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Strong second harmonic generation of a ruby laser in lithium iodate
Volume 29A, number 2
PHYSICS LETTERS
7 April 1969
w h e r e ~ i s the e x t e r n a l e l e c t r i c field due to ¢ , ~-1 i s the t h e r m a l e n e r g y , 0(7) is the unit step function, and the zero s u p e r s c r i p t denotes a v e r a g i n g o v e r the u n p e r t u r b e d e n s e m b l e . In this f o r m a l i s m , ( k l , k2) = = (k, k), ( - k , - k ) , ( k , k ) , o r (-/(, k). In p a r t i c u l a r , the d.c. t e r m ( ] ( ! = 0,t)) i s obtained by f o r m i n ~ t h e s u m of the p a i r of eq. (3) g e n e r a t e d f r o m (k, - k ) and ( - k , k). Let the l i n e a r and quadratic external conductivities (?alz and bag v be defined by the O h m ' s law:
(j~(r,t)>=
d~ f d3~ -~o
Vol
5au(~,-r)~(r-~,t-~)+f
dT1 f d~2 f d3~1 f
-~o
-~o
Vol
3
Vol
(4) ×E~(r-~l,t-~l)Ev(r-~2,
t-T2),
and let aa~z(kl,T 1) and ~ a g v ( k l , k 2 , T1,72) be t h e i r spatial F o u r i e r t r a n s f o r m s . Then f r o m (3) and (4) one u l t i m a t e l y o b t a i n s the u s u a l l i n e a r Kubo conductivity r e s u l t [2] and the following e x p r e s s i o n for the q u a d r a t i c conductivity: ^
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aa#v ( k l ' k 2 ' TI' T2) = ~ o l 0(T1 ) 0(~'2 - T1 ) × (( J g ( - k l ' t - 71 )Jr ( - k 2 , t-T2 )Ja(kl + k2, t))° + (5) iklg +
( [ P ( - k l , t - T1), Jv(-k2, t -r2)]ja(kl +k2't))°) •
~k 2
References 1. R. L. Peterson, Rev. Mod. Phys. 39 (1967) 69. 2. R. Kubo, J. Phys. Soc. Japan 12 (1957) 570. $ * $ $ $
STRONG SECOND HARMONIC GENERATION A R U B Y L A S E R IN L I T H I U M I O D A T E
OF
G. NATH
Physik Department der Technischen Hochschule Mi~nchen, Germany and
S. H A U S S U H L Institut j~r Kristallographie der Universititt K~ln, Germany Received 17 February 1969
LiIO3 shows strong second harmonic generation of 3470 .~ when irradiated with a ruby laser. A LiIO3 crystal of only 0.13 cm thickness shows a much higher second harmonic output than KDP crystals several cm in length. A f t e r the finding of m a t e r i a l s such a s LiIO 3 [1,3] showing u n u s u a l l y high n o n l i n e a r optical c o n s t a n t s , the phase matched SHG of N d - l a s e r r a d i a t i o n has b e c o m e e x t r e m e l t efficient. We r e p o r t in this l e t t e r a l s o a v e r y high n o n l i n e a r b e h a v i o r of the s a m e c r y s t a l at higher f r e q u e n c i e s ,
which allows p r o d u c t i o n of u . v . light p u l s e s f r o m incident ruby l a s e r r a d i a t i o n with an efficiency much higher than those p r e v i o u s l y reported. M a t e r i a l s being m a i n l y used until now for the g e n e r a t i o n of 3470 A a r e c r y s t a l s of the KDP group [3], such as KH2PO4, NH4PO 4 and 91
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Fig. 1. Dependence of the second harmonic intensity on the deviation from the phase matching angle 0 m . K H 2 A s O 4. T h e p h a s e m a t c h e d n o n l i n e a r c o n s t a n t s of t h e s e m a t e r i a l s a r e n e a r the v a l u e of t3~DP [4]. T h e n o n l i n e a r c o n s t a n t t31 of L i I O 3 , h o w e v e r , w h i c h i s e f f e c t i v e f o r p h a s e - m a t c h e d SHG of both Nd- and ruby laser radiation, exceeds this value by a f a c t o r of a b o u t 30 [2]. In o r d e r to u n d e r s t a n d t h e p h a s e - m a t c h i n g c o n d i t i o n s of L i I