T)/n2 (T) « 1.

2.1.2.4 Combined Effect

The change of index will equal the sum of the contributions from

each of the effects. At this point it becomes convenient to assume

that f(t) has a Gaussian shape, i.e.,

f(t) = exp[-4t2/x

2

] , (16)

where x % 1.2 t. The change of index is then

e

6n = [n 0 (K) + n„(ES)] E

2 exp [-4t2

/x

2

] + n (T) E

2

[1 + erf(2t/x )], (17)

2 2 o e2o e

where

.075 a c n x dn

n

2 (T) = (16)

vTf C

p

p dT

and erf(x) is the error function. The maximum value of 6n occurs at

times

13
t = x n (T)/2v7[n_(ES) + ri_ (K) ] ; o e 2 2 2 (19a)

t

Q

= T en

2 (T)/2/7[n

2 (ES) + 2n (K)/3]. (19b)

The nonlinear index is then

n

2 = [n2

(K) + n

2 (ES)]expt-(2t

oAe

) 2

] + n

2

(T) [1 + erf (2t A ) ] (20a)

n

2.1.3 Experimental Procedure

The experimental apparatus is shown in Fig. 1 [30] . It contains

a Q-switched Nd: glass laser oscillator operating in the TEMQO mode.

The output of the oscillator has been characterized as to energy,

temporal pulse width, peak power, and beam profile.

The energy was measured by a thermopile and found to be constant

to within +_ 2%. The temporal pulse shape was monitored by a high-speed

photodiode and oscilloscope. The pulse width at half the maximum

power was 25 ns . The peak power was obtained by setting the pulse

energy equal to the integral of the pulse shape over time.

lens position by measuring the diameter of burn patterns on unexposed

developed Polaroid [31] film. The output of the laser is maintained

at constant pulse energy but is attenuated from pulse to pulse by

interposing calibrated attenuation filters between the oscillator and

the film. The burn pattern radius is plotted as a function of beam

2 2

energy and fitted to a Gaussian curve, H = H exp(-r /a ) where the

The beam profile of the laser beam is obtained at the focusing

o

14
CO

cu

M

0) o

Cm »w

to

CD

X P

-H rH ,c ft

II Q)> - i U H-l CU rH P tr) P ^

-H I rH CU ft C

(0

O

<3 o

<u XI o

rH

CON

0)

cu p

rH•H

M-lCo

•HP

fdG

CU PP mH O O -H P P H N H -H H M U (0

10 rH ° a nU

tO rH o 3u

•• -H

Cn

u

CH

M P O

co n-i CD P CD P

cu to Cn rH

us ft

Cme

cu .Q

CU p

cu>

to&irH

CU

10 P 1I

cu p

cu£

cu

cu

cu rH

•H

ft

rH

cu rC

-P 3P

rH

rdft II

rHu1

En II • v CO coH CO P c

nJ cu N rH -H . CDo • "H

Cn no •H O

En PO

.£

ft

a

CnCH

COo

rH

O

res ^

CU

Si II •H

rH

J
constant H is obtained in units of J/cm from

o

2 2 W = 2tt H / exp (-r /a ) rdr;

o

y (21)

o

W is the total pulse energy. Figure 2 shows a plot of the beam

profile together with the Gaussian which is fitted by eye. The pulse

energy is 99 mJ.

Damage threshold measurements for linearly and circularly

polarized radiation [17,18] were made by focusing the laser beam into

the samples using a lens of 181 mm focal length. The oscillator output

was linearly polarized in the horizontal plane with the ratio of

horizontal to vertical polarization greater than 200:1. Circularly

polarized light was produced by inserting a quarter-wave plate into

the beam. The quarter-wave plate consisted of a fused silica plate

under uniaxial compression [32] . The linear polarization damage

measurements were made by relaxing the stress in the plate. Measurements were also made with the plate stressed to a half-wave retardation;

the results were consistent with the unstressed plate measurements.

The damage thresholds were obtained by observing whether or not

damage occurred in the sample during any particular laser shot. Each

laser shot was focused onto a different position in the sample. The

energy of the laser pulse was attenuated in ^ 20% increments with

calibrated attenuation filters. Finer increments of energy were

obtained by varying the oscillator pump energy. The criterion for

damage was the presence of a fractured region in the vicinity of the

16
I .0

0 1.0 2.0 3.0

RADIUS (mm)

Fig. 2. Beam Profile. Energy per unit area as a function of

distance from laser beam axis as measured at the focusing lens.

The solid line is a Gaussian fit to the data.
focal spot. In all cases, a bright flash of visible radiation was

emitted when damage took place.

