Generation of Single Picosecond and Subpicosecond Light Pulses
A . P e n z k o f e r , D . v o n d e r L i n d e , A . L a u b e r e a u , and W . K a i s e r Physik-Department der Technischen Universität München, Germany
(Received 31 January 1972)
Picosecond light pulses passing through a saturable absorber show considerable pulse shortening. F o r instance, under special favorable conditions the pulse duration was found to be reduced from 8 to 2. 6 psec in a single transit. Using a multiple-absorber-amplifier system, light pulses were shortened from 8 to 0. 7 psec in five transits. The shortest pulse seen in our experiments had a duration of less than 0. 5 psec. Calculations based on a two- level approximation of the absorbing medium agreed well with the experimental results.
T h e c o m m o n technique f o r g e n e r a t i n g p u l s e s of p s e c d u r a t i o n c o n s i s t s of mode l o c k i n g a N d : g l a s s l a s e r .1 S e r i o u s d i f f i c u l t i e s w e r e encountered when p u l s e s of a d u r a t i o n of 1 p s e c o r l e s s w e r e attempted by t h i s m e t h - o d . It w a s found that the p u l s e d u r a t i o n changes d r a s t i - c a l l y d u r i n g the c o u r s e of the p u l s e t r a i n2: A t the b e - ginning of the t r a i n , p u l s e s of s e v e r a l p s e c d u r a t i o n (~5 p s e c ) a r e g e n e r a l l y o b s e r v e d , w h i l e at the end of the t r a i n the p u l s e s d i s i n t e g r a t e w i t h s u b p i c o s e c o n d s u b - s t r u c t u r e .3,4 T w o techniques have been r e p o r t e d to g e n - e r a t e p u l s e s of s u b p i c o s e c o n d d u r a t i o n : (i) the o p t i c a l c o m p r e s s i o n of f r e q u e n c y - m o d u l a t e d p u l s e s .5 O n a c - count of the d i f f i c u l t y of a c c u r a t e l y adjusting the c o m - p r e s s i o n to the c h i r p , the shape and peak p o w e r of the generated p u l s e s a r e quite u n c e r t a i n : ( i i ) the p u l s e s h o r t e n i n g through the t r a n s i e n t s t i m u l a t e d R a m a n ef- fect. 6 T h i s s y s t e m w o r k s w i t h the whole t r a i n of p u l s e s ; i t h a s to a w a i t f u r t h e r i n v e s t i g a t i o n s .
In t h i s l e t t e r w e w i s h t o p r e s e n t t h e o r e t i c a l and e x p e r i - m e n t a l i n v e s t i g a t i o n s of the s h o r t e n i n g of s i n g l e p s e c l i g h t p u l s e s u s i n g s a t u r a b l e a b s o r b e r s of l o w t r a n s m i s - s i o n i n conjunction w i t h s t a n d a r d l a s e r a m p l i f i e r s . F i r s t , the p u l s e s h o r t e n i n g i n a s i n g l e p a s s through a s a t u r a b l e a b s o r b e r i s i n v e s t i g a t e d . T h e n , the r e d u c t i o n i n p u l s e d u r a t i o n i s s t u d i e d f o r s e v e r a l p a s s e s through a b s o r b e r s and a m p l i f i e r s .
In o u r c a l c u l a t i o n s the s a t u r a b l e a b s o r b e r7 i s d e s c r i b e d by a t w o - l e v e l s y s t e m , and the t r a n s i e n t t r a n s m i s s i o n i s d e t e r m i n e d f o l l o w i n g R e f s . 8 and 9. R e c e n t l y , i t h a s been shown that t h i s m o d e l accounts q u a n t i t a t i v e l y f o r a m e a s u r i n g s y s t e m of peak i n t e n s i t i e s of p s e c l i g h t p u l s e s . 9 T h e i n t e n s i t y t r a n s m i s s i o n T of the s a t u r a b l e a b s o r b e r depends on s e v e r a l f a c t o r s : the i n i t i a l t r a n s - m i s s i o n T0 of the dye at l o w - i n t e n s i t y l e v e l , the peak i n - t e n s i t y I0 of the i n c i d e n t p u l s e , the shape of the input p u l s e s(t', r')=zs(t/Atini r / A ri n) , w h e r e A £l n and A rl n a r e the p u l s e d u r a t i o n ( F W H M ) and the b e a m r a d i u s
( H W H M ) of the input p u l s e , r e s p e c t i v e l y , and the r a t i o r / A £i n of the l i f e t i m e r of the e x c i t e d state of the dye to the p u l s e d u r a t i o n A £i n. W e have studied the i n t e n s i t y t r a n s m i s s i o n T n u m e r i c a l l y f o r a wide r a n g e of p a r a m - e t e r s . In t h i s l e t t e r we a r e i n t e r e s t e d i n the t r a n s m i t t e d i n t e n s i t y 7t r:
ItT=T[T0f I0s(t', r ' ) , T/A*l n]/0sU', r ' ) .