O 3 f o r r u b y l a s e r r a d i a t i o n , we measured the relevant principal refractive indices of LiIoO 3 by t h e m i n i m u m d e v i a t i o n m e t h o d . At 3470 A we found n ° = 1.984 and n e = 1.819. T h e i n d e x v a l u e s at 6940 A a r e n ° = 1.875 and n e = = 1.731. T y p e I [5] p h a s e m a t c h i n g of both the 6940 A and the 3470 A r a d i a t i o n i s p o s s i b l e , w h e r e a s t h e i n d e x c o n d i t i o n f o r t y p e II P M [5] c a n n o t be f u l f i l l e d . T h e c a l c u l a t e d [3] P M a n g l e h a s a v a l u e of 52.8 ° r e l a t i v e to t h e c - a x i s . T h e e x p e r i m e n t a l l y o b s e r v e d d i r e c t i o n w a s 52 ° + 1 °. T h e d e p e n d e n c e of t h e s e c o n d h a r m o n i c i n t e n s i t y on t h e d e v i a t i o n f r o m t h e P M a n g l e Om is shown in fig. 1. A p l a t e of LiIO3 of 0.13 c m t h i c k n e s s , cut f o r n o r m a l i n c i d e n c e , w a s i r r a d i a t e d w i t h a pulsed Q-switched ruby laser (intensity 50 M W / c m 2, b e a m d i v e r g e n c e A about 0.25°). T h e a n g u l a r width at half i n t e n s i t y is a p p r o x i m a t e l y 15' w h i c h i s r o u g h l y c o m p a r a b l e to KDP [6]. T h e a n g l e p b e t w e e n the e l l i p t i c a l and s p e r i c a l i n d e x s u r f a c e s at t h e m a t c h i n g a n g l e 8m h a s a v a l u e of 3 ° (in K D P p = 1.8o). T h e so c a l l e d c o h e r e n c e l e n g t h [7] / c o h = 2 / k l A s i n p, i s 0.055 c m f o r L i I O 3 and 0.11 c m f o r K D P w h e n A = 0.25 o. T h e c o h e r e n c e l e n g t h i s the l i m i t b e y o n d w h i c h t h e i n t e n s i t ~ of t h e s e c o n d h a r m o n i c no l o n g e r v a r i e s a s / a b u t a s l, w h e r e l i s t h e c r y s t a l 92
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length. T h e h i g h c o n v e r s i o n e f f i c i e n c y of L i I O 3 i s d e m o n s t r a t e d by a c o m p a r i s o n w i t h KDP. P l a t e s of L i I O 3 and of KDP h a v i n g the s a m e t h i c k n e s s , 0.13 c m , and both cut w i t h t h e P M d i r e c t i o n n o r m a l to the s u r f a c e , w e r e i r r a d i a t e d w i t h a l a s e r i n t e n s i t y of 50 M W / c m 2 and both a d j u s t e d f o r m a x i m u m s e c o n d h a r m o n i c output. T h e i n t e n s i t y of the s e c o n d h a r m o n i c f r o m the L i I O 3 c r y s t a l w a s 150 t i m e s h i g h e r than t h a t of KDP. T h e s a m e 0.13 c m p l a t e of L i I O 3 s h o w e d a second harmonic intensity still ten times greater t h a n a K D P c r y s t a l 1.3 c m in length. G i v e n a d i v e r g e n c e of the l a s e r b e a m not m u c h l o w e r than 0.25 ° we e x p e c t , t h a t K D P c r y s t a l s w i t h l e n g t h s of t h e o r d e r of 10 c m w o u l d be n e c e s s a r y in o r d e r to o b t a i n t h e s a m e s e c o n d h a r m o n i c o u t put g i v e n by a p l a t e of L i I O 3 o n l y 0.13 c m thick. M o r e o v e r , if l a s e r b e a m s w i t h f i n i t e a p e r t u r e of about 0.5 c m a r e u s e d , w a l k off p h e n o m e n a [7] w i l l s e n s i b l y r e d u c e the s e c o n d h a r m o n i c output of s u c h l a r g e c r y s t a l s . T h e m a x i m u m l e n g t h of a LiIO3 c r y s t a l up to w h i c h the s e c o n d h a r m o n i c i n t e n s i t y i n c r e a s e s i s about 0.25 c m . T h i s l i m i t i s i m p o s e d by the s t r