2.1.4 Results and Discussion

Damage threshold measurements have been made in borosilicate crown

glass (BSC 517) , fused silica, and dense flint glass (SF 55) . The data

are shown in Fig. 3. Solid points represent pulses that produced

damage; open points represent pulses that did not produce damage. The

scatter in the data is due to sample variability, laser energy variations

and the statistical nature of the actual damage process [33,34] . In all

cases the threshold for circularly polarized light P has been higher

than for linearly polarized light P .

We now proceed to calculate , n

2 (ES), n

2 (K), and n

2

(T) under the

assumption that the damage results from self-focusing. All the

necessary input parameters for the calculations are given in Table I.

The total nonlinear indices n„ and n„ are calculated from P^ and P^

2 2 t t

using Eq. (3). We calculate n

2 (ES) and n2 (ES) with Eqs . (12) and (13).

The numbers for p , P 10 , q, , , and q given in Table I have been

measured at visible wavelengths; however, we do not expect them to

differ significantly at 1.06 ym. The values for n

2 (K) and n

2

(T) are

calculated by numerically solving Eqs. (19) and (20) with the values

for n

2

, n

2

, n

2 (ES) and n

2 (ES) as input parameters.

We summarize our results in Table II. The limits of error arise

from the scatter in the experimental data. An examination of the

results indicates that the Kerr effect is the largest contributor to

18
1 <

LxJ

J z: J _i

I) p

cr

Jj < n _i p

Z>oO

cr<

LJ2

en oo • ooo • • oo • • DO • • • b« 1 1 1 1 1 1 1 1 1 1 1 1 1 D ooo o • o o • o • • • • • • • • o o • • • • o o 1 • • • • o o 1 1 1 1 I 1 1 1 1

rT3

0)

to o p -H

ll 1 jj*H

t-j

f-s, ftf > # 1 1 d) LO (/) r"Tt rri\j .p m r \ \~s f\\ \u CO N ra pn -r-( Uj

d)

D! fH w n

tti (/) T3 I—

Q ,—

Qi

C

d)

rrj 4_) , | o Q o

^1 0) •iH -H •H

-p

V

O

Gi o T3 H C o H •H •H

0)Oo c

-P -P O enC W 0) rH

O

C

CM LD ||

O f5 U5 U o o

ft

a) e ^ ei

-P CO C rH

(M>l) d3M0d >IV3d »
Table I. Input Parameters Necessary for Calculating the

Contributions to Self-Focusing.

BSC 517 Fused Silica Dense Flint (SF 55)

6 -1 -1

C (10 erg g K ) P

8.6

b

7.5

C

8.4

p (g cm ) 2.5ia 2.2 4 . 72

I dn/ a i ) \ IV K ) P O.J 9 7

S

y . /

_ -6 -1,

$ (10 K ) 20.0 1.5 24.6

-13 2 qil^

10 Cm /^Y^ 0. 315

f 0.4189 1.7

-13 2 q12

(10 cm /dyn)

q 2.71y ^ ^h

2.2

P-,

,

^11 0.115

f 0.1209 0.21h

P12

0.221 0.2709 0.23

V 0.2043 0.164 0.247°

n (1.06 urn) o 1.507 1.450 1.733

aTaken to be the same as BK 7 , see ref. c. b

A. B. Sosman, The P roperties of Silica (Chemical Catalogue

Hew York , 1927) , p. 314.

'Catalogue, Schott Optical Glass, Inc., Duryea, Pennsylvania,

dCalculated from dn/dT given in ref. c and from the elasto-optic

coefficients

.

20
Table I. (continued)

Calculated from dn/dT given in J. B. Austin, "A Vacuum Apparatus of

Measuring Thermal Expansion at Elevated Temperatures, with Measurements

on Platinum, Gold, Magnesium, and Zinc," Physics, vol. 3, pp. 240-267

(1932) , p. 248, and from the elasto-optic coefficients.

fRef . [19] : X = 587.6 nm.

g

W. Primak and D. Post, "Photoelastic Constants of Vitreous Silica and Its

Elastic Coefficient of Refractive Index," J. Appl. Phys., vol. 30,

pp. 779-788 (1959): X = 546.1 nm. h

Ref. [17].

