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Prog. CryStal Growth and Charact.1990. Vo l. 20. pp. 5,9-113 0146.-3535/90 $0-00 .50Printed in Great Bri ta in . 13J0 Perga monPress pie

Lawrence

P R O G R E S S I N N O N L I N E A R O P T I C A LM AT E R I A L S F OR H I G H P O W E R L A S E R S *

D. Eimerl, S. Velsko, L. Davis and F. Wang

Livermore National Laboratory, P.O. Box 5808. Livermore, California94550, U.S.A.

ABSTRACT

Over the la st few years, substant ial progress has been made at theLawrence Livermore National Laboratory tn nonlinear materials for highpower laser applicati ons . Spec if ic al ly , we are developing materia ls forfrequency conversion of lasers used in laser drtven, thermonuclear fustonexperiments and in high average power laser systems. He have developed

new experimental procedures for f u l ly charac teriz ing the li near andnonllnear opti cal properties of mtcrocryst als. Using new theoreticalre su lt s we have developed a systematic method of select ing and opt imiz ing

nonlinear crys ta ls fo r high-power and high-average-power laserappl icat ions . Our molecular engineering strategy for developing new

materlals for the fusion application has resulted in the discovery ofseveral new materia ls with more att rac t ive parameters than KDP.

*Hork performed under the ausptces of the U.S . Department of Energy by theLawrence Ltvermore Natlonal Laboratory under Contract No. H-7405-ENG-48.

5 9

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60 D . E i m e r l e t a l .

CONTENTS

I Introduction

2 Selectlon and Optimizatlon of Nonllnear Materials

3 Threshold Power

4 Database on Nonllnear Optical Materials

5 Microcrystal Characterization Techniques

6 Double Splndle Stage Refractometer

7 The Nonllnear Optical Gonlometer

8 Organic Materlals for ICF Applications

g Optlcal Properties of Chiral Acid Crystals

lO L-Arginine PhosphateII High Average Power Materials

12 Future Directions

Appendix: 3acobl E11iptic Function Subroutines

PBge

60

62

69

80

81

83

87

97

101

10 310 6

10 7

I I 0

I. Intro~vction

Over the last few years, experiments in laser-driven inertial ly

confined fusion (ICF) have shown clearly that targets use the drive laser

energy more efficiently when irradiated with short wavelength

lasers. 1'2 However, the efficiency of the ICF laser driver tends to

decrease at shorter wavelengths. The optimum wavelength will be a

compromise between target efficiency and laser technology, and will

almost cer tainly be in the range 250 nm-500 nm. The most effective laser

architecture to reach this range uses harmonic generation of an effici ent

near-lnfrared laser source.

KDP (Potassium Dihydrogen Phosphate),3 the material currently used

in Nd:glass lasers for ICF research, is not ideal for future ICF drivers

because i t has a low threshold for optical damage and its conversion

efficiency is compromised by a combination of i ts acceptance angle and

nonlinear coefficient. To be economically viable, future Nd:glass or

other near-IR ICF lasers (which are very large) wi ll require harmonic

generators which are both very effici ent, and cost-effectlve. He have

therefore organized an investigation of new nonlinear materials, wi th the

goal of developlng, and eventually deploylng, a materlal which is more

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No nl inea r opt ica l mater ia ls ~ r h igh powe r las41rs

e f f i c i e n t a n d l e s s expen s ive than KDP. At l ea s t one such m ate r ia lh a sbeen i d e n t i f i e d (d-LAP, d eu t e r a t ed 1 - a rg tn tn e phospha t e ) 4a n d i s

cu r r e n t ly under deve lopment . M ate r ia l s whtch improve on KDP can be used

In many o th e r a pp l i ca t i o ns where h tgh power l a se r s a r e Invo lve d . He

t h e r e f o r e e x p e ct t h a t d e s p i t e t h e r e l a t i v e l y n a rr ow n e a r -t e rm f o c u s ,p r o g re s s I n t h e I CF a p p l i c a t i o n w t l l a l s o b r i n g i n e x p e n s i v e new m a t e r i a l sf o r m an y o t h e r a p p l i c a t i o n s .

F o r t h e I CF a p p l t c a t l o n , c r y s t a l s g r o w n e t t h e r b y a q ue o u s s o l u t t o n o r

by low temp era ture B r tdgman methods a re l i k e ly to be the mos t economica l ,and t n t h t s c a t ego ry, we have i d e n t i f i e d s eve ra l c l a s se s o f mo lecu l a r

c r y s t a l s w i t h a p p r o p r i a te p r o p e r t i e s . I n p a r t i c u l a r , w e a reI n v e s t i g a t i n g m o l e c u l a r c r y s t a l s b a s e d o n a m t no a c i d s . T h e s e m o l ec u le si n c l u d e b o th a c h t r a l c e n t e r , a nd a r e l a t l v e l y s t ro n g h a r m o n i c -g e n e r a t in g

u n i t , and a r e t o n i c a l l y bonded. Most a r e more no n l ine a r t han KDP, and

they possess a wtde range of b t re f r tng en ce (0 .01 to 0 .1 5) . They a l so

have t he advan tage o f be ing o p t i c a l l y b t a x t a l . Us ing new expe r imen ta l

m eth od s, c h a r a c t e r i z a t i o n o f I n d i v i d u a l c r y s t a l s t s c a r r i e d o u t o n

I r r e g u l a r l y s h ap e d m t c r o c r y s t a l s 0 . 05 t o 0 . 25 mm t n s i z e . F r o m s uchsamples we measure the re f r a c t iv e ind ice s from be low 400 nm to 1100 nm,and ca r ry ou t a d i r e c t de t e rmina t i on o f t he phasematchtng l o cus , and theno n l in ea r coup l tng and ang u la r a ccep tance a long t ha t l ocus . He can a l so

measure the tempe ra ture bandwidth , i f needed. By us ing such e as t ly

ob t a ina b l e s amp le s , we avo id t he need fo r t ime -consuming c ry s t a l g rowthof a large number of materlals, and are able to concentrate crystal

growth activity on Just those materials which are promising. Using these

methods, we have Identlfled several salts of amino acids which are better

than KDP. These Include LAP, and other arginlne salts, such as the

fluorlde, chlorlde, bromide, and acetate. There are in fact many

crystals in this class, and many of them are ef fi ci ent nonlinear

materials for hlgh power lasers.

In addition to the ICF appllcatlon, we are also Interested Indeveloplng nonllnear materlals for hlgh average power applications.

Under these conditions thermal distortions arise from the 11near optlcal

absorption of the crystals, and In general the beam qual ity of the laser

source degrades, albelt slowly, with increasing average power. Thus high

average power cal ls for nonllnear materials with very low absorption,

high resistance to thermal fracture, and a tolerance for thermooptlc

effects and imperfect beam qual ity. For the average power appllcation,

we have concentrated on characterlzlng the commonly avaliable materlals

rather than developlng new ones. The level of characterization required

61

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62 O. Eimerl e t a l .

Is quite extenslve, 5 and is exemplified In our work on barium borate. 6

This paper reviews the research results at the Lawrence Llvermore

National Laboratory In new nonllnear materials and the strategy we have

developed to Iden ti fy new nonllnear materials for ICF applicat ions. This

paper addresses both the required materials parameters and figures of

mer it , ? and discusses new microcrystal experimental techniques. We

also review our recent work on new, inexpensive, frequency conversion

materials for ICF such as the arginines. Fina lly, we compare several

common nonlinear materlals for high average power applicatlons.

2. Selectlon and ODtlmlzatlon of Nonlinear Materials

I t is we11-known that the eff ic iency of frequency conversion is very

small unless the process Is phase-matched.8 Phasematching means that

the output waves orig inat ing from al l points within the nonlinear crystalare in phase wlth each other Just as they leave the crys ta l. For (Type

I) second-harmonlc generation, phasematching requires that the f i r s t and

second harmonic electromagnetlc waves have the same phase velocity; in

other types of frequency conversion I t gives a more complex rel ati onship

between the interacting waves' ve loc iti es . However, because of wavelength

dispersion, the refractive Indices of optically Isotroplc materials

Increase as the wavelength decreases, and phasematchlng is not posslble.

The most common way to achieve phasematching is then to use a

blrefr lngent crys tal , where the phase vel ocl ty ty pi ca ll y depends on the

di rect ion of propagation of the wave and on i ts polarlzatl on. By

adjusting the polarizati ons and the dir ect ion of propagation I t is

posslble to use the blrefringence to compensate for the natural

wavelength dispersion. In fact th is is ty pl ca l ly how nonlinear crys tals

are configured for frequency conversion.

For a par tl cul ar direction of propagation, the Interacti on Is exactly

phasematched, but f or neighboring di rections the waves no longer have the

same ve lo ci ti es and the conversion efficiency is reduced. The range ofangles over which the conversion eff iciency remains high is called the

acceptance angle of the cry stal , and i t is strongly anisotropic.

Referring to Fig. l , we define the sensitive plane to be the horizontal

plane, and the insensi ti ve plane to be ve rt lca l. The acceptance angle is

very large for beam divergence In the insensit ive plane, but in the

sensitive plane I t Is t yp lca l ly small, about I mrad for a crys tal I cm in

length. Consequently, the di rect ion and beam divergence of the laser in

the sensiti ve plane must be controlled preci sely to obtain high

conversion eff ic iency . Moreover, the acceptance angle of the crystal

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D

N o n l i n e a r o p t i c a l m a t e r i a l s f o r h i g h p o w e r l a s e r s

e

. C rys tal dim ensions fo r frequency conversion using collim ate d beams.

The larg er dimension, D , l ie s in the plane wtth the sm allest

angular se n si t i vi ty . The acceptance angle In the orthogonal plane,

containing D , is about 100 mrad or larger for both unlaxlal and

blaxlal crystals.

63

decreases as the length of the crysta l increases; i f I t is I mrad fo r a

I cm cr ys tal , I t Is 0.5 mrad for a 2 cm crys ta l. The longer the crys ta l,

the smaller the beam divergence in the sensit ive plane must be to

maintain high conversion eff iciency .

This has profound consequences. Diffrac tion provides a minimum value

for the beam divergence, which is typ lcal ly l mrad for a beam of

wavelength 1064 nm and diameter 1 mm. For the typlca l nonllnear crys tal

the acceptance angle is about I mrad for a 1 cm long cr ys ta l; a crystal

longer than I cm w111 therefore be less efficient , in general. To be

ef fi ci en t, a crystal with thi s sens it iv it y to beam mlsorlentatlon or

divergence must be suff iciently nonlinear to convert the laser beam in

less than I cm. Crystals with less angular sensi tivi ty can of course be

longer than th is . In general, high eff ici ency requires that the

conversion process proceed to saturation well before the effects of

phase-mlsmatch are evident.

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64 D. E imer l e t a l .

