LASER-INDUCED TRANSIENT GRATINGS : THE METHOD AND ITS APPLICATIONS

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LASER-INDUCED TRANSIENT GRATINGS : THE METHOD AND ITS APPLICATIONS

R. Casalegno

To cite this version:

R. Casalegno. LASER-INDUCED TRANSIENT GRATINGS : THE METHOD AND ITS APPLICA- TIONS. Journal de Physique Colloques, 1987, 48 (C7), pp.C7-405-C7-408. �10.1051/jphyscol:1987797�.

�jpa-00227102�

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JOURNAL DE PHYSIQIJE

Colloque C7, suppl6ment

au

n012, Tome

48,

decembre 1987

LASER-INDUCED TRANSIENT GRATINGS : THE METHOD AND ITS APPLICATIONS

R . CASALEGNO

Zaboratoire de Spectrombtrie Physique associb au CNRS,

Universite Scientifique, Technologique et Mbdical de Grenoble, B P 87, F-38402 Saint-Martin-d'Hclres Cedex, France

Abstract

-

Transient g r a t i n g techniques are shown t o bc a very w e l l adapted method t o f o l l o w t h e response o f a m a t e r i a l t o s h o r t laser. e x c i t a t i o n pulses. Besides i t s enhanced s e n s i t i v i t y t h i s technique i s s u i t e d f o r t h e study o f processes r e q u i r i n g a s p a t i a l l y modulated e x c i t a t i o n o f t h e medium. The choice o f experimental condi- t i o n s h ' i l l s e l e c t t h e response mechanisms and generate d i f f e r e n t types o f g r a t i n g s . Each type w i l l be i l l u s t r a t e d by an example.

INTRODUCTION

The development o f t h e t r a n s i e n t g r a t i n g techniquefollowed t h e c a p a b i l i t i e s o f laser sources : s h o r t e r pulses g i v e t h e p o s s i b i l i t y t o record f a s t e r t r a n s i e n t s o f a system. The g r a t i n g i s produced by c r o s s i n g two laser beams i n t h e material under in- v e s t i g a t i o n : t h e i r interference r e a l i s e s a s p a t i a l l y modulated i n t e n s i t y (and/or p o l a r i z a t i o n ) d i s t r i b u t i o n and t h e c o u p l i n g o f t h c l i g h t f i e l d w i t h t h e medium crea- t e s i n t u r n a s p a t i a l modulation o f t h e o p t i c a l p r o p e r t i e s o f t h e medium, i.e. a g r a t i n g . The system then e x h i b i t s a t r a n s i e n t behaviour and r e l a x e s w i t h one o r more c h a r a c t e r i s t i c times.

A

t h i r d laser (probe) beam i s d i f f r a c t e d on t h e g r a t i n g and t h e temporal e v o l u t i o n o f t h e s

i

yna

I

y i ves i nformat ions on t h e r e l a x a t i o n t ime(s)

.

The

me char^ i

sms

i

nvol vcd in, t h c g r a t i n g formation and decay can be selected by a proper choice o f experimental c o n d i t i o n s . As t h e f i e l d o f a p p l i c a t i o n s i s very wide and has already been i n t e n s i v e l y explored / I / , we s h a l l o u t l i n e here some s p e c i f i c features o f t h e method. We

w i l l

not consider t h e f o l l o w i n g s i t u a t i o n s more e a s i l y

i n t c r p r e t c d w i t h i n other

theoretical

frames : i ) zero o r near zero t i m delay between pump and probe pu

I

ses and i

i

) two pump pu

l

ses o f d i f f e r e n t frequency ( m v i ng g r a t

i

ngs

/ 2 / ) ,

s

i

t u a t ions more o f t e n and conven

i

ent

l

y analyzed by four-wave m

i

x i ng,

i i

i

) t

i

me delay between t h e two pump pu

l

ses more o f t e n def

i

ned as photon echoes.

BASIC PRINCIPLES

The ~ o m e t r y used f o r t h c production o f a g r a t i n g i s shown i n F i g . 1 . Two laser beams w i t h wave vectors

k

1and . k2, obtained by s p l i t t i n g a s i n g l e beam, i n t e r s e c t a t an angle 9 and create an ~ n t e r f e r e n c e p a t t e r n .

.-d,

Fiq. I Gratinq qeometry

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987797

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JOURNAL DE PHYSIQUE

The g r a t i n g wave-vector q i s such t h a t

kl-k

= + q and t h e spat

i

a

l

p e r i o d

A

^{= 2n/q}

i s r e l a t e d t o t h e e x c i t a t i o n

l i

ght waveleng&

'in

t h e m a t e r i a l ie by

A

= A / ( 2 s i n

e /

2).