21
Table II. Contributions of Kerr, Electrostrictive , and Thermal

Effects to Self-Focusing Thresholds. 3

BSC 517 Fused Silica Dense Flint SF 55

P (MW) 0.88 + .05 1.17 + .06 0.155 + .007

p' (MW) 1.10 + .07 1.45 + .07 0.205 + .007

10~ 13

esu) 1.21 + .07 0.92 + .05 6.9 + .3

10" 13

esu) 0.97 + .07 0.74 + .05 5.2 + .2

S) [10~ 13esu] 0.13 0.16 0.68

S) [10~ 13

esu] 0.11 0.13 0.68

[10~ 13

esu] 0.72 + .22 0.49 + .15 5.2 +0.7

n.(T) [10

-13

esu] 0.33 + .22 0.24 + .15 1.0 + 0.7

a (cm"

1

) (3 + 2) x 10~ 3 (9 + 6) x 10

_4

(5 + 4) x 10~ 3

aThe errors denote the scatter in the data.

22
self-focusing for the beam parameters of this experiment. The data

indicate that the electrostrictive effect is much smaller than the

Kerr effect. This conclusion differs considerably from our earlier

result [17] because in that work we had neglected two important effects

in addition to making a factor of two error in the equations for ^(ES)

and n^(ES) . (An appropriate correction for this error was made in

ref . [18] .) In our earlier paper, we had ignored the thermal effect

and we had ignored the constraining effects of the medium surrounding

the irradiated portion of the sample when calculating the electrostrictive effect. Additionally, the data upon which we base our

calculations here have been taken with a longer focal length lens than

the earlier work [17] and thus more accurately indicate the selffocusing threshold. The importance of using a long focal length lens

for self-focusing measurements has been pointed out by Zverev and

Pashkov [16] . They showed that the threshold measured with a short

focal length lens would be more indicative of the intrinsic damage

threshold, because for a given pulse power, the energy density would

be higher at the focal spot.

Our results indicate that the thermal effect is of considerable

importance for self-focusing with 25 ns pulses. Because of the pulse

width dependence of (T) , the importance of the thermal effect for

shorter pulses decreases. However, because of its integrating nature,

thermal self-focusing can be very important in high repetition rate

systems even though the individual pulses are quite short. It is of

interest to deduce the absorption coefficient necessary to account for

23
n

2 (T) . These values are presented at the bottom of Table II. The

numbers obtained are consistent with parameters for optical glasses.

Our value of a for BSC 517 is close to the value for a similar glass,

BK 7 (a = 3 x 10

3 cm ) , as reported by McMahon [35] . The absorption

coefficient for our fused silica is significantly larger than the

-4 -1

largest value measured by Rich and Pinnow (a = 1.6 x 10 cm ) [36]

.

There are several explanations for the discrepancy. First, the fused

silica we used may actually have a higher absorption coefficient. Second,

our assumption that the damage thresholds we measure are the self-focusing

thresholds may not be valid. The threshold values, especially the value

for circular polarization, are of such a magnitude that they may be more

indicative of the intrinsic damage threshold than of a self-focusing

threshold. The result would be to make the ratio p

t/pt come closer to

unity, resulting in an apparently larger thermal effect. It is most

likely that some self-focusing is taking place since, in the absence of

self-focusing, we would expect p

t/pt = !•

A comparison of our results with the data of other workers is

shown in Table III. Owyoung et al . [20] have calculated n^ from the

rotation of the principal axes of elliptically polarized light from a

single frequency ruby laser. Their data agree quite favorably with

ours. The differences observed could be explained by dispersion effects,

by differences in the glasses, and by corrections to Eq. (3) . We

justify the use of Eq. (3) instead of V ^ of ref. [22] for two reasons:

The size of the thermal effect would be increased by a factor % 4,

yielding larger absorption coefficients than seems reasonable; the
Table III. Comparison of Nonlinear Index Coefficients in Units

of 10 esu.

n

2^ nW- n2

mW n^K)^ n^K)^

Fused Silica 1.2 0.92 0.49

BK-7 1.7 0.6 1.0

BSC 517 1.2 0.72

SF 7 6.9

SF 55 6.9 5.2

LaSF 7 3

Reference [20] -X - 0.69 ym

This work -X = 1.06 ym

Reference [35] -A = 1.06 urn

"^Reference [14] . For comparison with our results the numbers given

are half the values in the reference because of the differences in the

methods used.

25
results we obtain using Eq. (3) give better agreement with the work of others.

The excellent agreement for the flint glasses (SF 55 and SF 7) is

probably fortuitous.

Our value of ^(K) in BSC 517 agrees quite well with the value

obtained by McMahon [35] from self-focusing measurements with picosecond

pulses in BK 7. The agreement is also good compared to the value from

Duguay and Hansen [14] . Their value for LaSF 7, a dense flint glass,

agrees with our value for SF 55 flint glass within a factor of two.