In F i g . 1 w e p r e s e n t c a l c u l a t i o n s of the n o r m a l i z e d t r a n s m i t t e d i n t e n s i t y Iir/I0 a s a function of the n o r m a l - i z e d t i m e t/Min f o r s e v e r a l v a l u e s of the input peak i n t e n s i t y 70; the p a r a m e t e r s T0, r/Atin, and s(t',r') w e r e kept constant: T0— 10~7, r = 9 . 1 p s e c (see R e f . 7), A £i n= 8 p s e c and G a u s s i a n input p u l s e shape. F o r r e a d y c o m p a r i s o n the i n c i d e n t G a u s s i a n p u l s e i s i n c l u d e d i n F i g . 1 ( b r o k e n l i n e ) . It i s c l e a r l y seen f r o m F i g . 1 that f o r h i g h input i n t e n s i t i e s (e. g . , 5 x 109 W / c m2) the peak i n t e n s i t y and p u l s e d u r a t i o n a r e l i t t l e affected by the s a t u r a b l e a b s o r b e r ; only the l e a d i n g p a r t of the p u l s e e x p e r i e n c e s the s t r o n g a b s o r p t i o n of the d y e . O n the o t h e r hand, at l o w e r input i n t e n s i t y (e. g . , 1. 2 x i o9 W / c m2) the t r a n s m i t t e d p u l s e i s d r a s t i c a l l y r e d u c e d i n i n t e n s i t y (factor of 300) w i t h s m a l l e r r e d u c t i o n i n p u l s e d u r a t i o n (see, a l s o , F i g . 2). T h e r e i s a definite o p t i - m u m f o r the s h o r t e n i n g of the input p u l s e : A t I0= 1. 8 x 1 09 W / c m2 the t r a n s m i t t e d p u l s e i s r e d u c e d to a d u r a - t i o n of A £t r = 0 . 3 5 A £i n (see F i g . 1). U n d e r these c o n d i - t i o n s the output peak i n t e n s i t y i s down by a f a c t o r of 5, and the t o t a l e n e r g y i s r e d u c e d by a f a c t o r of 400 f o r a G a u s s i a n c r o s s s e c t i o n of the input b e a m .
In F i g . 2, the p u l s e - s h o r t e n i n g r a t i o Attr/Atin i s d e p i c t - ed a s a function of the peak i n t e n s i t y of the input p u l s e I0 f o r v a r i o u s i n i t i a l t r a n s m i s s i o n s T0. The c u r v e s a r e c a l c u l a t e d f o r a n input p u l s e d u r a t i o n of A /i n= 8 p s e c , f o r a G a u s s i a n input p u l s e shape, and f o r p a r a m e t e r s of the s a t u r a b l e a b s o r b e r g i v e n i n R e f . 7. F i g u r e 2 shows quite c o n v i n c i n g l y that the p u l s e s h o r t e n i n g obtainable i n
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INPUT PEAK INTENSITY IQ [W/cm*]
FIG. 1. Changes of the pulse shape after a single pass through a saturable absorber. Broken curve: normalized intensity of the input pulse ( A £i n= 8 psec, Gaussian pulse shape). Solid curves: normalized intensity of the transmitted pulse for several values of the input peak intensity 70. Dye parameters:
10- r = 9.1 psec.