The response o f t h e mater

i

a

l

i s expressed by a m o d i f i c a t i o n o f t h e c o k

l

ex r e - f r a c t

i

ve index = n +

i

k . An and

A K

w

i l l

be t h e modulation depths o f t h e r e f r a c t i ve

index n and o f t h e absorption constant

K.

A K = 0 defines a pure phase g r a t i n g and An = 0 a pure absorbing g r a t i n g .

The d e t e c t i o n o f t h e g r a t i n g i s performed by d i f f r a c t i n g a t h i r d laser beam. 'Wen t h e temporal e v o l u t i o n i s not t o o r a p i d , f a s t d e t e c t o r s can be used t o d i r e c t l y time resolve t h e signal generated by a continuous o r quasi-continuous beam. When higher t i m e r e s o l u t i o n i s r e q u i r e d a sampling method i s used : t h e g r a t i n g i s probed by a retarded t h i r d laser pulse, t h e delay o f which w i t h respect t o t h e punp pulses i s convenient

l

y r e a l

i

zed by means o f an o p t i c a l delay

l i

ne

/3/.

The geometr ica

l

arrangement must take i n t o account t h e thickness d o f t h e g r a t i n g : f o r a t h i n g r a t i n g which roughly s a t i s f i e s t h e c o n d i t i o n Ad

<<

A ' , several d i f f r a c t i o n orders are ob- served whereas f o r a t h i c k g r a t i n g only one d i f f r a c t e d wave-vector

k

respects t h e Bragg c o n d i t i o n

kd

=

kl - k

+

k

where

k

i s t h e probe wave-vector . d ~ i g .

1

shows a p o s s i b l e geometry f o r a

t&i&

& a t ing wyth a probe pulse o f wavelength longer than t h e pump one. General d i f f r a c t i o n t h e o r i e s u s i n g a plane-wave approximation g i v e t h e f u l l expressions o f t h e d i f f r a c t i o n e f f i c i e n c y rl i n both t h e cases o f t h i n and t h i c k g r a t i n g s

/1,4/.

The c o n d i t i o n s o f v a l i d i t y o f t h i s approximation a r e F u l f i I I c d i f t h e laser beams are not t o o much focused and

i f

t h e medium i s o n l y s l i g h t l y absorbing. I n t h e

l i m i t

where t h e v a r i a t i o n s o f t h e complex index o f r e f r a c t i o n are very small, i.e. when 2rrlAE;ild/~ <<

1,

a c o n d i t i o n which i s almost always v e r i f i e d , both t h e d i f f r a c t i o n e f f iciencyPfor a t h i c k g r a t i n g i n t h e Bragg c o n d i t i o n and t h e inten- s

i

t y d i f f r a c t e d

i

n t h e

f i

r s t order

f

rom a

t h

i n g r a t i n g are p r o p o r t

i

ona

l

t o

I AKI .

The l a s t step c o n s i s t s i n r e l a t i n g A; t o t h e parameters o f t h e system which o f course has t o be done f o r each case studied.

ADVANTAGES

OF THE METHOD

As t h i s technique i s experimentally more demanding than f o r example a punp-probe scheme,

i t

i s necessary t o emphasize i t s main advantages. F i r s t , as t h e d i f f r a c t e d signal i s emitted i n a d i r e c t i o n w e l l 'separated from t h e t r a n s m i t t e d pump and probe beams (see Fig.

I ) ,

t h e signal i s co

l l

ected against zero background g i v i n g a good s e n s i t i v i t y . Second, t h e s p a t i a l l y p e r i o d i c arrangement o f t h e d i f f r a c t i n g sources r e a l

i

ses c o n s t r u c t

i

ve add

i

t i on o f t h e d

i f

f r a c t e d s i gna

l i

n se

l

ected

d i

r e c t ions ( f o r - ced s c a t t e r i n g )

,

w i t h a correspond

i

ng enhanced i n t e n s i t y and i ncreased s i g n a l

.

Third, t h e s p a t i a l modulation o f t h e e x c i t a t i o n i s c e r t a i n l y t h e most s p e c i f i c fea- t u r e o f t h e technique, which o f f e r s i t s best a p p l i c a t i o n s when t h i s s p a t i a l modula- t i o n i s r e q u i r e d i n order t o f o l l o w e x c i t a t i o n m o b i l i t y f o r example.