Duguay and Hansen measure (K) from the intensity induced birefringence

caused by picosecond pulse. Because of the different method of measurement, the numbers given in Table III are half the values in the

reference [14]

.

From our calculations we note that n^ (K) increases with refractive

index. This is in qualitative agreement with the work of Wang [37]

.

2.1.5. Conclusions

We have estimated the relative contributions of the Kerr effect,

electrostriction, and thermal effects to the self-focusing

thresholds of borosilicate crown glass, fused silica and dense flint

glass from an analysis of damage threshold data for linearly polarized

and circularly polarized radiation. For the beam geometry used, we

conclude that the Kerr effect is the largest effect in all the samples

tested. The thermal effect is also found to be significant, but the

electrostrictive effect is quite small. Both of the latter effects

are expected to be insignificant for an individual subnanosecond pulse;

26
however, because of its integrating nature, thermal self-focusing can

be important in high repetition rate laser systems.

The results we have obtained are in qualitative agreement with

the work of others. Absorption coefficients calculated from the

estimated thermal contribution to self-focusing appear to be reasonable for

commercial optical glasses. It would be of interest to measure the

absorption coefficient directly for a comparison with the value obtained

from the self-focusing measurements.

2.2. Self-Focusing Studies in Yttrium Aluminum Garnet (YAG) , Dense Flint

Glass (SF 55) , and Five Commercial Nd: Doped Laser Glasses .

2.2.1. Introduction

In this section of the technical report we present self-focusing

data on YAG, SF 55 glass, and five commercial laser glasses. We have

measured self-focusing lengths as a function of peak laser power using

both linearly and circularly polarized radiation. In all cases the

circularly polarized radiation had a higher damage threshold than the

linearly polarized radiation. To our knowledge, the self-focusing measurements in YAG are the first to be reported.

2.2.2. Self-Focusing Length Measurements

Recent experiments [33,38-41] have shown that the filamentary

damage observed when solids are exposed to high-intensity laser radiation

is due to self-focusing of the laser beam and that the self-focused spot

moves toward the laser source as the pulse power rises. Assuming that

the nonlinear index coefficient n 0 responds instantaneously to the laser

27
pulse shape, Dawes and Marburger [22] have made a detailed computer calculation which predicts the self-focusing length as a function of beam power.

We have produced damage filaments in optical glasses by focusing

the laser beam at different power levels P into samples using 181 mm and

362 mm focal length lenses. The experimental arrangement is the same

as reported in section 2.1.3. We have measured a length z^ from the

upstream end of the damage track to the sample entrance face and than

have calculated the self-focusing length z from the formula [41]

z = z

f - R (22)

where R is the radius of curvature of the laser wavefront at the sample

entrance face. R is calculated from the measured focal point of the lens

and the propagation characteristics of Gaussian beams. The normalized

-1 1/2 inverse self-focusing length (z*) is plotted as a function of P .

* 2 z = z/2ka ; (23)

k = 2-rm /X , (24) o

where a is the 1/e intensity point radius of a Gaussian beam, n

Q

is the

index of refraction, and X is the wavelength (1.06 urn)

2.2.3. Results and Discussion

2.2.3.1. YAG

* -1 1/2 Figure 4 shows a plot of (z ) vs. P for undoped YAG. The

square data points have been obtained with linearly polarized radiation;

28
— 00

CVJ

— o

CMI 30 *t• cvj O • •

zn [(MIAI) U3M0d]

COO

(0o

Iss E

aS (1) CO XI 4-> M '—

o c

as -H

<D >1 4-) rH

4-1 'h 0 0 (d H 0

-p 3 -p 0 CJ 0 >4 TJ N H CU O to a) 3 u

as

C CO 3 • tr' Js 1—I

0) CN

a; 5

CN'—'

X\ fji

4-> c

44

>1 cu CU rH rH cn o U

rd

H 3 c ai «S XX o o u

•H •H 0 II +J rH iw S U M

44 fo 1 an rH

aS 00 ra rH cu

Ul < .5ro a

CO XI 4-i 4-> CU tn c c n

CU (0 rH CP

CP

g

C 3 H C

(0 -H 3 e U 3 O rH

4-i rd 5 s

<H

O 1 •H

IK -P rH as -H

CU •H fi rH

C/3 *4 o

4-> <a CO

4-1

M

>! CD C

•H

zed Th

-H

•H

CU (3 10 rH 4J 0 0 ai
the circular points have been obtained with circularly polarized radiation. The data have been obtained by focusing the laser beam into the

sample with a 181 mm focal length lens along the [111] crystallographic

axis. Also plotted in the figure are the theoretical curves derived

by Dawes and Marburger. The curves are fitted empirically to the data

by varying only the critical power for self-focusing. The values that

we obtain are P = 0.49 MW and P = 0.61 MW. The agreement of theory

and experiment is very good. A preliminary analysis of the data indicates

that the Kerr effect is the main self-focusing mechanism with a sizable

thermal contribution. The electrostrictive effect is negligible because

YAG has exceedingly small stress-optic coefficients compared to the glasses

we have measured.