FIG. 2. Pulse-shortening ratio Attr/Atin as a function of the input peak intensity 70 for several values of initial dye trans- mission T0 (single pass). Input pulse: A £i n = 8psec, Gaussian shape. Experimental points are indicated for T0=10~3 and TQ= 10"7 by open and closed c i r c l e s , respectively.
a s i n g l e p a s s depends c r i t i c a l l y on the i n c i d e n t peak i n - t e n s i t y I0 and on the i n i t i a l dye t r a n s m i s s i o n T0. T h e m i n i m a of the v a r i o u s c u r v e s i n d i c a t e o p t i m u m input peak i n t e n s i t i e s 70 —10 (opt) f o r g i v e n t r a n s m i s s i o n s T0. T h e s e m i n i m a a r e r a t h e r b r o a d at l a r g e r t r a n s m i s s i o n v a l u e s w i t h s m a l l e r p u l s e r e d u c t i o n s . F o r s m a l l v a l u e s of T0 the s h a r p m i n i m a r e q u i r e a v e r y c a r e f u l c o n t r o l of the input peak i n t e n s i t y I0; i f I0 < I0 (opt) the whole p u l s e i s s t r o n g l y attenuated, i f 70> /0 (opt) the effect of p u l s e s h o r t e n i n g d e c r e a s e s r a p i d l y , and t r a n s m i t t e d p u l s e s s t r o n g l y a s y m m e t r i c i n t i m e a r e generated (see
F i g . 1). It should be e m p h a s i z e d that at IQ (opt) the peak i n t e n s i t y I0 t r and the e n e r g y of the t r a n s m i t t e d p u l s e a r e only m o d e r a t e l y r e d u c e d , e. g . , f o r T0 = 10"1 o r 10~4 0 we c a l c u l a t e I0> t r = 0. 6 /0 o r 0. 1J0 and an energy l o s s by a f a c t o r of 3 o r 4 x 103, r e s p e c t i v e l y ( G a u s s i a n b e a m p r o - f i l e ) .
We have made a s e r i e s of e x p e r i m e n t s w i t h s a t u r a b l e a b s o r b e r s of i n i t i a l t r a n s m i s s i o n s T0 = 10~3 (open c i r c l e i n F i g . 2) and T0= 1 0 "7 (full c i r c l e s i n F i g . 2). T h e p u l s e d u r a t i o n s of the i n c i d e n t p u l s e Atin and the t r a n s - m i t t e d p u l s e Attr w e r e d e t e r m i n e d by the two-photon f l u o r e s c e n c e t e c h n i q u e .1 0 T h e peak i n t e n s i t y of the i n c i - dent p u l s e w a s m e a s u r e d by the method of e n e r g y t r a n s - m i s s i o n through s a t u r a b l e a b s o r b e r s .9 F i g u r e 2 shows v e r y good a g r e e m e n t between the e x p e r i m e n t a l p o i n t s and the c a l c u l a t e d c u r v e s . T h e p r e d i c t e d i n t e n s i t y d e - pendence of the p u l s e s h o r t e n i n g i s c o n f i r m e d e x p e r i - m e n t a l l y (see c u r v e w i t h T0= 1 0 "7) . T h e o p t i m u m p u l s e s h o r t e n i n g i n a s i n g l e p a s s w a s found to be c l o s e to a f a c t o r of 3 ( To= 1 0 "7) .
We have extended o u r c a l c u l a t i o n s to c o n s i d e r the effect of different shapes and d u r a t i o n s of the input p u l s e s . O u r r e s u l t s a r e b r i e f l y s u m m a r i z e d as f o l l o w s : (1) T h e p u l s e - s h o r t e n i n g r a t i o A £t r/ A £i n c o m e s out to be s i m i l a r
for G a u s s i a n , L o r e n t z i a n , and h y p e r b o l i c secant p u l s e s o v e r a w i d e range of v a l u e s f o r A /i n/ r and T0 ( f r o m steady state to A£I N/ T = 0 . 1 , and f r o m T0 = 1 to T0
— 10"1 0). (2) T h e p u l s e - s h o r t e n i n g r a t i o i n c r e a s e s s l i g h t l y f o r s h o r t e r input p u l s e s ( f r o m A £t r/ A £i n- 0 . 3 at the steady state to A ^t r/ A ^i n ^ 0 . 4 5 at &tin/r = 0.1 f o r T0 — 10"7). (3) F o r d e c r e a s i n g d u r a t i o n s of the input p u l s e s , h i g h e r v a l u e s f o r IQ (opt) a r e r e q u i r e d . (4) S h o r t e r input p u l s e s give m o r e f a v o r a b l e r a t i o s of
70 t r/ /0, i . e . , h i g h e r output i n t e n s i t i e s at I0 (opt). W h i l e
i n the s t e a d y - s t a t e case ( A £i n» r ) , the p u l s e s h o r t e n i n g o c c u r s only on account of the i n t e n s i t y dependence of
NORMALIZED TIME t/At,
FIG. 3. Pulses generated in five transits through an absorber- amplifier system. Broken curve: input pulse of 8-psec duration and Gaussian shape. Solid curves: pulses after 1—5 passes through absorbers (and 0—4 transits through amplifiers). Dye transmission per pass: T0 = 2 x 10"4. Amplifier gain per pass:
r= 4 . i .