He have comple ted a tho rough s tudy o f the co nd i t ion s under wh ich

e s s e n t i a l l y c o l l i m a t e d b e a m s5 h ave a h i g h c o n v e r s io n e f f i c i e n c y. T he

e q u a t i o n s f o r t h e g e n e r a l t h r e e w a v e m i x i n g e x p e r i m e n t , w h e r e tw o w a ve s

o f f r e q u e n c i e s = a nd f 2 = m ix t o g e n e r a t e a w a v e a t f r e q u e n c y

(l+f2)~ are as follows:

df/ dz - - C g*h e iakz

dgldz - - f2.C f*h e ia kz

+i&kzdh/dz = (1+f2).C fg e

(1)

(2)

( 3 )

where the complex f ie ld amplitudes are f ,g and h fo r the three

frequencies u, f2 u, and (I+f2)~. Thus fo r th ir d harmonic generation,

f2 " 2, whereas for second harmonic generation f2 = I. I t is

convenient to normalize the f iel ds so tha t the inten si ty of the waves are

F- f ' f , etc. , with no other factors. With this f ie ld normalization, the

nonlinear coupling C Is

C I 2x(2Z0)112. deff /Xf. [ nfngnh I/2 (4)

where Z 0 = 377 Ohms is the impedance of fre e space, and the n' s are the

re fr ac ti ve Indices of the three waves. The term Ak in the exponent is

the wavevector mismatch between the three waves. In general Ak

receives contri but ions from beam divergence, temporal bandwidth, crysta l

homogeneity and temperature Inhomogenelty. Its minimum value i s

determined by the dl ff ract lve c ont ribut ion to the beam divergence. Thus

Ak = k f + kg k h ( 5 )

- Beae + other terms (6)

where AO is a measure of the beam divergence.

The conversion ef fi ci en cy n, is a function of only two parameters,

in general. These are the dr ive, ,10, and the dephaslng 6, defined

as follows.

n o = f2.C2.12.(F+G)

6 = (I12).Ak.I

(7 )

(B)

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Nonl inea r opt ica l mater ia ls for h igh p owe r lasers

w h e r e 1 i s t h e c r y s t a l l e n g t h . H e h av e

n = n m a x s n ( [ n o l n m a x ] I 1 2 , n ~ a x )

w h e r e s n I s a J a c o b l e 111 p t l c f u n c t l o n . ( A n a l g o r l t h m f o r t h e O a c o b le 111 p t l c f u n c t i o ns w h i c h I s s u l t ab l e f o r s m a l l d e s k - t o p c o m p u t er s I s

I n c l u d e d I n t h e A p p e n d i x . ) A s t h e a r g u m e n t o f t h e 3 a co b l s n f u n c ti o n

i n c r e a s e s , t h e e f f l c l e n c y p e a k s , a n d t he n f a l l s , f o l l o w l n g I t s

p e r l od l c l ty. T h e m a x i m u m e f f i c i e n c y I s

(9 )

112nm ax = 1 + 1 /2 x - [ 1 I x + 1 /4x 2 ] , ( 10 )

w h e r e

X - f 2 ( F + G ) C2 / A k 2 . ( 11 )

T h e c r y s t a l l e n g t h , a t w h t c h t h e m a xim u m e f f i c i e n c y t s a c h i e v e d t s

o b t a i n e d f r o m t h e v a l u e o f no a t t h e p e a k o f t h e J a c o b | f u n c t i o n ,name ly a t

2 2n o l n m a x = K ( n m a x ) ( 1 2 )

T h u s t h e o p t i m u m c r y s t a ll e n g t h l o p t i s g i v e n by

2 2

f 2 . C 2 l ~ p t . (F + G ) m n m a xK ( n m a x ) ( 1 3 )

T h e s e e q u a t l o ns s h o w h o w t o o p t i m i z e t h e c r ys t a l l e n g th , f o r a b e a m

o f g l v e n In p u t I n t e n s l t y I = ( F + G) , a n d e f f e c t l v e m i sm a t c h, & k . T h e r e

a r e s e v e r a l s l m p l e s c a l l n g l a w s c o n t a i n e d i n t h e s e r e s u l t s f o r n m a x

a n d l o p t . R e f e r r i n g t o F i g . I , l e t t h e b e a m o r c r y s t al a p e r t u r e b e

D | n t h e s e n s l t l v e d | r e c t l o n , a n d D I n t h e I n s e n s | t l v e d l r e c t l o n ,

a n d l e t t h e c r y s t a l l e n g t h b e I . T h e I n t e n s | t y I = P / D s D I , w h e r e P

i s t h e t o t a l p o w e r i n t h e l a s e r b e a m s ( I n t e n s l t y. a r e a p r o d u c t ) , a n d t h e

r e l e v a n t b e a m d i v e r g e n c e I s & e = Q . X / D s . w h e r e 0 I s r o u g h l y t h e

r a t i o o f t h e b e a m d i v e r g e n c e t o t h a t o f a d l f f r a c t l o n - 11 m | t e d b e a m o f t h e

s a m e a p e r t u r e . I n t e r m s o f t h e t o t a l p o w e r P a n d t h e b e a m q u a l l t y O , t h e

d r l v e a n d d e p h a s l n g a r e

n o = f 2 . C 2 . [ 1 2 /D s 0 ] P ( 1 4 )

8 = ( l l 2 ) . 6 e . X f . C l l D s ) . O (15 )

65

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66 D. E i m e r l e t a l .

An immediate consequence of these equations is the important observation

that both the drive and the dephaslng depend only on the crystal shade,

and not on i t s absolute size. I t is clear that Increaslng al l the

crystal dimensions (I ,D s, and D ) in the same ratio leaves n o and

unchanged. Thus, changing the beam intensity using telescopes fordown-colllmatlon leaves both P and Q unchanged and merely resul ts in a

shor ter optimum crysta l length. The optimum conversion ef fi ci ency and

the shape of the crysta l which achieves th is optimum are both unchanged.

From Eqs. (10) and (11), the optlmum ef fici en cy nma X is a

universal funct ion of X, which is a measure of the laser brightness and a

materlal figure of mer it, the threshold power. That is

X , P I Pth Q2. [4Os/D ] (16)

and the threshold power Pth is

Pth " I / f 2 . [BSXf/C] 2 (17)

Thus the maximum ef ficien cy is independent of the absolute size of the

beam, but is a unlversal function of the r at io p/Q2 and the threshold

power, a material fi gu re of meri t. Figure 2 plots the maximum ef fi ci ency

nma X against the (dlmensionless) laser brightness, X, and Fig. 3

plots the optimum drive n o at which the maximum effici en cy is reached.

Thus, given the task of optimizing the crystal dimensions for a

general three-wave process, the procedure is as follows.

(1)

(2)

Calculate the threshold power Pth for the three-wave process

from the materials constants, C and ~e"

Calculate the dimensionless laser brightness, X, from the laser

parameters P,Q, and Ds/D , and the threshold power.

(3) Read of f the maximum ef fi ciency from Fig. 2 (Eq. ( ]5 ))

(4) Read off the drive n o at which thi s eff ici ency occurs from

Fig. 3, and use equation (]3) to calculate the crystal

shade [ 1 2 / D s D i ] .

From th is procedure, i t wi l l be apparent whether the material can be

ef fi ci en t for the given laser source, and i f so, what the cryst al shape

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0 . 9

0 . 8

0.7

0 . 6

"6 O.5

' ~ 0 . 4

8

"S 0 . 3

0 . 2

o .1

o

.

Nonl inear opt ica l mater ia l s for h igh p owe r lasers

1.0 I

I I I [ I.0100 .1000 1 10 100 1000 1000

T he p ea k c o n v e r si o n e f f i c i e n c y f o r s p a t i a l l y an d t e m p o r a l l y f l a t

p u l s e s . X t s t h e ( d l m e n s t o n le s s b r i g h t n e s s , o r p o w e r p e r u n t t s o l i d

angle in the beam.

67

req u i re d w111 be . He reemohasize tha t no th tna tn th i s o rocedure f ix es

the abso l u t e s i z e o f t he c ry s t a l . I f t he beam ape r tu r e i s doub led u s ing

t e l e scope s , t hen t he opt imu m e ff i c i e n cy w i l l be re ached w t th a c ry s t a l

twice as long , and w i l l be ex ac t ly the same . The maximum conve rs ion

e f f i c i e n cy t s i n d e p e n de n t o f t he beam s i ze . I n con t r a s t t o a rgumen tso f t e n m ade i n t h e l | t e r a t u r e , t h e e f f i c i e n c y i s n o t o p ti m iz e d b yd o w n - c o l l im a t i n g t o a c h ie v e h i g h i n t e n s i t y ; d o w n - c o l l im a t i o n n e c e s s a r i l y

Inc r ea se s t h e be am d i v e rg en ce an d fo r ce s a sho r t e r c r y s t a l l eng th . Then e t r e s u l t t s t h a t t h e m axim um e f f i c i e n c y i s u n a l t e r e d b y

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68

._e

.u

8

c

8,J

o

._>=

c ~

12

10

D. Eimerl e t a / .

o ~ I I l i. 0 1 0 0 . 1 0 0 0 1 1 0 1 0 0 1 0 0 0 1 0 0 0 0

P ( 4 D s

3. The drive n o at which the peak eff iciency given in Flg. 2 is

reached. X is the (dimensionless brightness, or power per unit soli d

angle in the beam.

down-co]Iimation. The crystal size is determined by otherconsiderations. For example, i t is posslb]e to make the crystal as large

as is desired to avoid optical damage problems, or as small as desired to

avoid problems associated wlth optical absorption and thermal gradients.

This freedom to choose the size of the crystal without affect ing the

eFFiciency is extremely important in the design and optimization oF

nonlinear devices.

Thus the fl na l st ep in choosing the crys tal dimensions is

(5) Choose the beam aperture.

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N o n l i n e a r o p t i c a l m a t e r i a l s f o r h i g h p o w e r l a s e rs

This can be chosen on to s a t i s fy any number of requ i reme nts , no t a l l

o f which a re coa~)a t ib le . For example , the aper tu re i s min imized to

r educe t he und es i r ab l e e f f ec t s o f abso rp t i on o r made l a rge t o de s ignaround o pt ic a l damage i ssu es . I t may a l so be de te rmined s imply by the

s iz e o f a v a i l a b l e c r y s t a l s . I n t h i s c o n n e c t io n , i t i s i m p o r t an t to n o tetha t t he damage t h r e s ho ld o f a no n l ine a r c ry s t a l i s no t so much af u n c t i o n o f t h e c r y s t a l i t s e l f , as i t i s a f u n c t i o n o f th e i m p e r f e c t io n s ,

im pu r i t i e s and s t r e s se s i n t roduced du r ing c ry s t a l g rowth . Thus t he r e maybe a s i g n i f i c a n t s a m p le - to - sa m p le v a r i a t i o n i n t h e d am ag e t h r e s h o l d o f an

o p t i c a l c r y s t a l , d ep en din g o n t h a t p a r t i c u l a r s a m p le 's i n d i v i d u a lchemica l h i s t o ry . Tab le 1 l i s t s t he op t i c a l damage t h r e sh o lds fo r some

common n o n l i n e a r m a t e r i a l s , a s s u p p l i e d . S p e c i f i c i n d i v i d u a l c r y s t a l sg ro wn w i t h fe w e r i m p u r i t i e s an d i m p e r f e c t i o n s w i l l e x h i b i t a h i g h e rdamage t h r e s ho ld t han ind i ca t e d i n t h i s t ab l e . On the o the r hand, l e s s

pe r f ec t example s w i l l be l e s s r e s i s t a n t t o damage.

