PHOTOTHERMAL EXCITATION OF ELASTIC WAVES BY 10 ns LASER PULSES AND DETECTION BY PHOTOELASTIC LASER-BEAM DEFLECTION

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PHOTOTHERMAL EXCITATION OF ELASTIC WAVES BY 10 ns LASER PULSES AND DETECTION

BY PHOTOELASTIC LASER-BEAM DEFLECTION

G. Wetsel, Jr, S. Stotts, C. Clark

To cite this version:

G. Wetsel, Jr, S. Stotts, C. Clark. PHOTOTHERMAL EXCITATION OF ELASTIC WAVES BY 10 ns LASER PULSES AND DETECTION BY PHOTOELASTIC LASER-BEAM DEFLECTION.

Journal de Physique Colloques, 1983, 44 (C6), pp.C6-67-C6-71. �10.1051/jphyscol:1983610�. �jpa-

00223169�

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JOURNAL DE PHYSIQUE

Colloque C6, suppl6ment au nO1O, Tome 44, octobre 1983 page C6- 67

PHOTOTHERMAL EXCITATION OF ELASTIC W A V E S BY

1 0 n s

LASER PULSES

AND

DETECTION B Y PHOTOELASTIC LASER-BEAM DEFLECTION

G.C. W e t s e l , J r . , S.A. S t o t t s and C.G. C l a r k

Department of Physics, Southern Methodist University, Dallas, Texas 7 5 2 7 5 , U. S. A.

RSsum.6

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On v g r i f i e expgrimentalement une t h g o r i e d e l ' e x c i t a t i o n photo- thermique d e s ondes S l a s t i q u e s d a n s l a m a t i s r e condensge p a r i m p u l s i o n l a s e r e n u t i l i s a n t l a d g v i a t i o n d ' u n r a y o n l a s e r i n d u i t e p a r e f f e t photo- S l a s t i q u e .

A b s t r a c t - A t h e o r y o f p h o t o t h e r m a l e x c i t a t i o n o f e l a s t i c waves i n condensed m a t t e r by s h o r t l a s e r p u l s e s i s e v a l u a t e d e x p e r i m e n t a l l y u s i n g p h o t o e l a s t i c l a s e r - b e a m d e f l e c t i o n .

The e x c i t a t i o n o f s h o r t e l a s t i c p u l s e s ( h i g h - f r e q u e n c y e l a s t i c waves) by p h o t o t h e r m a l means i s o f c u r r e n t i n t e r e s t b e c a u s e o f i t s r e l e v a n c e t o s e v e r a l a r e a s o f a p p l i e d p h y s i c s , i n c l u d i n g : t h e p h o t o a c o u s t i c microscope / I / , t h e r m a l - wave imaging / 2 / , d e t e r m i n a t i o n o f t h e r m o e l a s t i c m a t e r i a l p a r a m e t e r s , n o n d e s t r u c - t i v e e v a l u a t i o n o f d e v i c e s / 3 / , m o n i t o r i n g o f l a s e r d r i l l i n g /4/, and l a s e r a n n e a l i n g and m e l t i n g phenomena i n s e m i c o n d u c t o r s .