2.2.3.2. SF 55 Glass

* -1 1/2 Figure 5 shows a plot of (z ) vs P for SF 55 glass. The

square data points have been obtained with linearly polarized radiation;

the circular points have been obtained with circularly polarized radiation.

The data have been obtained by focusing the laser beam into the sample

with a 362 mm focal length lens. Also plotted in the figure are the

theoretical curves derived by Dawes and Marburger. The critical power

for self-focusing is obtained by empirically extrapolating the data to

* -1

the point (z ) =0. The values that we obtain are P = 0.30 MW and •

i P

fc = 0.41 MW. Agreement between theory and the data points is poor.

Earlier self-focusing measurements in SF 55 glass, in which a 181 mm focal

length lens was used, have given better agreement with theory [18]

30
CM 00o

CDO o

B]C

<1) a

<D

M < <0 QEo

5-1 6 -H M-i rd -P

0) n3 a> T3 f0 M fO

ft3 P W

CU CU a, t) >

a)

u

u-i

n 3 o M

(13 T3

O

O -H ^ ft O

(/I 0) ^M O 1>

rc ^ x:

tr >,

<U (0 to x: -h -p 3 nj U

N

4-1O

O cO 13

•H

C

X>

m o

•H

to

— o

iH

W

U

to (0

a)

w c S3CPC M

01

O

H 4-1

CPc m

-H LO 3 Pm O CO o

4-1I

CU CO

(0 r-. O TM • C CM M

in is 3H

(0 (0 S • 4-j

C7> •H <UC 4-) -O

13 [(MW) U3M0d]
In addition, the critical power values obtained with the 362 mm lens are

about twice the values obtained with the 181 mm lens (see Table II) . We

have not resolved the discrepancy at present.

2.2.3.3. Five Commercial Laser Glasses

* -1 1/2 Figures 6a-6e are plots of (z ) vs P for five commercial

laser glasses. The plus points have been obtained with linearly

polarized radiation; the circular points have been obtained with circularly

polarized radiation. The data have been obtained by focusing the laser

beam into the samples with a 181 mm focal length lens. No attempt was

made to fit the theory of Dawes and Marburger to the data because of the

gross discrepancy between theory and experiment. The experimental selffocusing lengths are much shorter than the values predicted by the theory.

The behavior of the different laser glasses is very similar. The data

to the left of the figures appear to follow a curve which is concave downward. This is the qualitative type of behavior that would be expected

for an intrinsic damage threshold with no self-focusing present. To the

right of the figures the data follow a curve which is concave upward.

This type of behavior is typical of se] f-focusing data. In all the glasses,

the lowest damage point for circular polarization occurs closer to the

laser source than the next more powerful laser shot. It is uncertain

at this time whether this is a physical effect or just an experimental

artifact. The effect is not as apparent with linear polarization.

A comparison of the different laser glasses suggests that glasses

A, D, and E have about the same damage and self-focusing thresholds.

Glasses B and C have about the same thresholds, but the values are slightly

lower than in A, D, and E.

32
Figs. 6a - 6e . Self-focusing lengths as a function of the

square root of peak beam power in five commercial laser glasses for

linearly (+) and circularly (0) polarized radiation. A lens with a

181-mm focal length was used to obtain the data.

33

*

M

H

3/1 [(AMI) feGMOd]
00

ro <NJ — • • •

zn [(MW) U3MOd

O 0) — O

— CD

N — ro

CsJ

— o

u
*

M

T3

3/1 [(MN)d3M0d]
*

M

CP H

fa

2/, [(MM) M3M0d]
2.3. Laser Triggered Spark Gap and Pockels Cell

A laser triggered spark gap has been constructed for producing

a short high-voltage electrical pulse in synchronization with the laser

pulse. When the electrical pulse is applied to a Pockels cell with an

appropriate time delay, we are able to extract from our laser pulse, a

pulse with a much shorter temporal width. Figure 7 shows the effect of

the laser triggered spark gap and Pockels cell upon our laser pulse.

Figure 7a is a tracing from an oscilloscope depicting the temporal

evolution of the laser pulse directly from the laser source. Figure 7b

depicts the portion of the pulse removed by the spark gap and Pockels cell.