So,

t r a n s p o r t phenomena

w i l l

f i n d t h e r e a p a r t i c u l a r l y w e l l s u i t e d method.

THE DIFFERENT TYPES OF GRATINGS

The mechanisms involved i n a g r a t i n g formation deperrd, o f course, upon t h e pump f i g h t p r o p e r t i e s . The choice o f t h e e x c i t a t i o n wavelength allows t o s e l e c t resonant, s t r o n g i n t e r a c t i o n s leading t o t h e creation, f o r example, o f an e l e c t r o n i c o r vibra- t i ona

l

ekc

i

t e d s t a t e g r a t

i

ng wh

i

ch may decay towards i ntermed

i

a t e e x c i t e d s t a t e s forming thereby a secondary g r a t i n g . With a proper choice o f t h e probe wavelength

i t

i s p o s s i b l e t o f o l l o w t h e r i s e and decay o f t h e intermediate e x c i t e d s t a t e s . F i n a l l y

i t w i l l

o n l y remain a heat d e p o s i t i o n i n t h e f r i n g e p a t t e r n g i v i n g r i s e t o a temperature g r a t i n g . Then t h e heat

w i l l

d i f f u s e acccmpanied by d e n s i t y v a r i a t i o n s . M e n t h e exc

i

t a t ion beams are b.oth po

l

a r

i

zed perpendi cu

l

a r t o t h e p

I

ane o f

i

nc

i

dence t h e

light

i n t e n s i t y i s modulated b u t i t s p o l a r i z a t i o n remains p a r a l l e l t o t h e i n c i - dent ones. This s i t u a t i o n i s reverse when one o f t h e two p o l a r i z a t i o n s i s s e t i n t h e plane o f incidence : t h i s gives no i n t e n s i t y modulation b u t a s p a t i a l l y p e r i o d i c r o - t a t i o n o f t h e p o l a r i z a t i o n . T h i s geometry may be i n t e r e s t i n g f o r d i c h o j c media and more g e n e r a l l y f o r an a n i s o t r o p i c p r o p e r t y study (see f i r s t example).

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The pulse d u r a t i o n t i s a fundamental parameter f o r two reasons. The f i r s t i s t h a t r e

l

axat ion processesPof character i s t

i

c t

i

me shorter than t are n o t obta

i

nab

l

e as t h e i r decay w

i l l

f o

l

low t h e exc

i

t a t ion pu

l

se tenpora

l

enve?ope. The second, more s p e c i f i c , concerns t h e e x c i t a t i o n o f an o s c i l l a t o r y response o f t h e system. A good example i s given by t h e impulsive generation o f hypersound waves o f wavelength

A

which i s p o s s i b l e

i f

t i s s u f f i c i e n t l y s h o r t (see t h i r d example).

F i n a l

l

y as t h e types

OF

g r a t i n g s appear t o be as numerous as t h e physical mchani sms c r e a t i n g them,

i t

seems t o be j u d i c i o u s t o introduce a c l a s s i f i c a t i o n according t o t h e i r wave-vector q which i s a s p e c i f i c parameter o f t h e method. Sq, we

w i l l

separa- t e q-independent g r a t i n g s f o r which t h e g r a t i n g spacing i s not a r e l e v a n t parameter o f t h e temporal evolution, from q-dependent ones where on t h e c o n t r a r y t h e value given t o

A

by t h e experimental geometry i s fundamental. I n t h i s second category, a f u r t h e r d i s t i n c t i o n can be made between o s c i l l a t o r y and n o n - o s c i l l a t o r y behaviors, as described below.

1 . q-independent g r a t i n g behavior

I f

t h e e x c i t a t i ~ n s d e c a ~ a t t h e

lace

they have been created t h e time e v o l u t i o n of

-

t h e signal i s independent o f q and t h e increased

C O N V E N ~ s e n s i t i v i t y o f t h e method t o measure v a r i o u s exci- ~ ~ ~ ~ ~ ~ t e d s t a t e l i f e times o r r e l a x a t i o n times i s used.

As an example ( a f t e r Ref.

/5/)

Fig.

2a

shows t h e s

i

gna

l

d

i

f f r a c t e d by a dye sol u t ion (9-ami noacr

i -

dine i n e t h y l ene-g

l

yco I ) when t h e e x c i t a t i o n

l i

ght pulses have t h e same p o l a r i z a t i o n , t h e probe l i g h t being p o l a r i z e d p a r a l l e l o r perpendicular t o t h e pump l i g h t .