3. The Th resh old PowerI t i s a p p a r en t t h a t t h e t h r e s h o l d p o w e r a p p e a ri ng t n t h e b r i g h t n e s s X

(Eq. 16 and 17, and Fig s. 2 and 3) , ts the fundamental f ig u re of m er i twh ich de te rmines whe ther a ma te r i a l c an be e f f i c i e n t w i th a g iven l a se rs o u rc e . P h y s i c a l l y, t t i s a p p r o x i m a t e ly t h e p e a k t o t a l l a s e r po we rr e q u ir e d i n a c i r c u l a r , d i f f r a c t i o n - l i m i t e d beam i n o r d e r to r ea ch a b ou t

4 0~ c o n v e r s io n e f f i c i e n c y. T h us , i n s e l e c t i n g m a t e r l a l s f o r a p a r t i c u l a rp r o ce s s , i t i s n e c e ss a ry ( b u t n o t a lw a ys s u f f i c i e n t ) t h a t t h e t h r e s h o l dp ow er o f t h e m a t e r l a l be s t g n l f l c a n t l y l e s s th a n p /Q 2 f o r t h e l a s e r

s o u rc e . C l e a r l y , t h e t h r e s h o l d p o w e r i s a u s e f u l f i g u r e o f m e r i t f o rr a n k i n g n o n l i n e a r o p t t c a l m a t e r i a l s ; t h e m a t e r i a l w i t h t h e lo w e rth r e sh o ld po wer i s cons ide red su pe r io r, because i t c an reach a h ighe re f f i c i e n c y a t i t s o p t i m i z e d s h a p e .

Because I t repres en ts the op t tmum ba lance be tween in te n s i t y and beam

d iv e rg e n ce e f f e c t s , t he t h r e s h o l d p o w er i s q u a n t i t a t i v e l y u s e f u l o n l y t othe ex t en t t ha t beam d ive rgence i s t he p r imary sou rce o f dephas tng . Fo rexample , i n sho r t pu l s e ap p l i c a t i o ns t he l a se r bandwid th i s t he p r imary

sou rce o f dephas tng , and t he re fo re r e qu i r i n g t ha t t he t h r e s ho ld p ower belo w e n o ug h i s a n e c e ss a ry, b u t i n s u f f i c i e n t c o n d i t i o n f o r h i g he f f i c i e n c y. T he i m po rt an c e o f t h e t h r e s h o l d p o w e r i s t h a t d i f f r a c t i v eco n t r i b u t i on s t o t he beam d ive rgence a r e a lways p r e se n t , and the re fo re i tis always a relevan t parameter.

The threshold power fo r doubling a 1.064 pm laser using a Type I I

process in KDP is about 80 MH. Thu s, fo r a twice d lf fr ac ti on -l lm it ed

6 9

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N o n l i n e a r o p t ic a l m a t e r i e l s f o r h i g h p o w e r l a s er s 7 1

1000

I

IBzO4 (U)

KDP (11) ~ " "

i . o P ( , )

100.4 0.6 0.8 1.0 1.2 1.4 1.6

Wa v e l e n g t h(microns)

4. The thr es ho ld po wer fo r second harmonic g ene ra t ion fo r some common

u n l a x l a l c r y s t a l s .

p r e sen t ed t n F ig s . 5 and 6 . Ca l cu l a t i o ns fo r some b t a x i a l c ry s t a l s a r eg iven t n F ig s . 7 , 8 and g . The da t a u sed t n t he se ca l cu l a t i on s t s l t s t e d

tn Tab les 2 and 3 . Ht th the knowledge th a t P th represe n ts the mtn tmalpeak power needed t o o b t a in roug h ly 50~ conve r s ion e f f i c i e n cy , t he

u t t l l t y o f a ma te r t a l f o r doub l tng can be tmmed la t e ly t n f e r r e d f rom these

g r a p h s .

T h e t h r e s h o l d p o w e r , o f c o u r s e , v a r i e s f r o m m a t e rl a l t o m a t e r l a l , b u t

i t ~ I s o v a r i e s a l o n g t h e p h a s e m a t c h l n g c u r v e f o r e a c h m a t e r l a l . F o r

e x a m p l e , I n K O P Ty p e I I d o u b l l n g t h e p h a s e m a t c h l n g c u r v e I s a c i r c l e ,

e . c o n s t a n t , e n c l o s l n g t h e p o l a r, o r z - a x l s. T h l s c l r c l e l i es

p a r a l l e 1 t o t h e x y p l a n e , a n d p o s l t l o n a l o n g t h e p h a s e m a t c h l n g c u r v e I s

s p e c i f i e d b y ~, t h e a n g l e b e t w e e n t h e r a d l u s v e c t o r a t a g i v e n p o l n t o n

t h e c l r cl e , a n d t h e x - a xl s . T h u s, - 0 w h e r e t h e p h a s e m a t c h l n g c u r v e

i n t e r s e c t s t h e x z p l an e , a n d ~ - = / 2 w h e r e I t I n t e r s e c t s t h e y z

p l a n e . A l o n g t h e p h a s e m a t c h l n g c u r v e , t h e n o n l l n e a r c o e f f i c i e n t f o r K OP,

d e l l , v a r l e s a s co s ( Z ~ ) , b u t t he a n g u l a r s e n s l t | v l t y B - 8 ( A k ) / a e I s a

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72

_>

p-

100

10

1

s = O 4 ( i)

1

103 (I)

D . E i m e r l e t a l.

I

r K D P ( I)

LJrea 11)

o ,I I I I I I, J , , IIL'N,~ ' '10.4 0.6 0.8 1.0 1.2 1.4 1.6

Wavelength (l.U11)

5. The angular senslt lv lt y, ~klBe, for the materials Included In

Fig. 4.

A

> ~

, , = ,

10

8

6

4

2

00.4

I ~ ) J I J I

-

, \ \ - - . . ~o , (,)

,,,KDP ( 1 1 ~

0.6 0.8 1.0 1.2 1.4 1.6Wavelength (pro)

6. The coupling C, (units: GH I12) for the materials included in Fig. 4

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Nonlinear optical materials for high power lasers

Table 2 . OotJca l Cons tan t s fo r Se lec ted UntaxJa l Nonl inea r M ate r ia l s

73

(DP

Jrea

LtIO 3

BBO

CD*A

LiNbO 3

(a) Se l lm ete r Parameters (~ tn um)

n2 I 1 + S1 + S2X2 + S3Z4 + S4X2/(X2-S~) + S6/(X2-S ~)

s s 2 s3 s4 s5 s6 s7

1.260476 0 0 12.99707 20 .0 0.01011279 0.1137646

1.133831 0 0 3.227935 20 .0 0.008653247 0.110875

1.1823 0 0 0 0 0.012 50 0.173205

1.51527 0 0 0 0 0.02 40 0.173205

2.39503 0 0 0.696664 6.5703223 0.059542 0.052416

1.92106 0 0 2.261063 24.46665 0.003362 0.178943

1.7405 -0.01 55 0 0 0 0 .0184 0.1338

1.3730 -0.00 44 0 0 0 0 .0128 0.1249

0.6278496 -0.01 82 20 0.0002813 0.780817 0.1407699 0

0.6236063 -0.00 933 9 0.0019654 0.724959 0.141485 0

1.392928 -0.026301 -0.000 087 2.520353 0.2170176 0 0

1.313283 -0.02 048 4 -0.000 237 2.266851 0.2097321 0 0

KDP

Urea

LI IO 3

B ~

CO*A

LtNbO3

(b )

d36

0 . 3 9

1 . 1 7

0 .60

No nl lnear Oot tca l Cons tan t s (om/V)

d15 d l l d22

4 .43

0 .2

4 . 6 4 2 . 4 5

1 . 4 0

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74

KTP

d-LAP

LF a

O. Eimerl e t a l .

Table 3. Ootlcal Constants for Selected Biaxlal Nonlinear Materlals

(a) Sellmeler Parameters (X in um)

n 2 l I + S + s2 X2 + s3 ~4 + s4~2/(X2-s ~) + s6/(X2-S~)

s 1 s 2 s 3 s 4 s 5 s 6 s 7

2.0129 -0.01664 0 0 0 0.03807 0.2070

2.0333 -0.01695 0 0 0 0.04106 0.2224

2.3209 -0.01763 0 0 0 0.05305 0.2441

2.2352 -0.00683 0 0 0 0.0118 0.1208

2.4313 -0.0143 0 0 0 0.0151 0.14632.4484 -0.0115 0 0 0 0.0172 0.1513

-1.606 -0.00131 -0.00083 2.44644 0.056364 0 0

-2.449 -0 .00610 -0.00149 3.600]6 0.063803 0 0

-0.230344 0.00580 -0.07841 1.47954 0.111192 0 0

(a) These Sellmeler parameters give accurate indices only in the region of

transparency, 0.19 - 1.2 ~m

(b) Nonlinear Ootlcal Constants (Dm/V)

KTP

LAP

LF

0 0 0 0 5.1 00 0 0 6.3 0 05.4 4.15 11.4 0 0 0

0 0 0 -0.58 0 0.40.4 0.92 -0.84 0 -0.58 0

0 0 0 -0.84 0 -0.580 0 0 0 0.95 00 0 0 -I .08 0 00.95 -I.08 1.58 0 0 0

c o n s t a n t . T h e r e f o r e t h e t h r e s h o l d p ow e r i s a m in im u m w h ere t h e c o u p l i n g

de f f i s a maximum, namely a t ~ = O. In g en er a l , the opt imumo p e r a t i n g p o i n t f o r a n o n l i n e a r m a t e r l a l i s t h a t p o i n t a l o ng t h e

phasematch tng cu rve where the th res ho ld power i s a mtnimum, bu t t h i s i s

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Nonlinear optical materials or high ow er lasers

not n ec es sa ri ly the po tnt at which def f ts a maximum. For the exampleof KDP, t t t s t rue tha t the th resho ld power t s a mtntmum where def f I sa maximum, because B ts a co ns tant along the phasematchtng curve .In gene ra l , f o r un t ax t a l m a te r i a l s , t he angu la r s e n s i t i v i t y ts always a

cons tan t a long the curve , and so tn genera l , for un tax ta l m ate r ia l s , theoptimum ope ra t ing po in t t s tha t which maximizes de ff . On the o the rh an d, th e an g u la r s e n s i t i v i t y f o r b t a x i a l m a t e r i a ls v a r i e s i n an o n tr tv ta l manner along the phase matchtng cu rve, and the optimumop era t ing po in t ts not tn general gtven by the maximum of de ff .