P I C O S E C O N D A N D S U B P I C O S E C O N D L I G H T P U L S E S 353
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F I G . 4. Experimental setup for multiple transits through the absorber-amplifier system. Beam splitter BS; saturable absorber cells DC1 (T0= 1. 4 xlO"2), DC2 (T0= 1. 4 xlO"2), DC3 (T0=7X10"3); photodetectors P I , P2; two-photon- fluorescence systems T P F 1 , T P F 2 ; spectrometer S P .
the dye t r a n s m i s s i o n , i n the t r a n s i e n t c a s e the r e d u c - t i o n of p u l s e d u r a t i o n i s m a i n l y an e n e r g y effect; the l e a d i n g p a r t of the p u l s e i s s t r o n g l y a b s o r b e d u n t i l the dye i s s u f f i c i e n t l y e x c i t e d .
T h e r e s u l t s p r e s e n t e d so f a r suggest the i n v e s t i g a t i o n of a s y s t e m w h e r e a p u l s e i s r e p e a t e d l y s h o r t e n e d i n a s a t u r a b l e a b s o r b e r and subsequently a m p l i f i e d i n a l a - s e r a m p l i f i e r . W e have made e x t e n s i v e c a l c u l a t i o n s of m u l t i p l e - a b s o r b e r - a m p l i f i e r s y s t e m s1 1 i n the p s e c d o - m a i n w i t h w i d e l y v a r y i n g p a r a m e t e r s . In F i g . 3 a t y p - i c a l e x a m p l e i s p r e s e n t e d w h i c h i n d i c a t e s a s i t u a t i o n of p r a c t i c a l i n t e r e s t ; the t i m e dependence of the i n c i - dent p u l s e ( b r o k e n l i n e ) and of five subsequent p u l s e s ( s o l i d l i n e s ) i s shown f o r a s y s t e m c o n s i s t i n g of f i v e a b s o r b e r s w i t h T0 = 2 x 10"4 each, and four a m p l i f i e r s e a c h of o p t i c a l gain y = 4 . 1 . A n i n i t i a l p u l s e d u r a t i o n of A £i n= 8 p s e c and a peak i n t e n s i t y of the i n c i d e n t p u l s e of 70 = 1. i x 1 09 W / c m2 w e r e a s s u m e d . In o u r c a l c u l a - t i o n s the i n d i v i d u a l p u l s e shape, after p a s s i n g one a b - s o r b e r c e l l , w a s u s e d as the i n i t i a l c o n d i t i o n f o r the p a s s a g e t h r o u g h the f o l l o w i n g a b s o r b e r . A m p l i f i c a t i o n w a s c o n s i d e r e d to be i n t e n s i t y independent. F i g u r e 3 g i v e s a v i v i d p i c t u r e of the d r a s t i c change i n p u l s e shape after e a c h a b s o r b e r . S t a r t i n g w i t h A £ ,n = 8 p s e c , one c a l c u l a t e s a f i n a l p u l s e of A£ = 0. 65 p s e c , i . e . , a r e d u c t i o n f a c t o r of 12. In t h i s c a s e the t o t a l t r a n s m i s - s i o n of the s y s t e m i s 3. 2 x 10~1 9. O n the other hand, i f a p u l s e of the s a m e i n i t i a l d u r a t i o n t r a v e r s e s j u s t once a s a t u r a b l e a b s o r b e r of the s a m e t r a n s m i s s i o n of T0