o n g a b s o r b t i o n of the s e c o n d h a r m o n i c light by t h e c r y s t a l i t s e l f . A s can be s e e n f r o m t h e t r a n s m i s s i o n c u r v e in ref. 2 t h e t r a n s m i s s i o n of a p l a t e of 2 m m thicknesSoWith E p a r a l l e l to the c - a x i s i s o n l y 46% at 3470 A. At 7 6 ° K we c o u l d not find a n o t i c e a b l e i n c r e a s e of t r a n s m i t t a n c e at t h e s a m e w a v e l e n g t h . We h a v e shown that a thin p l a t e of LiIO3 p r o d u c e s m u c h h i g h e r u.v. i n t e n s i t y than can e a s i l y be a t t a i n e d w i t h c o n v e n t i o n a l K D P c r y s t a l s . In a d d i t i o n , a s h a s b e e n r e p o r t e d e a r l i e r [2], L i I O 3 c r y s t a l s a r e not h y g r o s c o p i c and can be g r o w n f r o m w a t e r s o l u t i o n s with good o p t i c a l q u a l i t y * F u r t h e r g r o w t h e x p e r i m e n t s w i t h L i I O 3 in an e f f o r t to m i n i m i z e the i m p u r i t i e s and to i n c r e a s e the t r a n s m i t t a n c e at 3470 A a r e in p r o g r e s s . T h e a u t h o r s a c k n o w l e d g e d i s c u s s i o n s with K. Dransfeld about the manuscript. * Further informations on growth and supply of LiIO 3 crystals can be obtained by M. Gslinger, Physik Department der Technischen Hochschule Milnchen. References
1. S.K. Kurtz, T. T. P e r r y and I. G. Bergman J r . , Appl. Phys. Letters 12 (1968) 186. 2. G. Nath and S. Hausstlhl, Appl. Phys. Letters, to be published. 3. J . A . Giordmaine, Phys. Rev. Letters 8 (1962) 19. 4. R. C. Miller, Appl. Phys. Letters 5 (1964) 17. 5. J. E. Midwinter and J. Warner, Brit. J. Appl. Phys. 16 (1965) 1135. 6. P.D. Maker, R.W. Terhune, M. Nisenhoff and C. M. Savage, Phys. Rev. Letters 8 (1962) 21. 7. D.A.Kleinman, Phys. Rev. 128 (1962) 1761.
PHYSICS LETTERS
7 April 1969
w h e r e ~ i s the e x t e r n a l e l e c t r i c field due to ¢ , ~-1 i s the t h e r m a l e n e r g y , 0(7) is the unit step function, and the zero s u p e r s c r i p t denotes a v e r a g i n g o v e r the u n p e r t u r b e d e n s e m b l e . In this f o r m a l i s m , ( k l , k2) = = (k, k), ( - k , - k ) , ( k , k ) , o r (-/(, k). In p a r t i c u l a r , the d.c. t e r m ( ] ( ! = 0,t)) i s obtained by f o r m i n ~ t h e s u m of the p a i r of eq. (3) g e n e r a t e d f r o m (k, - k ) and ( - k , k). Let the l i n e a r and quadratic external conductivities (?alz and bag v be defined by the O h m ' s law:
(j~(r,t)>=
d~ f d3~ -~o
Vol
5au(~,-r)~(r-~,t-~)+f
dT1 f d~2 f d3~1 f
-~o
-~o
Vol
3
Vol
(4) ×E~(r-~l,t-~l)Ev(r-~2,
t-T2),
and let aa~z(kl,T 1) and ~ a g v ( k l , k 2 , T1,72) be t h e i r spatial F o u r i e r t r a n s f o r m s . Then f r o m (3) and (4) one u l t i m a t e l y o b t a i n s the u s u a l l i n e a r Kubo conductivity r e s u l t [2] and the following e x p r e s s i o n for the q u a d r a t i c conductivity: ^
82
aa#v ( k l ' k 2 ' TI' T2) = ~ o l 0(T1 ) 0(~'2 - T1 ) × (( J g ( - k l ' t - 71 )Jr ( - k 2 , t-T2 )Ja(kl + k2, t))° + (5) iklg +
( [ P ( - k l , t - T1), Jv(-k2, t -r2)]ja(kl +k2't))°) •
~k 2
References 1. R. L. Peterson, Rev. Mod. Phys. 39 (1967) 69. 2. R. Kubo, J. Phys. Soc. Japan 12 (1957) 570. $ * $ $ $
STRONG SECOND HARMONIC GENERATION A R U B Y L A S E R IN L I T H I U M I O D A T E
OF
G. NATH
Physik Department der Technischen Hochschule Mi~nchen, Germany and
S. H A U S S U H L Institut j~r Kristallographie der Universititt K~ln, Germany Received 17 February 1969