I n Fig.

2b,

t h e two e x c i t a t i o n pulses have crossed (b) p o l a r i z a t i o n s . The dye molecules w i t h a t r a n s i t i o n CROSSEO moment paral l e l t o t h e e x c i t a t i o n f i e l d are prefe- r = 7 7 0 p s e c r e n c i a l l y excited. These g r a t i n g s read out by a

p o l a r i z e d

light

pulse are seen t o decay w i t h a time simply r e l a t e d t o t h e o r i e n t a t i o n a l c o r r e l a t i o n t i - 2 me T and e x c i t e d s i n g l e t l i f e - t i m e r e x .

o r

I f

2.

q-dependent, n o n - o s c i l l a t o r y g r a t i n g behavior 0

-0.2 0 0.4 0.8 1.2 1.6 I n t h i s case, t h e decay time o f t h e g r a t i n g de- TIME ( n s e c l pends upon t h e f r i n g e spacing

.

This occurs when Fig.

2

t h e r e i s a m i g r a t i o n o f t h e e x c i t a t i o n s from a

r e g i o n o f high d e n s i t y ( b r i g h t f r i n g e s ) t o a r e - g i on o f lower density (dark f r i n g e s )

.

The technique has been app

l i

ed t o heat d

i

f f u - sion, mass d i f f u s i o n , c a r r i e r d i f f u s i o n i n semiconductors, charge and energy t r a n s - f e r

. . .

^Fig.

3,

a f t e r Ref.

/6./, i l

l u s t r a t e s such an appl i c a t i o n f o r s i n g l e t e x c i t o n t r a n s p o r t i n anthracene s i n g l e c r y s t a l s .

A

one- dimensional d i F f u s i o n equation f o r t h e density o f e x c i t a t i o n s w i t h l i f e - t i m e r and d i f f u s i o n constant

D

leads t o a g r a t i n g decay t i m e T

Y eas

i l

y r e l a t e d t o T and

D

by l/r, = 1 / ~ D q 2 .

I ^3.

q-dependent, o s c i l l a t o r y g r a t i n g behavior 4 .

0 1 J

0 2 4 6 8 1 0 The present case i s a very p a r t i c u l a r one as it e2 ¹10' v=rot.~s, concerns t h e formation o f hypersound waves o f

f i x e d wavelength equal t o t h e g r a t i n g spacing

A

Fig.

3 ,

i.e. determined by t h e angle 8 . The mechanism

invoked i n t h i s case i s e i t h e r

stimulated

B r i l - l o u i n s c a t e r i n g o r thermal expansion f o l l o w i n g

7-

^I⁸^cm2,sec ^Fig.

³

shows a p l o t o f K = 2/rG versus @ 2 ( q ^U =

k

~f e << 1)

g i v i n g r and

D.

P

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JOURNAL D E PHYSIQUE

a f a s t heat deposition i n the f r i n g e s o f an absorbing sample 17 1 . The pro- pagation produces an o s c i l l a t i o n o f the density and thereby o f the index o f r e f r a c t i o n . The second mechanism g i ves a much h i gher d i f f r a c t ion e f -

-'0°$

f i c i e n c y o f the form

;

n =

A ( l - exp(-at) cos 2nt/TI2 where

a

i s the acoustic attenuation and T the acoustic period. q ( t ) g i - ves a and T i .e. v the speed o f sourld. The method has been used f o r

300 350 /empero/ure K ³

the study o f acoustic properties o f

a polymer material undergoir~g a glass-rubber t r a n s i t i o n as shown i n Fig. 4 Fi?. 4. /8/. S i m i l a r l y , impulsive

s t ~ m u l a t e d B r i l l o u i n s c a t t e r i n g has been used f o r t.he w n e r a t i o n o f transvcrse,,acoustic waves and applied t o investiga- t i o n s of' s t r u c t u r a l phase t r a n s i t i o n i n KDYP /9/.

This r a p i d survey o f t h c t r a n s i e n t g r a t i n g techniques shows t h a t i t i s very s e n s i t i - ve f o r the de$ection

of

small v a r i a t i o n s o f the o p t i c a l properties o f a material ( 1 ~ 7 1

=

10- ~ s e a s ~ l ~ dctcct.able), w i t h a w i d e f i e l d o f application. Moreover i t becomes very well adapted when a spat.ial m o b i l i t y o f t h e irlduced modification o f t h e medium i s expected

R e f