= 3. 2 x 1 0 "1 9, a m o s t f a v o r a b l e r e d u c t i o n of the p u l s e d u r a t i o n i s c a l c u l a t e d to be a f a c t o r of 4. 5 only (see F i g . 2). T h e a b s o r b e r - a m p l i f i e r s y s t e m i s m o r e e f f e c - t i v e i n p u l s e s h o r t e n i n g because the d i s t r i b u t e d a m p l i f i - e r s b r i n g the p u l s e i n t e n s i t y back to the o p t i m u m v a l u e s f o r p u l s e s h o r t e n i n g i n the f o l l o w i n g a b s o r b e r s . O u r c a l c u l a t i o n s show that the peak p o w e r of the f i n a l output p u l s e depends s t r o n g l y on the o p t i c a l gain y . F o r v a l - ues of y < 4 . 1 (input p u l s e and dye p a r a m e t e r s as i n F i g . 3), the s u c c e e d i n g p u l s e s d e c r e a s e quite s t r o n g l y i n peak i n t e n s i t y ; they a r e of no p r a c t i c a l i n t e r e s t . F o r gain v a l u e s y > 4 . 1 , the peak i n t e n s i t i e s of the p u l s e s i n - c r e a s e c o n t i n u a l l y . F o r e x a m p l e , w i t h the same p a r a m - e t e r s u s e d i n F i g . 3 but w i t h y = 4. 3, one c a l c u l a t e s a
f i n a l peak i n t e n s i t y of 30 t i m e s the i n c i d e n t peak i n t e n - s i t y J0; at the s a m e t i m e the p u l s e d u r a t i o n i s r e d u c e d f r o m A £i n= 8 p s e c to A£ = 0 . 9 6 p s e c .
E x p e r i m e n t a l l y , we i n v e s t i g a t e d a folded a b s o r b e r - a m - p l i f i e r s y s t e m w i t h p a r a m e t e r s s i m i l a r to the e x a m p l e d i s c u s s e d i n F i g . 3. O u r e x p e r i m e n t a l setup i s d e p i c t - ed s c h e m a t i c a l l y i n F i g . 4. T h e o p t i c a l s w i t c h p r o v i d e s u s w i t h a s i n g l e p u l s e cut f r o m the l e a d i n g p a r t of the p u l s e t r a i n . T h i s p u l s e i s a n a l y z e d by T P F 1 to be of A £i n~ 8 p s e c . T h e p u l s e p a s s e s e f f e c t i v e l y five t i m e s t h r o u g h a b s o r b e r s and four t i m e s through an a m p l i f y i n g N d : g l a s s r o d ( a m p l i f i e r 1). A f i n a l l a s e r a m p l i f i e r ( a m p l i f i e r 2) i s u s e d to i n c r e a s e the p u l s e f o r ready d e - t e r m i n a t i o n of the energy ( P 2 ) , the p u l s e d u r a t i o n ( T P F 2 ) , and the frequency bandwidth ( s p e c t r o m e t e r S P ) . T h e t o t a l t r a n s m i s s i o n of the s y s t e m w a s T0= 10"1 7, and the t o t a l g a i n ( a m p l i f i e r 1) was a p p r o x i m a t e l y 300. O u r e x p e r i m e n t a l r e s u l t s gave c l e a r e v i d e n c e of the d r a s t i c p u l s e s h o r t e n i n g . T h e t w o - p h o t o n - f l u o r e s c e n c e t r a c k ( T P F 2 ) showed a s i n g l e s h a r p peak. W e e s t i m a t e a d u r a - t i o n of the output p u l s e of A£ = 0. 7 p s e c . W i t h somewhat s h o r t e r input p u l s e s we o c c a s i o n a l l y obtained output p u l s e s of At < 0 . 5 p s e c . T h e m e a s u r e d s p e c t r u m of the output p u l s e gave a frequency w i d t h of A i / = 9 x 1 01 1 H z ( A ? = 30 c m "1) . W i t h these n u m b e r s we obtain a p r o d u c t AtAv^ 0. 6, i n d i c a t i n g that o u r p u l s e s a r e n e a r l y b a n d - w i d t h l i m i t e d . W e have n o t i c e d i n our i n v e s t i g a t i o n s that the output p u l s e r e a c t s s t r o n g l y to changes of the input peak i n t e n s i t y IQ and of the gain y .1 2 T h i s o b s e r v a t i o n w a s expected f r o m o u r c a l c u l a t i o n s as d i s c u s s e d above i n connection w i t h F i g . 3.