The maxtmum e ff ic ie nc y obta ina ble wt th a p a r t i cu la r mater| a1 t sobta |ned for tha t c r ys ta l o r ie n t a t io n a long the phasematchtng curve wherethe thre sh old powe r ts a mtntmum. Th ere are some circumstances whe re t tmay be de s i rab le to opera te a t some o ther po tn t , bu t I t w t l l se ldom be

advantageous to do th ts . Pos stble m otiva t ion s fo r choosing a non-optimalope ra t ing po tn t t nc lude : ( a ) avo id ing o r r educ tng o r i en t a t ion -depe nden te ff ec t s such a s s t imu la t ed Raman sca t t e r ing , ph o to re f r a c t tv t t y , non l inea rse lf-f o cu ss in g, thermal expansion and thermal s t re ss es , and l tn ea rop t i ca l abso rp t ion , (b ) avo td tng poss | b le compl ica t ions t n the cu t t t ng ,

1 0 4

lOa LAP (l)-

Z,o! / /F- lo-'

E

10 3 [0 . 4 0 . 6 0 . 8 1 . 0 1 . 2 1 . 4

7.

1 .6

Wavelength (microns)

The thresh old power for second harmonic genera t ion for the b tax ta l

c r ys ta l s , l i th iu m formate monohydra te (LF) , KTP, and d-LAP.

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7 6

E

>

CQ

= I

C

D . E i m e r le t a l .

1 0 0 ( I l i I I

~K T P ( i m )

o . i I I I I I

0 . 4 0 . 6 0 . 8 1 . 0 1 . 2 1 . 4

W ~ e l e n g t h ( ~ m )

1 . 6

8 . T h e a n g u l a r s e n s i t i v i t y , a ~ k l e e , f o r t h e m a t e r l a l s i n c l u d e d i n F i g . 7

I f J I ]

1 4 -

1 2 -

ee

o

= 8

0

4 - L

I I K T P )

00 , 4 0 . 6 0 . 8 1 , 0 1 . 2 1 . 4 1 . 6

Wa v e l e n g t h ( ~ m )

9 . The coupl ing C, (u nt t s : GH 112) for the m ater ia l s inc luded in F ig . 7

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78

T a b l e 4 .

D . E i m e r l e t a l .

No nc r lt l ca l Havelenath fo r Second H~rmgnJ~ Generatlon

Havelength Mater ial Propagation T y p e Coupling

(nm) Ax is a (pmlV)

327 LF 8 I I 0.95

378 LIIO 3 y I 4.43

386 LF y I I - -

400 LIIO 3 y I - -

409 BBO y I 0 .2

464 d-LAP 8 I - -

480 Urea - - I - -

488 d-LAP y I - -

519 KDP (x y )/ 42 I 0.39

527 BBO - - I I - -

589 Urea (x+ y)/ 42 I I 1.17

626 d-LAP 8 I I - -

658 d-LAP y I I 0.4

7 1 8 LF = I - -

736 KTP 8 I - -

737 KDP - - I - -

801 KTP = I - -

990 KTP 8 I I 5.1

I045 CD*A (x+y)142 I 0,6

1062 LINbO 3 y I 4.6

I081 KTP = I I 6,3

(a) For bla xl al crys tal s ny > n B > n . For uni axl al cry sta ls

(xyz) are crystallographic coordinate systems.

about I ~m and 1.1 ~m the phasematching curve intersects the low

bJrefrlngence (xy - ab) plane where the angular se ns it i v it y is small.

KTP has two no nc r i t i c al wavelengths, one at each end of t hi s spectr al

region. The threshol d power goes to zero at these non cr it ic al

wavelengths and because the an gular s e n s i t i v i t y i s small between them,

the th re shold power remains low throughou t the en t ir e 1 - 1.1 l~m band.

Si mi la rl y for li th iu m formate monohydrate, there is a no nc rl ti ca l

wavelength close to 900 nm, but l i t h ium formate does not have a low

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N~lim NIr optical mamnals~ r high power eINl~

b t r e f r t n g e n c e p l a n e , a nd t h e r e f o r e t h e t h r e s h o l d p o w e r d i p s t o z e r o n ea r

9 00 nm , b u t q u i c k l y r i s e s t o l a rg e v a lu e s o n e i t h e r s t de o f t h i s

n o n c r i t i c a l wa ve length . On the o the r hand , LAP does have a low

b t r e f r | n g e n c e p l a n e , a nd t h i s g i v e s r i s e t o a l ow t h r e s h o l d p o w e r b an d

~us t be low 500 nm, where the Type I coupl tng t s l a rge and the angula rs e n s i t i v i t y t s s m a l l . Th t s ba n d t s ve ry na r row, abou t 20 nm wtde , and t s

qu t te fa r tn to the UV, where the abso rp t ion a t the second harmonic near

240 nm may be s i g n i f i c a n t . LAP a l so has Type I I n o n c r i t i c a l wave l eng th s ,b u t th e c o u p l tn g v a n l s h e s f o r t he s e c o n f i g u r a t i o n s . T h er e t s n o

w a v e le n g th a t w h ic h t t s t h r e s h o l d p o w e r d t ps t o z e r o .Graphs such as F tgs . 4 and 7 tn e f fe c t summ ar ize the tech nolo gy of

n o n l i n e a r o p t t c s . I d e a l l y , t t w o u ld be d e s i r a b l e to ha ve a s u t t e o f

m a te r i a l s suc h t h a t f o r w h a t e v e r p roce s s t s be ing cons ide r ed , a low

thr es ho ld power m ate r ta l w ould be av a i la b l e . However, f rom Ftgs . 4 and 7t t t s c l e a r t h a t o v e r m o st o f t h e W - v i s i b l e s p ec tr um lo w t h r e s h o l d p ow er

m a t e r i a l s a r e l a c k i n g . T he se g ra p hs a l s o s ho w t h a t u n t a x t a l m a t e r i a l s

a re n o t , t n g e n e r a l , as w a v e l e n g t h - f l e x i b l e a s b t a x i a l m a t e r i a l s . E a ch

new un i ax t a l m a t e r i a l b r t n gs one no nc r i t i c a l wave l eng th where t he

thr es ho ld power can be low, and a smal l b and of wave lengths to the red

f rom th i s w ave l eng t h where t h e t h r e s ho ld power i s sm a l l . On t he o the r

h a nd , a b t a x t a l c r y s t a l h as t h e p o t e n t i a l f o r tw o r e l a t i v e l y c l o se

n o n c r i t i c a l w a v e l e n g th s . T h t s t s I l l u s t r a t e d b y t h e KTP c u rv e s i nF i g . 7 . S u c h a c r y s t a l e x h t b t t s a b a n d o f lo w t h r e s h o l d p ow er b e h a v i o r ,

b ou nd ed b y t h e tw o n o n c r i t i c a l w a v e l en g t hs . B e t w e e n t h e tw o n o n c r i t i c a l

wav e l en g t h s , t he p hasematchtng c u rve In t e r s e c t s a low b t r e f r t ng en ce

p l a n e , w h ere t h e a n g u l a r s e n s i t i v i t y i s s m a l l . To h av e tw o n o n c r i t i c a l

wa ve l e ng t h s c l o s e t og e th e r, a b t a x t a l c ry s t a l mus t have two i nd i ce s o f

r e f r a c t i o n c l o s e to g e t h e r , and b o th m us t be s t g n t f l c a n t l y d i f f e r e n t fro m

t h e t h i r d . I n o t h e r w o rd s , t h e c r y s t a l m u st b e c l o s e t o u n t a x t a l . T he

s i g n a t u r e o f a lo w b t r e f r tn g e n c e p l an e ( an d t h e r e f o r e o f tw o c lo s e

n o n c r i t i c a l w a v e le n g th s ) i n a b t a x t a l m a t e r ta l t s t h a t i t s o p t t c a n g le besma l l bu t no t ze ro , perhaps no t l a r ge r than about 45 deg . The sm al le rt h e o p t i c a n g l e , t h e c l o s e r t h e c r y s t a l i s t o u n t a x t a l , a n d t h e n a rr o w e r

the band o f l ow t h r e s ho l d power. On t he o the r hand , f o r l a r ge r op t t c

ang l e s t he s e p a r a t i o n be twee n t he n on c r i t i c a l wave l eng th becomes l a rge

( a s i n l t t h t u m f o rm a t e ) an d t h e l o w t h r e s h o l d p o w e r b a n d d o e s n o t r e a l l ye x t s t . I n a n y c a s e, t h e p o t e n t i a l f o r t w o n o n c r i t i c a l w a v e le n g th s t n

b t a x t a l c r y s t a l s m ake s t he m m o re a t t r a c t i v e t ha n u n t a x t a l m a t e r i a l s asc a n d i d a te s f o r t h e d e s i r e d s u i t e o f n o n l i n e a r m a t e r i a l s . O t h e r t h t n g s

b e t ng e qu a l , t h e t e c hn o l og y o f no n l i n ea r op t t c s be ne f i t s more from a new

79

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80 D. Eimerl e t a l .

btaxt al crys tal whose line ar opti cal properties are close to, butdi st i nc t from, unlaxlal behavior, than from a new unlaxlal material.

4. Database on Non!lnear Ootlcal Matertal~

He have seen above tha t the threshold power is the c r i t i c a l figure ofmeri t in ranking nonlinear materials fo r appli cat ions, and that graphs ofthe threshold power as a function of wavelength are a very useful aid insummarizing the technology of frequency doubling from a materials

standpoint. Of course, simi la r su n~rt es can be generated fo r anythree-wave in te ract ion; for example th ir d harmonic generation by mixingthe f i r s t and second harmonics has been studied fo r the KDP famtly of

tsomorphs 3 and the result s published. Hhtle t t is useful to summarize

the threshold powers of commonly avai lab le materials, i t would be much

more useful to summarize the capa bi li ty of al l known nonlinearmat eri als . Also, i t would be useful to generate a summary fo r frequencymixing and opt ica l parametric osci ll at or s as well as for frequencydoubling. Only with th ts information , can an informed choice be made

regarding which known materials should be developed. Also, from suchgraphs, i t wi l l be evident which spect ral regions are under-representedby nonlinear opttcal materials.

To th is end, a database has been constructed which contains thenonllnear coef fi cien ts and Sellmeter data for every known nonllnear

material for which such data is availabl e in the lit er at ur e. 7 Aboutone hundred materials are su ff ic ie nt ly well-cha racter ized for inclus ion

in thi s database, and some materials are represented more than once to

re fl ec t co nf li ct ing data in the li te ra tu re , This database in accessed by

a btax tal phasematchtng code which calculates the phasematchtng curve fo reach matertal and phasematchtng type requested, and determines theminimum threshold power along the phasematchtng curve. No te that fo rbtaxt al crys ta ls the coupling tn more than one octant of the index

el li ps oi d must be calculated. The code is completely general, and treatsthe general three-wave in te ract ion and all phasematching types. The codecalculates the threshold power for each materi al, and pr in ts out a l i s tof those materials fo r which phasematchtng is possib le, ordered by the irthreshold power. The data represented in Figs. 7, 8, and 9 was generatedusing thi s expert system. A ful le r descrip tion of t his expert system

wi ll be published elsewhere.