Figure 7c shows the transmitted pulse whose width at half the maximum

power is 2.5 ns. This apparatus will permit us to make damage and selffocusing studies with shorter pulses than we had available previously.

2.4. Acknowledgments

We thank Roland De Wit of the National Bureau of Standards for

his help in calculating the electrostrictive strains. We also thank

Norman Boling of Owens-Illinois Glass Company, Erlan Bliss of the

Lawrence Livermore Laboratories, Edwin Kerr of the Perkin-Elmer Corporation, and A. Owyoung of Sandia Corporation for valuable discussions

concerning this work.

39
20 ns/div

20 ns/div

laser

laser- trxggered spark gap and Pockels cell upon

of

temporal pulse shape. (a) Pulse from oscillator. (b) Portion pulse removed from oscillator pulse. (c) Transmitted pulse
2 . 5 References

[1] S. P. Akhmanov, A. P. Sukhorukov, and R. V. Khokhlov, "SelfFocusing and Diffraction of Light in a Nonlinear Medium,"

Usp. Fiz. Nauk vol. 93, pp. 19-70 (1967) [Soviet Phys. —Usp .

,

vol. 93, pp. 609-636 (1968)].

[2] R. M. Waxier, "Laser Glass Composition and the Possibility of

Eliminating Electrostrictive Effects," IEEE J. Quantum Electronics,

vol. QE-7 , pp. 166-167 (1971).

[3] R. Y. Chiao, E. Garmire, and C. H. Townes, "Self-Trapping of Optical

Beams," Phys. Rev. Letters, vol. 13, pp. 479-482 (1964).

[4] Ya. B. Zel'dovich and Yu. P. Raizer, "Self-Focusing of Light.

Role of Kerr Effect and Striction," Zh. Eksperim. i Teor. Fiz. Pis'ma

Redaktsiyu, vol. 3, pp. 137-141 (1966) [Soviet Phys. JETP Letters,

vol. 3, pp. 86-89 (1966)].

[5] Y. R. Shen, "Electrostriction , Optical Kerr Effect and SelfFocusing of Laser Beams," Phys. Rev. Letters, vol. 20, pp. 378-380

(1966) .

[6] A. A. Chaban, "Self-Focusing of Light in Solids Via the Electrostriction Mechanism," Zh. Eksperim. i Teor. Fiz. Pis'ma Redaktsiyu,

vol. 6, pp. 487-490 (1967) [Soviet Phys. JETP Letters, vol. 6,

pp. 20-23 (1967) ] .

[7] E. L. Kerr, "Track Formation in Optical Glass Caused by Electrostrictive Laser Beam Self-Focusing," Phys. Rev. A, vol. 4, pp.

1195-1218 (1971) .

41
[8] A. A. Chaban, "Self-Focusing of Light in the Kerr Effect," Zh.

Eksperim. i Teor. Fiz. Pis'ma Redaktsiyu, vol. 5, pp. 61-64 (1967)

[Soviet Phys. — JETP Letters, vol. 5, pp. 48-51 (1967)].

[9] A. G. Litvak, "Self-Focusing of Powerful Light Beams by Thermal

Effects," Zh. Eksperim. i Teor. Fiz. Pis'ma Redaktsiyu, vol. 4,

pp. 341-345 (1966) [Soviet Phys. — JETP Letters, vol. 4, pp. 230-233,

(1966) ] .

[10] Yu. P. Raiser, "Self-Focusing of a Homogeneous Light Beam in a

Transparent Medium Due to Weak Absorption," Zh. Eksperim. i Teor.

Fiz. Pis'ma Redaktsiyu, vol. 4, pp. 124-128 (1966) [Soviet Phys. —

JETP Letters, vol. 4, pp. 85-88 (1966)].

[11] Yu. P. Raiser, "Self-Focusing and Defocusing, Instability and

Stabilization of Light Beams in Weakly Absorbing Media," Zh. Eksperim.

i teor. Fiz. Pis'ma Redaktsiyu, vol. 52, pp. 470-482 (1967) [Soviet

Phys. — JETP, vol. 25, pp. 308-316 (1967)].

[12] F. W. Quelle, "Self-Focusing in Glass," in Damage in Laser Materials,

ASTM STP 469 , American Society for Testing and Materials, 1969, pp.

110-116.

[13] M. A. Duguay, J. W. Hansen, and S. L. Shapiro, "Study of Nd: Glass

Laser Radiation," IEEE J. Quantum Electronics, vol. QE-6, pp. 725-

743 (1970).