LiIO3 shows strong second harmonic generation of 3470 .~ when irradiated with a ruby laser. A LiIO3 crystal of only 0.13 cm thickness shows a much higher second harmonic output than KDP crystals several cm in length. A f t e r the finding of m a t e r i a l s such a s LiIO 3 [1,3] showing u n u s u a l l y high n o n l i n e a r optical c o n s t a n t s , the phase matched SHG of N d - l a s e r r a d i a t i o n has b e c o m e e x t r e m e l t efficient. We r e p o r t in this l e t t e r a l s o a v e r y high n o n l i n e a r b e h a v i o r of the s a m e c r y s t a l at higher f r e q u e n c i e s ,
which allows p r o d u c t i o n of u . v . light p u l s e s f r o m incident ruby l a s e r r a d i a t i o n with an efficiency much higher than those p r e v i o u s l y reported. M a t e r i a l s being m a i n l y used until now for the g e n e r a t i o n of 3470 A a r e c r y s t a l s of the KDP group [3], such as KH2PO4, NH4PO 4 and 91
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Fig. 1. Dependence of the second harmonic intensity on the deviation from the phase matching angle 0 m . K H 2 A s O 4. T h e p h a s e m a t c h e d n o n l i n e a r c o n s t a n t s of t h e s e m a t e r i a l s a r e n e a r the v a l u e of t3~DP [4]. T h e n o n l i n e a r c o n s t a n t t31 of L i I O 3 , h o w e v e r , w h i c h i s e f f e c t i v e f o r p h a s e - m a t c h e d SHG of both Nd- and ruby laser radiation, exceeds this value by a f a c t o r of a b o u t 30 [2]. In o r d e r to u n d e r s t a n d t h e p h a s e - m a t c h i n g c o n d i t i o n s of L i I O 3 f o r r u b y l a s e r r a d i a t i o n , we measured the relevant principal refractive indices of LiIoO 3 by t h e m i n i m u m d e v i a t i o n m e t h o d . At 3470 A we found n ° = 1.984 and n e = 1.819. T h e i n d e x v a l u e s at 6940 A a r e n ° = 1.875 and n e = = 1.731. T y p e I [5] p h a s e m a t c h i n g of both the 6940 A and the 3470 A r a d i a t i o n i s p o s s i b l e , w h e r e a s t h e i n d e x c o n d i t i o n f o r t y p e II P M [5] c a n n o t be f u l f i l l e d . T h e c a l c u l a t e d [3] P M a n g l e h a s a v a l u e of 52.8 ° r e l a t i v e to t h e c - a x i s . T h e e x p e r i m e n t a l l y o b s e r v e d d i r e c t i o n w a s 52 ° + 1 °. T h e d e p e n d e n c e of t h e s e c o n d h a r m o n i c i n t e n s i t y on t h e d e v i a t i o n f r o m t h e P M a n g l e Om is shown in fig. 1. A p l a t e of LiIO3 of 0.13 c m t h i c k n e s s , cut f o r n o r m a l i n c i d e n c e , w a s i r r a d i a t e d w i t h a pulsed Q-switched ruby laser (intensity 50 M W / c m 2, b e a m d i v e r g e n c e A about 0.25°). T h e a n g u l a r width at half i n t e n s i t y is a p p r o x i m a t e l y 15' w h i c h i s r o u g h l y c o m p a r a b l e to KDP [6]. T h e a n g l e p b e t w e e n the e l l i p t i c a l and s p e r i c a l i n d e x s u r f a c e s at t h e m a t c h i n g a n g l e 8m h a s a v a l u e of 3 ° (in K D P p = 1.8o). T h e so c a l l e d c o h e r e n c e l e n g t h [7] / c o h = 2 / k l A s i n p, i s 0.055 c m f o r L i I O 3 and 0.11 c m f o r K D P w h e n A = 0.25 o. T h e c o h e r e n c e l e n g t h i s the l i m i t b e y o n d w h i c h t h e i n t e n s i t ~ of t h e s e c o n d h a r m o n i c no l o n g e r v a r i e s a s / a b u t a s l, w h e r e l i s t h e c r y s t a l 92