In establi shing th is database, a thorough review of the ll t er at ur ewas necessary, and'many of the Sellmeter parameters were calcula ted from

the li te ra tu re data for the f i r s t time. A surp risin g discovery was made

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Nonlinearo~ ical ma terials~ r high power asers

t h a t t h e r e t s a s i g n i f i c a n t d i s ag re e m e n t r e g a r d i n g th e n o n l i n e a rc o e f f i c i e n t d ~ o f KDP t t s e l f , w he re t h e sp re a d t n r e p o r t e d

~ o 1n - -va lues. . . . . Is 0.39 pmlV to 0.78 pm/V, whereas the standard referencetables II report 0.63 pmlV. There are rel at lv el y few absolute

d e t e r m i n a t i o n s o f t h e n o n l l n e a r c o e f f i c i e n t s o f KDP a nd I t s t so m o rp h s,and most were made tn the 196 0's . The e a r l y ex perim ents used a focussedbeam g e o m e tr y, a nd t h e i r i n t e r p r e t a t i o n t s c o m p l ic a te d b y t h e e f f e c t s o fbeam walk-off , and the nonuniform laser p rofl le near the focus. The most

tel la bl e measurements are more recent and use dl ff ra ct lo n- ll mt te d or

s tng l e mode , h lgh ene rgy, pu l s ed l a se r s t o measu re t he conve r s ione f f i c i e n c y o f h l g h l y c o l l im a t e d b e a m s. T he a d va n ta g es o f a la rg e

a p e r t u r e a nd c o l li m a t e d g eo me try a r e : ( 1 ) b ea m w a l k - o f f I s n e g l i g i b l e ,

(2 ) t he r e i s no d i f f r a c t i o n a s t he beam p ropaga t e s th rough the s ample ,

and (3 ) the beam dive rgen ce can be made much les s than the acceptanceangle o f the sample . The p lane-wave exper iments a l l agree to w i th in 2%o n t h e n o n l i n e a r c o u p l i n g o f K D P. F o r Ty p e I I d o u b l tn g t h e c o u p l i n g i s

C = o.g5 GW 1 /2 (18)

which corresponds to

d36 - 0.39 pm/V (19 )

The large aperture results for C tn the 11terature also agree exactlywlth our (unpubllshed) experience wlth frequency conversion of the NOVA

l a s e r. U n f o r t u n a t e l y, d i f f e r e n t a u th o rs use d i f f e r e n t d e f t n l t t o n s o f t hed - c o e f f i c i e n t ; t h e d e f i n i t i o n u se d h e re t s t h e sa me a s t h a t i n Z e r n t keand Mid win t e r. 8 The d e f in i t i o n s u sed t he o the r co l l im a te d beamexperlments g'10 d if fe r from th ls by a factor of two, and quote

0.78 pm/V. The discrepancy between the co111mated beam, hlgh intensity

experiments and the other determinations of d36 remains unexplained.

5. Hlcrocrvstal Characterization Technlaues

Characterization Is an essentlal element In the development of new

nonllnear optlcal materlals. The minimum data requlred are the angular

sens l t lv l ty and the nonlinear coupllng throughout the transmlsslon range

of t he m a te r i a l . F rom these da ta t he t h r e sho ld power can be compu ted,and t he ma te r i a l c an be r anked aga in s t o th e r, known no n l in ea r ma te r i a l s .U n t i l r e c e n t l y, t h i s c h a r a c t e r i z a t i o n was p o s s t b le o n l y w t t h c r y s t a l s

a b o u t 10 mm t n s i z e , s u f f i c i e n t t o p e r m i t a p r e c i s e d e t e r m i n a t i o n o f t h e

81

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8 2 D . E i m e r l e t a l .

Individual c o m p o n e n t s o f t h e d-tensor, and also of the refractive indicesthroughout the transparency range of the crys ta l. I t was necessary togrow crys ta ls of htgh opttca l qu al it y a t about the 1 cm 3 size in orderto compute the threshold power and thereby to rank the material agains t

other mate rial s. However, we 22 have recent ly developed new techniquesof mtcrocrystal characterization which can determine the necessaryparameters ustng I rr eg ul ar ly shaped crys ta ls ju st 50 - 250 microns tn

size. Using these new techniques, i t is posstble to measure the relevant

matertal parameters without the costly and time-consuming step of crystal

growth to the 10 m scale. Often, crys ta ls of suf f ic ie nt size areobtained as a rout ine re su lt of chemical synthes is. By avoiding theIntermediate crys ta l growth step, these techniques provide a rapid and

cost -e ff ec ti ve way to evaluate a new nonlinear matertal at an early stage

of study. Subsequent crys ta l growth ef for ts can then be directed towardsmateria ls whtch have been already characterized at the mtcrocrystal

scale, and are therefore known to possess at t ra c ti ve propert ies.He have developed two new microcrys tal devices and cha racter izat ion

techniques which apply Ful ly to all cry stal symmetries Including blaxtalcr ys tal s, and indeed, the ir power li es in the ease with which they handle

such op t ic al ly complex mate rial s. The f t r s t instrument determines the

ltnear opttcal properties using the double splndle stagerefrac tometer, 14 a modif ication of a pol ar iz ing microscope used in

opt tcal mineralogy to characte rize minerals. The double sptndle stage

refractometer determines the refractive indices throughout the visible

and near infra red with an accuracy of about 0.0001. The sample must be a

stngle cr yst al , but i t s shape can be nonsphertcal, and it s slze can be assmall as 25 microns. Crystall t tes of 50 to 100 micron dimensions are

preferred , depending on th ei r btref rtngence. The same instrument is alsocapable of determining thern~optlc coef fi cient s in the range0.0001 "K -1. The second new devlce is a nonlinear op tl ca l

gontometer,22 which measures the nonlinear opt tcal properties andphasematchtng cha rac ter ist ics di re ct ly on small mlcrocryst als (sl ze) .Hlth thts instrument, the phasematchlng locus for any three-wave processcan be dt rect ly measured. I t also determlnes the nonlinear coupling andthe angular sens i t i v i t y along that locus. An extension of the instrumentallows it to determine the temperature and wavelength sens|tlvtty of thecrys tal as wel l. The sample for th is instrument must also be a stnglecrystal, which may be asphertcal. The sample stze can be as small as100 microns, but the accuracy of the data is highest for crystals

250 - 500 microns tn size.

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N o n l i n e a r o p t i c a l m a t e r i a l s ~ r h i g h p o w e r la s e m

6. The DQuble $o tnd le S tage Refrac tometerThe doub le sp tnd le s t age r e f r ac tom e te r t s a m od i f i ca t ion o f t he

( s t ng le ) sp tnd le s t age mlc roscope developed by B loss . 12 '13 I t t se s s e n t i a l l y a p o l a r i z i n g t r a n s m i s s i o n m i cr os co p e w t t h c o i l | m a t e d

i l l u m in a t io n o f t he sample . The sample t s he ld tn a sma l l t empera tu rec o n t r o l l e d c e l l a l o ng w t t h a n o t h e r s m a ll re f e r e n c e c r y s t a l . A s t h eo r i e n t a t i o n o f t h e c r y s t a l t s c ha ng ed , t h e t ra n s m i s s i o n t h ro u g h t hec rossed mic roscope po la r i ze r s va r i e s . By de t e rm in ing the m tc roc rys t a lo r i e n t a t i o n s f o r c om p le te e x t i n c t i o n , t h e o p t i c a xe s o f t h e c r y s t a l ca nbe f o u n d , and t h e m t c r o c r y s t a l ca n t h e r e f o r e b e o r i e n t e d o p t i c a l l y . I np a r t i c u l a r, t t ca n be o r i e n t e d so t h a t a ny o ne o f t h e t h re e p r i n c i p a lo p t i c a l d i r e c t i o n s l i e s t n t h e p l a n e o f t h e m i cr os co p e s ta g e( h o r i z o n t a l ) , and p e r p e n d i c u l a r t o th e d i r e c t i o n o f l i g h t p r o pa g a t io n

{ v e r t i c a l ) . O n c e t he p r i n c i p a l o p t t c a l d i r e c t i o n s o f t h e sa m p le h avebeen de t e rmined , t he sample can be o r i en ted so tha t t he r e l e van t i ndex o fr e f r a c t i o n f o r l i g h t p a r a l l e l t o th e ( v e r t i c a l ) a x i s o f t he m ic ro sc op e t sany one o f t he th ree p r in c ip a l l nd tc es . The se can then be de t e rmined byotl immersion methods.

T yp ica l ly o t l immers ion me thods a re , however, sub jec t t o sys t ema t i ce r ro r s a s soc ia t ed wt th the deg rada t ion o f t he o t l ove r t ime . Ther e f r a c t i v e i nd e x o f a n o t l t s a f f e c te d b y t he l o s s o f v o l a t t l ecomponents , con tam inat io n , and o th er u navoida ble ag ing proce sses .

Accura t e work the re fo re r equ i r e s t ha t t he Immers ion o t l s be ca l ib ra t edr e g u l a r l y. I f t h t s c a l i b r a t i o n t s n o t c a r r i e d o u t w i t h ev e ry e x pe ri m en to n a m t c r o c r y s t a l , s y s te m a t i c e r r o r s ca n o c c u r. T h t s c a l i b r a t i o n e r r o ri s e l i m i n a t e d t f t h e r e f r a c t i v e i n d e x o f t h e o t l t s d e te r m in e d t n s t t u ,at the same t tme and tem peratu re as the sa mp le is measured. To th tspurpose , a re feren ce cr ys ta l t s tnc lu ded wt th the sample tn the immers iono t l , a nd i s u s e d t o d e te r m in e t h e r e f r a c t i v e i n d e x o f t h e o11 . I nes sence, t he doub le sp tnd le s t age compares the r e f r a c t iv e index o f t he

sa mp le d i r e c t l y w t t h th e r e f r a c t i v e i nd e x o f t he re f e re n c e c r y s t a l . T h u sthe sys t em a t i c e r ro r a s so c ia t ed wt th the use o f an immers ion o t l t sv i r t u a l l y e l i m i n a t e d .

Figu re 10 shows how a unta xta l c r ys ta l on a sp tn dle ax is serves as am l c r o r e f r a c t o m e t e r t o o b t a l n t h e o l 1 ' s r e f r a c t i v e i n d e x f o r a p a r t i c u l a r

w a v e l e n g t h o f l i g h t . T h e r e f e r e n c e c r y s t a l i s p r e c i s e l y m o u n t e d w i t h i t s

u n i q u e ( o p t i c ) a x l s p e r p e n d i c u l a r t o t h e s p i n d l e a x l s a n d a l i g n e d i n a

p l a n e p a r a l l e l t o t h e m i c r o s c o p e ' s p o l a r i z e r . A s t h e r e f e r e n c e c r y s t a l

I s r o t a t e d o n t h e s p i n d l e , t h e f u l l r a n g e o f i n d i c e s a r e o b s e r v e d - f r o m

l i g h t v i b r a t i n g p a r a l l e l t o t h e o p t i c a x i s , n . t o l i g h t v i b r a t i n g

83

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8 4 O . E i m e r le t a l .