S i n c e p h o t o t h e r m a l l y - g e n e r a t e d u l t r a s o n i c waves c a r r y i n f o r m a t i o n c h a r a c t e r - i s t i c o f t h e g e n e r a t i n g medium and a d j a c e n t media, o n e - d i m e n s i o n a l t h e o r e t i c a l models have been developed w i t h t h e g o a l o f u n d e r s t a n d i n g t h e b a s i c m a t e r i a l e f f e c t s on t h e g e n e r a t i o n p r o c e s s . The i n i t i a l s t u d i e s i n v o l v e d frequency-domain c a l c u l a t i o n s o f s u r f a c e and b u l k h e a t - s o u r c e models / 5 , 8 / . The b u l k - h e a t i n g model c o n s i s t s o f a n o n a b s o r b i n g b a c k i n g m a t e r i a l t h r o u g h which t h e i n c i d e n t l i g h t p r o - p a g a t e s , an a b s o r b i n g f i l m , and a n o n a b s o r b i n g sample. As an a i d i n u n d e r s t a n d i n g t h e e s s e n t i a l p h y s i c s o f t h e phenomenon, a s u r f a c e h e a t i n g model w i t h t h e ab- s o r b i n g f i l m r e p l a c e d by an i n f i n i t e s i m a l s u r f a c e s o u r c e was a l s o t r e a t e d . Calcu- l a t i o n s o f t h e t e m p e r a t u r e , e l a s t i c - d i s p l a c e m e n t a m p l i t u d e and p h a s e , and u l t r a - s o n i c i n t e n s i t y a s f u n c t i o n s o f p o s i t i o n , s t r u c t u r e d i m e n s i o n s , and o p t i c a l ab- s o r p t i o n c o e f f i c i e n t were made f o r s e v e r a l m a t e r i a l c o m b i n a t i o n s . The p r e d i c t i o n s o f t h e s e models a r e i n s u b s t a n t i a l agreement w i t h what e x p e r i m e n t a l e v i d e n c e i s a v a i l a b l e . These one-dimensional models p r e d i c t t h a t t h e e l a s t i c d i s p l a c e m e n t a m p l i t u d e , A , i n t h e sample i n c r e a s e s w i t h i n c r e a s i n g o p t i c a l a b s o r p t i o n c o e f - f i c i e n t , B , u n t i l e s s e n t i a l l y a l l t h e i n c i d e n t l i g h t beam i s a b s o r b e d i n t h e f i l m ; A i n c r e a s e s w i t h f i l m t h i c k n e s s , d , f o r a g i v e n f3 u n t i l d i s e q u a l t o a b o u t 5/B, t h a t i s , about 5 a b s o r p t i o n l e n g t h s . However, A may c o n t i n u e t o i n c r e a s e w i t h f u r t h e r i n c r e a s e s i n d i f t h e f i l m i s t h e r m a l l y t h i n . The f r e q u e n c y dependence o f A i s a f u n c t i o n o f t h e m a t e r i a l p a r a m e t e r s o f t h e backing, f i l m , and sample; how- e v e r , i t i s a d e c r e a s i n g f u n c t i o n o f f r e q u e n c y , and i n i n t e r e s t i n g c a s e s / 7 / i s dominated by w An i m p o r t a n t r e s u l t o f t h i s modeling i s t h a t , f o r t h e most e f - f i c i e n t p h o t o t h e r m a l e l a s t i c - w a v e e n e r a t i o n , e i t h e r sample o r b a c k i n g ( o r b o t h ) s h o u l d have a l a r g e v a l u e o f u ( D ) ~ $ ~ and t h e r e s h o u l d n o t be a g r e a t a c o u s t i c - impedance mismatch of b a c k i n g and sample, where o i s e f f e c t i v e l y t h e thermal-ex- p a n s i o n c o e f f i c i e n t and D i s t h e t h e r m a l d i f f u s i v i t y . With r e g a r d t o thermal-wave imaging, where t h e d e t e c t e d u l t r a s o n i c wave i s i n t e n d e d t o p r o v i d e i n f o r m a t i o n t h a t i s p r i n c i p a l l y c h a r a c t e r i s t i c o f t h e h e a t e d volume o f t h e f i l m o r sample, t h e b a c k i n s h o u l d have r e l a t i v e l y s m a l l v a l u e s o f t h e r e l e v a n t p a r a m e t e r s , v i z . a ) . Thus, thermal-wave imaging measurements might b e s t be made w i t h a vacuum b a c k i n g .

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983610

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C6-68 JOURNAL DE PHYSIQUE

The most e f f e c t i v e experimental e v a l u a t i o n of t h e above models of photothermal e l a s t i c - w a v e g e n e r a t i o n would make use of t h e frequency domain. This approach i s p r e s e n t l y i m p r a c t i c a l s i n c e i t would i n v o l v e t u n a b l e , broad-band microwave-frequency modulation of l i g h t . Pulsed l a s e r s a r e r e a d i l y a v a i l a b l e , but t h e r i s e time of d e t e c t o r s i s a problem and t h e models must be solved i n t h e time domain. We have r e c e n t l y extended c a l c u l a t i o n s based on models s i m i l a r t o t h e above t o t h e time domain, and have designed a d e t e c t i o n scheme t h a t i s s u f - f i c i e n t l y f a s t t o e x p e r i m e n t a l l y e v a l u a t e t h e t h e o r y .

Photothermal g e n e r a t i o n was accomplished u s i n g 8 n s , ^%400 kW p u l s e s from a Molectron W22 Ng f a s e r with a v a r i a b l e p u l s e - r e p e t i t i o n frequency up t o 100 H z . This "pump" l a s e r was focused on s o l i d s and l i q u i d s having o p t i c a l a b s o r p t i o n a t

337 nm. Because o f t h e r i s e time (%3ns) of t h e l a s e r p u l s e , it would be necessary t o have f a s t - r i s e t i m e t r a n s d u c e r s and e l e c t r o n i c s t o d e t e c t t h e u l t r a s o n i c waves i n t h e u s u a l way. The requirement of broad brandwidth, t h e f e a t u r e of i n t e g r a t i n g a s opposed t o l o c a l i z e d d e t e c t i o n , and t h e u l t r a s o n i c bonding problem argue a - g a i n s t t h e use o f e l e c t r o m e c h a n i c a l t r a n s d u c e r s . T h e r e f o r e , t h e u l t r a s o n i c p u l s e s were d e t e c t e d u s i n g a probe l a s e r (Ar+) beam d i r e c t e d p e r p e n d i c u l a r t o t h e d i - r e c t i o n o f wave p r o p a g a t i o n . The probe beam i s d e f l e c t e d by t h e p h o t o e l a s t i c e f f e c t when t h e e l a s t i c wave t r a v e l s through t h e probed r e g i o n of t h e sample. A f a s t (c0.5 ns r i s e t i m e ) photodiode placed behind an a p e r t u r e o r k n i f e edge de- t e c t e d t h e d e f l e c t i o n s i g n a l , which was connected t o a T e k t r o n i x 7854 waveform- d i g i t i z i n g o s c i l l o s c o p e . The o s c i l l o s c o p e i n t e r f a c e d with a Hewlett-Packard 9825T computer and 9872B g r a p h i c s p l o t t e r t o produce a permanent r e c o r d of t h e s i g n a l s .