[14] M. A. Duguay and J. W. Hansen, "Measurement of the Nonlinear Index n^

of Glass Using Picosecond Pulses," in Damage in Laser Materials

(NBS Special Publication 341) , pp. 45-50.

42
[15] G. N. Steinberg, "Filamentary Tracks Formed in Transparent Optical

Glass by Laser Beam Self-Focusing. I. Experimental Investigation,"

Phys. Rev. A, vol. 4, pp. 1182-1194 (1971).

[16] G. M. Zverev and V. A. Pashkov, "Self-Focusing of Laser Radiation in

Solid Dielectrics," Zh. Eksperim. i Teor. Fiz. Pis'ma Redaktsiyu,

vol. 57, pp. 1128-1138 [Soviet Phys. — JETP, vol. 30, pp. 616-621

(1970) ]

.

[17] A. Feldman, D. Horowitz, and R. M. Waxier, "Relative Importance of

Electrostriction and the Kerr Effect to Self-Focusing in Optical

Glasses," Appl. Phys. Letters, vol. 21, pp. 260-262 (1972).

[18] A. Feldman, D. Horowitz, and R. M. Waxier, "Relative Contribution of

Kerr Effect and Electrostriction to Self-Focusing," in Laser Induced

Damage in Optical Materials; 1972 , NBS Special Publication 372

(U.S. Government Printing Office, Washington, D. C. 20402, 1972)

pp. 92-99.

[19] R. M. Waxier and C. E. Weir, "Effect of Hydrostatic Pressure on the

Refractive Indices of Some Solids," J. Res. Natl. Bur. Standards,

vol. A69, pp. 325-333 (1965).

[20] A. Owyoung, R. W. Hellwarth, and N. George, "Intensity-Induced

Changes in Optical Polarizations in Glasses," Phys. Rev. B, vol. 5,

pp. 628-633 (1972)

.

[21] W. G. Wagner, H. A. Haus , and J. H. Marburger, "Large-Scale SelfTrapping of Optical Beams in the Paraxial Ray Approximation,"

Phys. Rev., vol. 175, pp. 256-266 (1968).

43
[22] E. L. Dawes and J. H. Marburger, "Computer Studies in Self-Focusing,"

Phys. Rev., vol. 179, pp. 862-868 (1969).

[23] P. D. Maker and R. W. Terhune, "Study of Optical Effects Due to an

Induced Polarization Third Order in the Electric Field Strength,"

Phys. Rev., vol. 137, pp. A801-A818 (1965).

[24] J. F. Nye, in Physical Properties of Crystals , (Oxford University

Press, London, 1957), p. 257.

[25] H. Osterberg and J. W. Cookson, "The Piezodielectric Effect and

Electrostriction in Anisotropic or Isotropic Media," Phys. Rev.,

vol. 51, pp. 1096-1101 (1937).

[26] P. W. Forsbergh, Jr., "Piezoelectricity, Electrostriction and

Ferroelectricity , " in Encyclopedia of Physics Vol. XVII, Dielectrics

(Springer Verlag, Berlin, 1956), edited by S. Flugge, p. 360.

[27] A. A. Maradudin and E. Burstein, "Relation Between Photoelasticity

,

Electrostriction, and First Order Raman Effect in Crystals of the

Diamond Structure," Phys. Rev., vol. 164, pp. 1081-1099 (1967).

[28] M. A. Jaswon and R. D. Bhargava, "Two-Dimensional Elastic Inclusion

Problems," Proc. Camb. Phil. Soc, vol. 57, pp. 669-680 (1961).

[29] G. M. Zverev, E. A. Levchuk, E. K. Maldutis, and V. A. Pashkov,

"Thermal Self-Focusing of Laser Radiation in Media with Negative

dn/dT," Zh. Eksperim. i Teor. Fiz. Pis'ma Redaktsiyu, vol. 11,

pp. 177-181 (1970) [Soviet Phys. — JETP Letters, vol. 11, pp. 108-111

(1970) .

[30] A. Feldman, R. Waxier, and D. Horowitz, "Laser Induced Damage

Studies," in NRS Technical Note 703, ARPA-NBS Program of Research
on High Temperature Materials and Laser Materials, edited by A. D.

Franklin and H. S. Bennett, pp. 12-36.

[31] Certain commercial equipment, instruments, or materials are identified

in this paper in order to adequately specify the experimental

procedure. In no case does such identification imply recommendation

or endorsement by the National Bureau of Standards, nor does it imply

that the material or equipment identified is necessarily the best

available for the purpose.