S

z

III . . . . . ~ / / I

I I/ / ! i p

S $f s ~ / /

j l, |

I # S

I 4

! s t

10. The ordi nary (o ), and extraordinary (e) pol arl zat lons fo r a plane

wave In a unla xla l crysta l wlth wave normal s.

p e r p e n d i c u l a r , no . O nc e an o t l t s found w hich m atches the d es i red

r e f r a c t i v e in d e x o f t h e u nk no wn c r y s t a l a t t h e w a v ele n gth o f i n t e r e s t ,

t he re f e r e n c e c r y s t a l I s r o t a te d b y a n g le e u n t t l I t s e x t r a o r d i n a r y

t n de x n ( e ) m a tc he s t h e o t l . T he m u tu al r e f r a c t i v e i n d i c e s o f th e

standard, oi i and unknown are then determined from Eq. (20).

n~n 0n ( e ) - 2 s t n 2 B ) i / 2 ( 2 0 )(n e cos2e + no

Here , e I s the ang le be tween the d i re c t io n o f index match ing and the

opt ic axls of the reference cryst al and n e and n o are the prlnclpal

re fr ac ti ve indices of the reference crystal at the wavelengths of

In te re st . The procedure may be repeated for add lti ona l wavelengths un t ll

a su f fi ci ent number of data points to characterize the dispersion curve

are determined. At least four data points are required, and prefera bly

about eig ht evenly separated wavelengths shou ld be used. Because a

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Nonlinearoptical materials~ r high power ase~

re f e r ence c ry s t a l has a 11mtted r ange o f r e f r a c t i v e t nd t ce s , s eve ra l

pos s tb l e r e f e r ence c r y s t a l s , spanntng t he r ange f rom 1 .335 t o 1 .908 a re

11s ted tn Table S .

A sch em t t c d r awtng o f a sp tnd l e s t age microscope con f igu re d fo r t h t s

t ype o f r e f r a c to ee t ry t s shown tn F tg . 11. The most e l egan t p r ev tousr e a l i z a t i o n o f t h e " d o u b l e s p t n d l e s t a g e r e f r a c t o m e t e r " c o n s t r u c t e d t odate ts de scr ibe d by Nedanbach. 14 However, th ts and pre vtou s devtceshave been 11mired to v l s tb le 11ght . 15 '16 To assess f requen cy

c o n v er s io n c h a r a c t e r i s t i c s f o r n e a r t n f r a r e d a nd u l t r a v i o l e t 11 g ht ,a c c u r a t e v a lu e s o f r e f r a c t i v e t n d l c e s t n t h o se s p e c t r a l r e g t o n s ar eneces sa ry. S tmp le ex t r ap o l a t i on s o f d i spe r s ion da t a measu red t n t he

v t s t b l e a r e u s u a l l y I na d e q u at e f o r t h t s p u rp o se . T h e r e f o r e , a f e a t u r e o four sp tn dle s tage re f rac tom ete r des tgn was a CCD camera coupled to onepo r t o f t he mic roscope t ha t pe rmi t t ed tmag tng o f t he r e f e r ence and

unknown c ry s t a l f rom 0 .38 t o 1 .10 pm on a t e l e v i s i o n m on t to r. Thet n d t c e s o f r e f r a c t i o n f o r t h e r e fe r e n c e c r y s t a l s w ere a l s o m ea su re d

th rough th t s spe c t r a l r eg ton on l a rg e r s amp le s cu t f o r p r l sm spec t rome t ry.Re f r ac t i ve t nd t ce s co l l e c t e d a t a s e r t e s o f wave leng ths a r e

l e a s t - s q u a r e s f t t t o th e S e l l m e l e r e q u a t i o n :

n2 - A + _ L _ + DX2 (21)X2+C

where X t s t he wave l eng th i n I~m and n i s t he p r in c ip a l r e f r a c t i v eindex o f i n t e r e s t . To a s se s s t he accu racy o f ou r appa ra tu s ove r t he fu l lr ange o f wave l eng ths , we measured t he r e f r a c t i v e t nd l ce s o f s eve ra l known

m a t e r i a l s . I n c l u d i n g d e u t e r a te d 1 - a rg i n t n e p h os ph a te ( d -L A P ) . 4A c c u ra t e d i s p e r s i o n d a t a f o r t h e th r e e p r i n c i p a l i n d i c e s o f L A*P h av ebeen de t e rmined p re v io us ly by p r l sm spec t rome t ry. 4 The In d i v id ua l

85

Table ~, Reference Crystals for Solndle Staae Refractometrv

Compound ne no

NaNO3 1.335 1.585

CaCO 1.4 86 1.658

BaB204 1.553 1.670

ZnCO3 1.621 1.849

Lt103 1.754 1.908

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8 6 D. E imer l e t a l .

[ C a m e r a

FP ~ ) F P

S a m p l es p i n d l e

, ~ R e f e r e n c es p i n d l e

Graded interference .......... . ...... . ..........

f ilte r Lamp i ~

I I . Schematic of splndle stage refractometer (ol l cell not shown).

and P2 - pola ri zers ; F.P. - focal plane.

Pl

r e f r a c t i v e in d e x v a lu e s d e te r m in e d by s p t n d l e s t a g e r e f r a c t o m e t r y d e v i a t ef rom the mo re acc ura te pr i sm va lues by as much as 0 .002 . However, thesede v ia t i on s appea r t o be r andom, and a r e due in p a r t t o t he u nc e r t a in ty i nde t e rm in ing the p rec i se m a tch o f s t and a rd , unknown and o i l . TheS e l l m e t e r f o rm u l a ( Z ] ) a nd v a lu e s o f t h e r e f r a c t i v e i n d i c e s w e re o b t a i n e da t each wave leng th by use o f b e s t - f l t cu rves . The da t a a r e shown inF ig . 12 . Tab le 6 shoes t ha t t he se va lues , r epo r t ed fo r t he Nd:YAGfundamental and second harmonic wavelength, compare more favorably to the

prism data, with a standard deviation of 5 x 10 4 .

The main source of errors are relat ed to sample qual it y. Strai n,

poor surface qua li ty and the shape of the grain a ll af fe ct the qual it y of

the conoscoplc 13 figur e used to ori ent the cr yst al . In addi tion, an

unambiguous match between ol l and crysta l is dependent on the gral n's

boundaries, with sharp and clean surfaces at the edges providing the most

sensitive conditions.

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Nonlinear optical materials for high po wer lasers1 . 6 8 0

1.4903,000 S,O00 8,000 11,000

Wa velength (A)

12. D1sperslon of d-LAP. The curves are a Sellmeler f i t to the data.

87

Table 6. Refractive Indices fo r LA*P Determined bv Minimum Deviat ion

(M.D.) and Solndle Staae Refractometrv (S.S.) for Selected Havelenqths

Principal Index X(vm) nM.D. ns.s.

n 1.064 1.4960 1.4941

0.532 1.50go 1.5089

nB 1.064 1.5579 1.5577

0.532 1.5759 1.5754

n 1.064 1.5655 1.5651Y

0.532 1.5846 1.5845

7. The Nonllnear Ootlcal Gonlometer

Untll recently, the most common approach to new nonlinear optlcal

materlals has relied on powder SHGmethods to identify new phasematchable

second harmonic generators. 17 Large crystals of at tractive candidates

are then grown for careful evaluation of refractive index dlsperslon 18

and nonllnear coefflclents. Ig From this "global" Informatlon, the

theoretlcal efficiency for mlxlng any pai r of incident wavelengths can be

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8 8 D. Eimerl eta l .

computed. 20 To da te , ove r one hundred m ate r ta]s have beenc h a r a c t e r i z e d a t t h i s l e v e l o f d e t a t l . 11 ' 2 1 H ow ev er, t h i s

ch a r ac t e r i z a t i o n me th o d i s q u i t e s low because SHG powde r t e s t s on t he i r

own g i ve i n s u f f i c i e n t , and o f te n q u a n t i t a t i v e l y u n r e l i a b l e d a t a, and

p r o g re s s i s m a d e a t t h e r a t e t h a t r e l a t i v e l y l a rg e c r y s t a l s ca n beg rown. T he n o n l i n e a r o p t i c a l gon lome te r i n con t r a s t pe rmi t s a ccu ra tec h a r a c t e r i z a t i o n o f a new m a t e r ta l s u f f i c i e n t t o r an k i t a g a i n s t o t h e r

n o n l i n e a r m a t e r i a ls w i t h o u t r e q u i r in g r e l a t i v e l y l ar g e c r y s t a l s .

The no nl ine ar o p t ic a l gontometer de te rmines the phasematch tng curve

fo r an y f r e que nc y con v e r s i o n p roce s s o f i n t e r e s t , and measu res t he

c o u p l i n g and a n g u l a r s e n s i t i v i t y a l on g t h a t c u r v e. I t r e q u i r e s o n l y o ne

h i g h q u a l i t y , s i n g l e c r y s t a l s e v e r a l h u nd re d m i c ro n s i n s i z e . S u c h

c r y s t a l s a re o f t e n a v a i l a b l e a t t h e t n t t t a l s ta ge s o f s y n t h e s i s w i t h o u t

s p e c t a l e f f o r t , a nd e x h i b i t t h e s am e p ha se m a t ch in g p r o p e r t i e s a s l a rg e r

c r y s t a l s . T h i s l e v e l o f m a t e r i a l c h a r a c t e r i z a t i o n i s i n te r m e d i a t e

between pow der SHG measurements on the one hand, and de ta t le d l t n e a r and

n o n l i n e a r s u s c e p t i b i l i t y d e t e r m i n a t i o n s o n t h e o t h e r .In a d i re c t phasematch tng measurement, a l a se r beam (or beams) i s

p as se d t h ro u g h a c r y s t a l , a nd t h e a n g u l a r o r i e n t a t i o n o f t h e c r y s t a l i s

a d j u s t e d u n t t l a s h ar p i n c re a s e i n h a rm o n ic l t g h t i n t e n s i t y

c ha ra c t e r i s t i c o f p has em a tchtng i s f ound . 23 Fo r a g iven i nc ide n t

w a v e l e n g t h , an d a g i v e n s e t o f p o l a r i z a t i o n s , t h e c o n ti n u o u s s e t o f s uc ho r i e n t a t i o n s c o m p r is e s t h e p hasema tchtng l ocus . 24

Three bas ic k inds of in format ion about phase-matched harmonic

gen e ra t i o n c an be ob t a i n e d f rom c ry s t a l s by d i r e c t measuremen ts , a s

I l l u s t r a t e d i n F i g s . 1 3 -1 6 . T he s l m p l e s t is t h e p o s i t i o n o f t h e p h as em a t c hi ng l o c u s f o r a g i v e n p r o c e ss , i . e . Ty p e I , I I o r I I I m t x fn g 6 o f

t he wa v e le n g t h s o f i n t e r e s t . F igu re 13 shows a s e t o f phasema tchtng l oc i

f o r d o u b l l n g , t r i p l i n g a nd q u a d r u p l in g o f t h e N d:YAG fu n da m e n ta l i n a

1 nln d i ame te r c r y s t a l o f a new b l a x t a l ha rmon ic gen e ra to r, L -a rg tn tne

f l u o r i d e ( I. A F). I n a c l a s s i c pape r, 25 Hobden ob t a ined l oc i such a st h i s i n ( r e l a t i v e l y ) l a rg e c r y s t a l s o f som e o t h e r c om po un ds b y d i r e c t

measurement, bu t on ly to con f i rm the accu racy o f loc t computed f romr e f r a c t i v e i n d e x d a t a . The d a ta i n F ig . 13 r e p r e s e n t th e d i r e c t

de t e rm ina t i o n o f t he p has ema tchtng l ocus o f a m ic ro c ry s t a l o f LAF in t he

~ b~ en ce o f r e f r a c t i v e i n d e x d a t a .In LAP, the phasematch tng 1oct fo r do ub l ing 1064 nm are a lmos t

c f r c u l a r e l l i p s e s e n c l o s i n g th e l ow in d e x a x i s ( ) , a s s h ow n i nF i g . 1 4. T he e f f e c t i v e c o u p l i n g v a r i e s a l o n g t h es e l o c l , an d i n F i g . 1 4

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Nonlinearopticelmaterials or highpowerasers

~ 3 0 ) Type

1 3 . P h a s e n ~ t c h l n g I o c l f o r d ou b l i ng , t r i p l i n g a n d q u a d r u p l i n g 1 . 0 6 l~n

o b t a i n e d I n a l nvn d i a m e t e r c r y s t a l o f L a rg l n l n e f l u o r i d e . T h e 3 ~

Ty p e I l o c us I s n o t s h o w n s i n c e I t n e a r l y o v e r l a p s 2 = Ty p e I I .