T h e q u e s t i o n now a r i s e s as to the s h o r t e s t p u l s e s w h i c h can be generated i n an a b s o r b e r - a m p l i f i e r s y s t e m of the type i n v e s t i g a t e d h e r e . W h i l e we f e e l that f u r t h e r p u l s e s h o r t e n i n g i s p o s s i b l e w i t h m o r e t r a n s i t s , t h e r e a r e s e v e r a l p r a c t i c a l and p r i n c i p a l l i m i t a t i o n s . W i t h an i n c r e a s i n g n u m b e r of a b s o r b e r s and a m p l i f i e r s , the s y s t e m b e c o m e s m o r e s e n s i t i v e to v a r i a t i o n s of I0 and y . A s a r e s u l t , the output p u l s e v a r i e s between s m a l l v a l u e s of peak i n t e n s i t y and v a l u e s of peak i n t e n s i t y high enough that other n o n l i n e a r effects o c c u r i n the dye s o - l u t i o n o r i n the a m p l i f i e r r o d ( e . g . , s t i m u l a t e d l i g h t s c a t t e r i n g , s e l f - p h a s e - m o d u l a t i o n ) . It s h o u l d be noted that peak i n t e n s i t i e s e x c e e d i n g 1 01 0 W / c m2 a r e r e a d i l y generated i n a b s o r b e r - a m p l i f i e r s y s t e m s . A p r i n c i p a l l i m i t to the p u l s e d u r a t i o n i s set by the s p e c t r a l w i d t h of the amplifying m e d i u m ; i n N d : g l a s s the l i m i t i n g p u l s e d u r a t i o n i s expected to be 10"1 3 s e c . In a d d i t i o n , f o r p u l s e d u r a t i o n s s h o r t e r than the t r a n s v e r s e r e l a x a t i o n t i m e of the a m p l i f e r m e d i u m [T2 ( A ) ^ 0. 6 p s e c1 3] , c o - h e r e n t effects d e t e r m i n e d by the a r e a u n d e r the e l e c t r i c f i e l d 0 = (ß/fi)f^Edt have to be c o n s i d e r e d . In o u r c a s e , w i t h I0 = 1 01 0 W / c m2, At = 0. 5 p s e c and a d i p o l e m a t r i x e l e m e n t 1 0 "1 9 e s u ,1 3'1 4 we e s t i m a t e 6^0. 5; under these c o n d i t i o n s the a m p l i f i e r g a i n i s expected to be constant without b r e a k u p of the l i g h t p u l s e .1 4 ) 1 5 The t r a n s v e r s e r e l a x a t i o n t i m e of the s a t u r a b l e a b s o r b e r T2 (dye) i s e s t i m a t e d to be T2 (dye)< 10"1 3 s e c .1 6'1 7
F o r At<T2 (dye), the r a t e equations u s e d i n o u r c a l c u - l a t i o n s a r e not a p p l i c a b l e any l o n g e r .
In c o n c l u s i o n , we w i s h to say that w i t h p r o p e r l y adjusted a b s o r b e r s and a m p l i f i e r s , p u l s e s of ~ 5 X 1 0 "1 3 sec have
been obtained w i t h the p o s s i b i l i t y of g e n e r a t i n g p u l s e s of a p p r o x i m a t e l y 1 0 "1 3 s e c . T h e technique d i s c u s s e d h e r e should be useful f o r p u l s e s h o r t e n i n g i n o t h e r l a s e r s y s - t e m s as w e l l .
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7The material parameters of the dye used are T= 9.1 psec and absorption cross section cr=l. 84 xiO"1 6 c m2; see Eastman Kodak dye No. A9860 data release.
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J E T P 29, 830 (1969)]. The steady-state calculations of this reference are not applicable for psec pulses.
1 2We have observed a decreasing amplifier gain for high peak intensities of the traversing pulse. This result has a stabilizing effect on our system. See also N . G . Basov, I.
Kertes, P . G . Kryukov, Y u . V . Matveets, Y u . V . Senatskii, and S . V . Chekalin [Sov. Phys. J E T P 33, 289 (1971)].
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