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length. T h e h i g h c o n v e r s i o n e f f i c i e n c y of L i I O 3 i s d e m o n s t r a t e d by a c o m p a r i s o n w i t h KDP. P l a t e s of L i I O 3 and of KDP h a v i n g the s a m e t h i c k n e s s , 0.13 c m , and both cut w i t h t h e P M d i r e c t i o n n o r m a l to the s u r f a c e , w e r e i r r a d i a t e d w i t h a l a s e r i n t e n s i t y of 50 M W / c m 2 and both a d j u s t e d f o r m a x i m u m s e c o n d h a r m o n i c output. T h e i n t e n s i t y of the s e c o n d h a r m o n i c f r o m the L i I O 3 c r y s t a l w a s 150 t i m e s h i g h e r than t h a t of KDP. T h e s a m e 0.13 c m p l a t e of L i I O 3 s h o w e d a second harmonic intensity still ten times greater t h a n a K D P c r y s t a l 1.3 c m in length. G i v e n a d i v e r g e n c e of the l a s e r b e a m not m u c h l o w e r than 0.25 ° we e x p e c t , t h a t K D P c r y s t a l s w i t h l e n g t h s of t h e o r d e r of 10 c m w o u l d be n e c e s s a r y in o r d e r to o b t a i n t h e s a m e s e c o n d h a r m o n i c o u t put g i v e n by a p l a t e of L i I O 3 o n l y 0.13 c m thick. M o r e o v e r , if l a s e r b e a m s w i t h f i n i t e a p e r t u r e of about 0.5 c m a r e u s e d , w a l k off p h e n o m e n a [7] w i l l s e n s i b l y r e d u c e the s e c o n d h a r m o n i c output of s u c h l a r g e c r y s t a l s . T h e m a x i m u m l e n g t h of a LiIO3 c r y s t a l up to w h i c h the s e c o n d h a r m o n i c i n t e n s i t y i n c r e a s e s i s about 0.25 c m . T h i s l i m i t i s i m p o s e d by the s t r o n g a b s o r b t i o n of the s e c o n d h a r m o n i c light by t h e c r y s t a l i t s e l f . A s can be s e e n f r o m t h e t r a n s m i s s i o n c u r v e in ref. 2 t h e t r a n s m i s s i o n of a p l a t e of 2 m m thicknesSoWith E p a r a l l e l to the c - a x i s i s o n l y 46% at 3470 A. At 7 6 ° K we c o u l d not find a n o t i c e a b l e i n c r e a s e of t r a n s m i t t a n c e at t h e s a m e w a v e l e n g t h . We h a v e shown that a thin p l a t e of LiIO3 p r o d u c e s m u c h h i g h e r u.v. i n t e n s i t y than can e a s i l y be a t t a i n e d w i t h c o n v e n t i o n a l K D P c r y s t a l s . In a d d i t i o n , a s h a s b e e n r e p o r t e d e a r l i e r [2], L i I O 3 c r y s t a l s a r e not h y g r o s c o p i c and can be g r o w n f r o m w a t e r s o l u t i o n s with good o p t i c a l q u a l i t y * F u r t h e r g r o w t h e x p e r i m e n t s w i t h L i I O 3 in an e f f o r t to m i n i m i z e the i m p u r i t i e s and to i n c r e a s e the t r a n s m i t t a n c e at 3470 A a r e in p r o g r e s s . T h e a u t h o r s a c k n o w l e d g e d i s c u s s i o n s with K. Dransfeld about the manuscript. * Further informations on growth and supply of LiIO 3 crystals can be obtained by M. Gslinger, Physik Department der Technischen Hochschule Milnchen. References
1. S.K. Kurtz, T. T. P e r r y and I. G. Bergman J r . , Appl. Phys. Letters 12 (1968) 186. 2. G. Nath and S. Hausstlhl, Appl. Phys. Letters, to be published. 3. J . A . Giordmaine, Phys. Rev. Letters 8 (1962) 19. 4. R. C. Miller, Appl. Phys. Letters 5 (1964) 17. 5. J. E. Midwinter and J. Warner, Brit. J. Appl. Phys. 16 (1965) 1135. 6. P.D. Maker, R.W. Terhune, M. Nisenhoff and C. M. Savage, Phys. Rev. Letters 8 (1962) 21. 7. D.A.Kleinman, Phys. Rev. 128 (1962) 1761.