A s t e r i s k s m a r k t h e o p t i c a x i s p o s i t i o n s .

the maxima of def f a re represented by dark c i rc le s , whereas the zeros

are represented by open ct rc le s . The low symmetry of UkP al lows fou rIndependent relevant d- tensor components , and the complexi ty in theva r ia t io n of def f t s shown in F tg . 15 and i s a consequence of thein t e r f e r en ce and canc e l l a t ions o f t he con t r ibu t ions from these fou rcomponents. The se data were used in Ref. 4 to determine the r e la t tv esigns of the d -ten so r components, and to loca te the opt imum phasematchtngd i r ec t ion (marked I IA tn F tg . 14 ) . By mon i to r ing the In t e n s i ty o f SHG

along the locus , the va r ia t io n o f def f can be obta ined . By carefu lcomparison with a s tanda rd, the approximate value o f de f f ts obta ined .F l n a ll y, b y d l r e c t l y s c a n ni n g t h e c r y s ta l o r i e n t a t i o n I n a d l r e c t l o n

o r t h og o n a l t o t he l o c u s , t h e a n g u l a r s e n s i t i v i t y c a n b e d e t e r m i n e d f r o m

t h e p h a s e m a t c h l n g " s i g n a t u r e " a s s h o w n I n F i g . 1 6 .

T h e d i r e c t m e a s u r e m e n t t e c h n i qu e m a k e s t h e c h a r a c t e r i z a t i o n o f

u n l a xl a l m a t er i a l s n e a r l y t r i v ia l b e c a u s e t h e p h a s e m a t c h i n g I o c l a r e

s i m p l e c o n e s a b o u t t h e u n i q u e a x i s , t h e e f f e c t i v e c o u p l i n g v a r i e s

s l n u s o l d a l l y a l o n g t h e l o c u s , a n d t h e a n g u l a r s e n s i t i v i t y i s a c o n st a n t .

T h e r e a l p o w e r o f t he t e c h n iq u e I s re a l i ze d i n th e c h a r a c t e r i z a t i o n o f

b l a x l a l c r y s t a l s , w h i c h e x h i b i t n o n t r l v l a l v a r i a t i o n s o f c o u p l i n g a n d

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90 O . E imer l e t a l .

=o

14. The phasematchlng loci for second harmonic generation in LAP are

e11Ipses encloslng the low index axls (~). The closed circles

represent local maxima in def f, and open circles represent zeros of

def f

angular acceptance along a locus, and whose loci can have complicated

topologles.25 Thi s data, along with the location of one or two

crystallographic planes determined by x-ray di ffraction on the same

sample, is suff icient to determine the orientation of cuts to produce

desired doublers or mixers from large crystals once they become

available. In certain cases, i t is possible to determine the signs and

magnitudes of individual d coefficients by combining x-ray data and the

positions of maximum or vanishing nonlinear coupling when the

crystallographic point group is known. 26

Of course, this level of characterization gives information only

about the processes di rectly studied, and thus is less general than prism

and wedge measurements. On the other hand, from a series of direct

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m

J

e,-

o

~ 2 ~ 1

Nonlinear optical materials for high power lasers

1 I I I I

0

IA

zx

, s =

60 120 180 ~ 240 ~ 300 ~

A

91

|o0

I

LAP 20} II

I,,

0 60"

IIC

I I I I

lid

I I

liB

120 180 240 300 360

15. Var i a t i on of second harmonic In t ens i t y a long the phasematching locus

for Type I I doub l tn g of 1 .064 ida tn d-LAP. The sol id l t ne i s the

cal cul a te d curve . These data were used to determin e the re la t i ve s ign

of the d- tensor components for d-LAP.

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92 D . E i rn e r l e t a / .

LAP:Type U A

-10 0 10

An gle to plate normal (degrees)

16. Angular acceptance data for d-LAP Type II at the point IIA of Fig.

14, where the coupllng C Is a maximum. Solld line Is least squares

f i t to the function sJnc 2 (I/2I~BL).

measurements at discrete wavelengths, the behavior of the materlal for

other processes can often be assessed by Interpolation.

I t is important to note the smallest crystal slze for which i t is

theoretlcally posslble to make direct phase matching measurements. The

sole cr iter ion which must be satisfied is that the true phasematching

positions be distinguishable from subsidiary intensity maxima where the

coherence length is local ly maximum, but not in finite. For this to be

true, the slze of the part icle must exceed the inverse of the angular

sensitivity:

>> 2~/~ e (22)

For example, for Type II doubllng of 1.06 ~m in potassium dihydrogen

phosphate (KDP) which has an angular sensitivity of 2500 cm-I/rad , a

part icle size of 100 microns is suff icient to resolve the phase matching

locus. I t is , perhaps, surprising to note that this cr iterion is exactly

the same as the one derived by Kurtz and Perry 17 to determine when

phasematched SHGdominates the powder signal of a material. Thus, I f

materials are synthesized with crys tal lite sizes large enough to

determine whether or not they are phasematchable by a powder test, then

i t is possible to obtain much more precise information about their

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Non l inear op tica l mate r ia l s ~ r h igh powe r la se rz

pr op er t ies by d i re c t measurements . The sam ple ha nd l ing methods we

cu r r e n t l y e mploy a l l o w us to s t u dy pa r t i c l e s a s sma ll a s 300 l~m in

d iam eter, bu t improvements which w t l l pe rm i t the s tudy of 100 I~n s izedsamples appear feas ib le .

Samples fo r d ir e c t phasematchtng m easurements can be produced by avar iet y of methods. I n l t l a l attempts at crystal synthesis, eith er byhigh temperature melt growth or by evaporation or cooling of solutions,often re su lt in po ly crys ta ll in e masses with single cr yst al domains a fewhundred microns in size. In add it ion , submlll lmeter sized samplesproduced by fa st f ibe r pu lli ng technlques 27 or by growth inca pl ll ar le s 2B are ideal for these studies. Hhile i t is possible tomake measurements on cr ys ta l l l tes in th ei r natura l habi ts or on cleavagepla tes , we have found i t convenient to grind samples in to a spherical or

el ll ps ol da l shape, in part because i t is much simpler to estimate theoptical path length as a function of orientation in a spheroidal sample.In addi tion , a well rounded sample presents an entrance surface which isnearly normal to the laser beam for al l ori en ta tions, making ref rac tio ncorrections less serious. Fina ll y, manipulation of the crys talor ie nt at io n fo r mounting (see below) is much easier for rounded samples.Figure 17 shows the morphology of a typica l sample af te r rough grindingin a commercially avai lable sphere former. Subsequent polishing bytumbling with fine g r l t or solvent etching is often possible. In anycase, s cat ter ing due to poor surface qu al it y is grea tly reduced byimmersing the sample in an index matching f lu id when measurements aremade. This also reduces the lens ing effe ct of the spherical sample sincethe focal length of a sphere of radius r and index n A immersed in af lu id of index nBls given by F - rnA/2(n A -n B) . The refr act iveindices of the f lu id and sample can usually be matched to better than0.Ol . although for very bir ef ri ngen t samples th is may necessi tatechanging the matching fl u id for di ff ere nt phase matching types.

Samples are permanently bonded to the glass fibers in pa rti cu la rori ent ati ons with respect to the princip al d ie le ct ri c axes. Figure 18shows a cry st al mounted on a glass fibe r and suspended in immersion f lu idand shows th at the transparency of even a roughly ground sample isreasonable when immersed in a fl u id with a near index match. The

positions of the princ ipal axes of the ref ract ive index el li ps oi d of thesmall crystallite are located by principal and optic axis interferencefig ures , using the same techniques as the spindle stage microscope. 12'13These pr in ci pa l axes are label led ~, ~ and y with the convention that

93

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9 4 D . E i r n e r l e t a / .

17. Spheroldal sample of barlum metaborate produced by ai r tumbling.

n < n B < n . Typi cal ly, two orientati ons are suff ici ent to

obtain the entire locus for any frequency mixing or doubling process in a

biaxi al cry st al . In the fi r s t , the crystal is mounted with the glass

fi ber par al lel to the 8 axis (perpendicular to the optic plane, using the

convention n < n B < n ). In the second, the fiber is paral lely

to the highest index dir ecti on (y). For uniaxial cr ystals, a single

ori entati on, eit her with the optic axis paral lel or perpendicular to the

fi ber , is usually suf fi ci ent to obtain a part icu lar locus.

The apparatus for measuring SHG in small crystal s is shown

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N o n l i n e a r o p t ic a lm a t e r i a l s f o r h i g h p o w e r l a s er s 95

18. Crystal immersed in refract ive index matching f lui d.

schematically In Fig. 19. Part of the laser beam is spl l t of f and

doubled (with low efficiency) in a separate nonlinear crys ta l. The

doubled l igh t intensi ty serves as a normaIizatlon slgnal to account for

laser power fl uctuat ions . The second harmonic signal from the sample is

detected in a photomulti pller , using a ground fused si l lca plate to

diffuse and depolarize the detected l ight and cal ibrated neutral density

f i l t e rs to attenuate the signal into the linear range of the detector.

The second harmonic and normalization signals are col lected, averaged and

di gi ti zed for analysls. As the phasematchlng curve is traced out, the

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9 6 D . E i m e r l e t a l .

2r . . . . . . ~I i,

A A ; . 2 , I F1 / F2

T , ~ . ; w 2 1 .