[32] R. M. Waxier and E. N. Farabaugh, "Photoelastic Constants of Ruby,"

J. Res. Natl. Bur. Standards, vol. 74A, pp. 215-220 (1970).

[33] M. Bass and H. H. Barrett, "The Probability and Dynamics of Damaging

Optical Material with Lasers , " in Damage in Laser Materials : 1971 ,

NBS Special Publication 356 (U.S. Government Printing Office,

Washington, D. C, 1971), pp. 76-90.

[34] M. Bass and H. H. Barrett, "Laser-Induced Damage Probability at

1.06 urn and 0.69 ym," in Laser Induced Damage in Optical Materials

:

1972 , NBS Special Publication 372 (U.S. Government Printing Office,

Washington, D. C, 1972), pp. 58-69.

[35] John M. McMahon, "Damage Measurements with Subnanosecond Pulses,"

in Laser Induced Damage in Optical Materials : 1972 , NBS Special

Publication 372 (U.S. Government Printing Office, Washington, D. C,

1972) , pp. 100-103.

[36] T. C. Rich and D. A. Pinnow, "Total Optical Attenuation in Bulk

Fused Silica," Appl. Phys. Letters, vol. 20, pp. 264-266 (1972).

45
[37] Charles C. Wang, "Empirical Relation Between the Linear and the ThirdOrder Nonlinear Optical Susceptibilities," Phys. Rev. B, vol. 2,

pp. 2045-2048 (1970)

[38] G. M. Zverev, E. K. Maldutis and V. A. Pashkov, "Development of SelfFocusing Filaments in Solid Dielectrics," Zh. Eksperim. i Teor. Fiz.

Pis'ma Redaktsiyu, vol. 9, p. 108 (1969) [Soviet Phys. — JETP

Letters, vol. 9, p. 61 (1969)].

[39] C. R. Giuliano, "Time Evolution of Damage Tracks in Sapphire and

Ruby," in Damage in Laser Materials: 1971 , NBS Special Publication

356 (U. S. Government Printing Office, Washington, D. C., 1971),

p. 44.

[40] C. R. Giuliano and J. H. Marburger, "Observations of Moving Self-Foci

in Sapphire," Phys. Rev. Letters, vol. 27, p. 905 (1971).

[41] J. Marburger, "Theory of Self-Focusing for Fast Nonlinear Response,"

in Damage in Laser Materials: 1971 , NBS Special Publication 356

(U. S. Government Printing Office, Washington, D. C. , 1971), p. 51.

46
form NBS-114A d-71)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

V. PUBLICATION OR REPORT NO.

NBSIR 73-119

2. Gov't Accession No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Laser Damage in Materials

5. Publication Date February 1973

6. Performing Organization Code

NBSIR 73-119

7. AUTHOR(S) Albert Feldman,

Deane Horowitz, and Rov M. Waxier

8. Performing Organization

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/ Work Unit No. 3130440

11. Contract/Grant No. 2Q16/3D10

12. Sponsoring Organization Name and Address Advanced Research Projects Agency

ARLINGTON, Virginia 22209

13. Type of Report & Period Covered Semi-Annual Te4h.

8-1-72 to 1-31-73

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or iiterature survey, mention it here.) The relative contributions of the Kerr, electrostrictive , and thermal

effects to the self-fccusing thresholds of borosilicate crown glass, fused

silica, and dense flint glass have been estimated from an analysis of damage

threshold data for linearly polarised and circularly polarized radiation.

The measurements were made with a Nd: glass laser operating in the TEMOQ mode

with a temporal pulse width of 25 ns. The Kerr effect appears to. be the

largest effect. The thermal effect is also significant. The electrostrictive

effect is smallest. Reasonable values of absorption coefficient are calculated

from the thermal contribution. The results are in qualitative agreement with

the work of others . Self-focusing data obtained with linearly polarized and

circularly polarized radiation are presented for yttrium aluminum garnet (YAG)

and five commercial Nd: doped laser glasses. The YAG data agree with the theory

of self-focusing. Near the threshold the laser glass data appear to indicate

intrinsic damage rather than self-focusing. Differences between the various

laser glasses are small. Self-focusing data obtained in dense flint glass

with a longer focal length lens are also presented. An electro-optic shutter

actuated by a laser triggered spark gap is discussed.

7. KEY WORDS (Alphabetical order, separated by semicolons) Absorption coefficient; damage threshold;

electrostrictive self-focusing; electrostriction ; Kerr effect; laser damage ,- nonlinear index of refraction; self-focusing; thermal seif-focusing

.

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21. NO. OF PAGES

46

22. Price

USCOMM-OC 6G244-P7I