1B o x c a rt r igger I

N o r m a l i z a t i o nsignal

PMT

19. Schematic of apparatus for phasematchlng measurements.

A: aperture; PD: photodiode; KTPI and 2: doubling crys ta ls;

HI,W2: waveplates; Fl, F2: f i l t e r s ; L: 20 cm focal length lens; P:

po lar izer. The segment enclosed by the dashed line is inserted for

3~ and 4~ experiments.

azimuthal () and polar (8) angles of the crystal in the iaboratory

frame are recorded. The coupling C is determined from the signal for

points exactly along the phasematching curve,

2Ip = [Cp. p. l l n c] (23)

Here l in c is the incident in tens it y, and the point P(e,) li es on

the curve. The optical thickness of the sample Ip is calculated by

modeling the sample as an el lipsoi d. The accuracy of this calculation

for typical samples is about 5%, although very occasionally, an oddly

shaped sample result s from the grinding process, and the e11ipsoidal f i t

is less accurate. Phase mismatch and walK-off are negl igible because the

confocal parameter of the focused beam greatly exceeds the crystal size,

as does the walkoff length due to double re frac ti on. The absolute

magnitude of the coup]ing is obtained by careful comparison with a

sui table standard. The angular sensi tivi ty at the point P is measured by

scanning along the arc at P perpendicular to the phasematchlng curve. I f

is the angle describing location along thi s arc then

I p ( ~ ) ~ s i n c 2 ( ~ p ~ ) ( 2 4 )

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N o n l i n e a r o p t ic a l m a t e r ia l s ~ r h i gh p o w e r l a i r s

where s lnc (x ) . s l n (x ) /x , and ~p I s t he angu la r s e n s i t i v i t y a t thepo in t P. The q ua l t ty o f the f i t to the phase matching s ign ature (24) i sa c r i t e r i o n f o r Ju dg in g c r y s t a l q u a l t t y and t he r e l i a b i l i t y o f th ea n g u l a r s e n s i t i v i t y a n d i n t e n s i t y d a t a .

HJth the m ethods des cribed above, ph ase matching ang les can bedetermined to = 25 mrad, angular s e n s i t iv i t ie s to b e t t e r than 20"I. andde f f values in good q u a lt t y samples to 25% fo r second harmontcgen erat ion at 1.064 microns. The major sources of er ro r fo r the angularacceptance and in te n s i t y measurements are the sample surface q u a lt t y , andthe un ce r t a in ty tn op t t ca l path leng th . Fo r work in the u l t r a v io l e t , t here l a t tve d i spe r s ion o f a va i l ab l e t ranspa ren t immers ion o t l s exace rba te sthe tndex mismatch problem. The accuracy o f Cp is redu ced to z 50%,but th is i s s t t11 accura te enough to e va lua te and rank the m ate r ia l .

very accura te va lues of J C p I2 a re ob ta ined , i t i sfsome times poss ib l e t o deduce va lues o f t he In d iv id ua l d -c oe ff i c i e n t s byf i t t i n g the observed var la tlo n of Cp along

course, one must know the crystal class of

number of independent d-coef fi cl ents . The

Cp Is often marginal fo r thi s purpose, but

1ocatlon of i t s maxima, and of those zeros

the phasematchlng curve. Of

the sample must to reduce the

accuracy of the magnitude of

much can be deduced from the

not required by crystal

symmetry. Relatlve, signed values for ind ividual d-coeff lcl ent s were

obtained using thi s method for two materlals, d-LAP, 4 and

NaLaF4.26 K1elnman symmetry 8 reduces the number of unknowns, and

is usually well with in the uncer tainty of these measurements. For

blaxl al crys ta ls in point groups I , 2, m, and mm2, some convention must

be chosen for the posit ive dir ect ion of the polar axls to uniquely define

the re la ti ve signs. For unlaxial crysta ls in 3, 3m, 6 and 4 i t is

necessary to find the 1ocatlon of the maximum def f relat ive to the

(lO0) or (010) dir ect ions. Nlth the op tl ca ll y oriented cryst al mounted

on a gonlometer head, i t is straightforward to determine the complete

rel atl onshlp between the optical and crystallographlc axes by x-ray

dlff ract ion. 12

97

8. Oraanlc Nonllnear Materials for ICF Aoolications

The laser required for an economlcally vlable power stat ion using ICF

is large. Energy of I - 10 MJ in a nomlnally lOns pulse, with a beam

divergence not greater than 0.1 mrad, at a wavelength in the near

ul t ravi ol e t and posslbly large frequency bandwidth are cur ren tly thought

to be requlred. I '2 This wavelength range can be reached by frequency

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98 D . E i m e r l e t a l .

conversion of an ef fi ci en t infra red laser.

For the ove ral l lase r system to be cost -e ff ec ti ve , the frequencyconversion must be very ef f ic ie nt . That is , the nonlinear materlal must

have a low threshold power, and must not have si gn if ic an t absorptions at

any of the relevan t wavelengths. However, al l materials which sa ti sf y apa rt icul ar threshold power cr it er io n are not equally suitable inpractice. In the f i r s t place, detalled calculatlons show that a very

nonllnear material would necessarily be configured as a thin plate to

avoid back-converslon. 2g Thin plates are mechanlcally weak and cannot

be fabricated Into large area plates, 11mltlng the Indlvldual aperture

size. In the second place, the cost of the laser driver increases

signi fica nt ly with the the sum of the areas of a11 the output apertures.

There is a minimum value (and therefore a minimum cost) fo r the to ta l

aperture which is determlned by materials liml ts on the int en si ty or

fluence. Thus, the tot al area w111 be affected by damage thresholds of

optl cal elements, and by any other Int en sl ty -l lml tl ng effects such as

two-photon absorption, st|mulated Raman or Br111ouln scattering and

self-focusslng and/or phase-modulatlon. The las t three processes are

determined by the chemical composition and structure of the material,

while the damage threshold is determined by the presence of inclusions,

defects, or impurities incorporated during crystal growth.

Thus, ICF applications call for a hlgh damage threshold

(20 - 40 J/cm 2 at 10 ns, a11 wavelengths), 1'2 an ef fec ti ve coupllng

about 2 - 4 times as large as that of KDP, and a low absorption. The

angular se nsi t ivi ty, stimulated Raman gain, and nonlinear re fr acti ve

index must be comparable to or smaller than those of KDP. The material

must be inexpensive to grow, fabricate and pol lsh, would preferably be

posslble to ant l-re flec tion coat. We believe that a11 of these

conditions can be met by certain molecular crystal s of slmple organic

compounds.

Many organic crys tals with second harmonic generatlng properties areknown, II '2 1' 30 and are of in ter est prlmaril y due to t he ir large

nonllnear lty, the SHG moiety is a conjugated ring or i ts der ivati ve.

However, the conjugated ring is not sultable for ICF because i t exhibi ts

photochemical processes in the near ul travlolet , as well as losses due to

11near and nonlinear absorption losses. However, since the nonl ineari ty

required is not much larger than that of KDP, other SHG molties can be

used, such as the conjugate C02 group. Indeed, usi ng the expert

system described earlier, we calculated the threshold power of all

(s uff Ic len tl y well characterized) known materials ? for doubling or

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100 D . E i m e r l e t a l .

these crysta ls are similar and they are a l l lonlcal ly bonded, many other

properties which re ly less c r l t l c a l l y on structu ral deta ils w111 show

marked re gu la rl ti es . In par tl cuI ar , th ei r mechanlcal strength, and the

li near and two-photon absorption properties, which arise from slmll ar

spectroscopic tr ansl tl on s, are not expected to vary strongly from crysta lto cr ys ta l. Of course, these properties may well have an or lentat lonal

dependence which varles with structure.

Thus, In fol lowing th is strategy, the focus of ICF research is on the

11near optlcal properties: adequate nonl ln ea rl ty is more common than

su ff ic len t ly low angular s en si t iv it y. In f act , most of the compounds we

have examined have adequate blrefrlngence for second- and thlrd-harmonlc

generation of 1.064 ~m, but most have a larger angular sensl t l vl ty than

KDP because the blrefrlngence Is sl gn l flcantly larger. He have found

several crys tals with n onl inear it les 2 - 4 tlmes greater than the

d36(KDP). Table 7 gives the phase matching parameters for several

crysta ls we have characterized recently using the mlcrocrysta111ne

techniques. These Include L-arglnlne phosphate (LAP), L-arglnine

fluorlde (LAF), and dlammonlum tartrate (DAT). Crystals of DAT and ~F

T~ble 7. ProDertles of some ionic oraanlc crysta ls for doubllna 1.064 um

Material

LAP

Type deff(pm/V) a) (cm-I/rad) Pth(MW)

I 0.99 6900 63

I I 0.93 4]00 26

LAF I 1.24 4900 21

I I 0.93 4100 26

DAT I 0.53 5700 154

I I 0.37 2150 47

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

KDP I 0.25 4900 500

I I 0.35 2500 70

(a) Maximum def f for the given type. Based on d36 - 0.93 pm/V.

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N o n l i n e a ro p t i c a l m a t e r i a l s f o rhigh pOwer lase rs

a n d o t h e r c o m p o u n d s h a v e b e e n g r o w n b y s l m p l e e v a p o r a t l o n o r c o o l l n g

t e c h n l q u e s t o v o l u m e s b e t w e e n I a n d 1 0 c m , a n d c r y s t a l s o f L A P t o

a b o u t 1 0 0 c m a n d l a r g e r .

9 . Oo t t ca l p rooe r t1~s o f Ch t r a l Ac td Crvs t a l sT he u l t r a v i o l e t e d g e t s d e te rm i ne d by s t ro n g ~ - ~ * t r a n s i t i o n s

a s soc i a t ed w t th t he sma l l con juga t ed g roups . Th t s edge t s g en e ra l l y a twavelengths lower than 250 nm fo r carb oxy la te o r guanadyl groups , and may

be somewhat re ds h t f ted fo r tm |d azo ly l (F tg . ZO). However, LAP exh tbJ t s as i g n i f i c a n t a b s o r p t i o n f e a t u r e 4 ( 1 - 3 ~ /cm ) i n t h e r e g i o n b e tw e e n 2 50and 300 nm. Thts Js p rob ably due to n - ~* t r a n s l t t o n s . The

wave l eng th o f t he se t r a n s i t i o n s Jn ca rb oxy l l c ac td s ha s been shown tod ep en d s i g n i f i c a n t l y o n t h e m o l e cu l a r s t r u c t u r e , 3Z b u t v e r y l t t t l e

In fo rm a t ion t s known abou t t h e t r behav to r t n o the r k inds o f o rgan i cs a l t s .

I n t he nea r i n f r a r e d , ( 0 .9 -1 .5 Fm) ove r tone abso rp t i ons o f N-H,O - H , a nd C-H s t r e t c h i n g v i b r a t i o n s ca n be q u t t e s t r o n g . T h e s e c r y s t a l sa re e x t e ns ive ly hydrogen and conse quen t ly have over tone a bso rp t io ns whtchlead to losse s o f 10-20~/cm at the Nd:YAG fundamental wa vele ng th. 33

D e u t er a tJ o n ca n r ed u ce t h t s a b s o r p t i o n s i g n i f i c a n t l y . 4 C-H s t r e t c h i n g

ove r tones a r