An example o f t h e p r o b e - l a s e r d e f l e c t i o n s i g n a l a s a f u n c t i o n of time is shown i n F i g . 1 f o r a q u i n i n e s u l f a t e s o l u t i o n i n 0.04 M HC1,a good t e s t sample w i t h s t r o n g a b s o r p t i o n a t t h e pump-laser wavelength of 337 nm but r e l a t i v e l y t r a n s p a r e n t a t t h e p r o b e - l a s e r wavelength of 514 nm. Propagation of t h e photo- t h e r m a l l y generated d i s t u r b a n c e was s t u d i e d by t r a n s l a t i n g t h e sample p a r a l l e l t o t h e d i r e c t i o n of pump-laser beam p r o p a g a t i o n . By measurement of t h e time d e l a y of t h e probe-beam d e f l e c t i o n s i g n a l a s t h e sample was t r a n s l a t e d , i t was d e t e r - mined t h a t t h e d e l a y i s c h a r a c t e r i s t i c of t h e compressional wave v e l o c i t y i n

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Fig. 1. Probe-beam d e f l e c t i o n s i g n a l v s . time f o r q u i n i n e s u l f a t e i n 0.04 M H C 1 ; pump-laser p u l s e width = 8 n s , p h o t o s i g n a l width '2 80 n s .

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water and t h u s t h a t t h e primary probe-beam d e f l e c t i o n was due t o a t r a v e l i n g e l a s t i c wave i n t h e sample. Secondary s i g n a l s c h a r a c t e r i s t i c of echoes i n t h e q u a r t z w a l l s o f t h e c u v e t t e c o n t a i n i n g t h e sample were a l s o observed.

A one-dimensional model c o n s i s t i n g of two s e m i - i n f i n i t e media, a t r a n s p a r e n t backing and an o p t i c a l l y absorbing sample, was developed f o r purposes of analyzing photothermal g e n e r a t i o n and propagation of e l a s t i c p u l s e s i n t h e time domain. A bulk h e a t source c h a r a c t e r i z e d by o p t i c a l a b s o r p t i o n c o e f f i c i e n t , 6, was t r e a t e d a s t h e source term i n t h e t h e r m a l - d i f f u s i o n e q u a t i o n , i n t h e usual way / 7 / . The t h e r m a l - d i f f u s i o n and e l a s t i c - w a v e e q u a t i o n s along with t h e concomitant boundary- value problem were s o l v e d i n t h e Laplace transform domain. The e l a s t i c s t r a i n i n t h e sample was computed a s a f u n c t i o n of time by numerical Laplace i n v e r s i o n . Some p r e l i m i n a r y r e s u l t s of c a l c u l a t i o n s of t h e e f f e c t s of B , m a t e r i a l parameters, and propagation a r e shown i n F i g s . 2 - 4 . I n each c a s e , t h e absorbed l a s e r i n - t e n s i t y was assumed t o v a r y with time a s s i n 2 ( = t / . r ) , where T = 10 n s , f o r Ozt5-c;

t h e a c t u a l l a s e r p u l s e i s approximated by t h i s f u n c t i o n . The m a t e r i a l parameters were t a k e n from t h e l i t e r a t u r e / 7 / .

The c a l c u l a t e d e l a s t i c s t r a i n i s shown i n F i g . 2 a s a f u n c t i o n of time f o r 5 v a l u e s of x , where x i s t h e d i s t a n c e i n t h e sample (water) from t h e i n t e r f a c e with t h e backing ( q u a r t z ) . The o p t i c a l a b s o r p t i o n c o e f f i c i e n t of t h e sample i s assumed t o be 1 0 0 c m - ~ , which corresponds t o an a b s o r p t i o n l e n g t h ( 6 - I ) of 0 . 1 mm.

The s t r a i n p u l s e s h i f t s from b i p o l a r toward u n i p o l a r a s i t p r o p a g a t e s , with a g r a d u a l change i n shape. The e v e n t u a l shape of t h e p u l s e i s f a i r l y well e s - t a b l i s h e d a f t e r it has propagated about 5 a b s o r p t i o n l e n g t h s , o r about 0.5 mm, i n t h i s c a s e .

The c a l c u l a t e d s t r a i n , d i v i d e d by 6, i s shown i n F i g . 3 a s a f u n c t i o n of time f o r w a t e r / q u a r t z f o r s e v e r a l v a l u e s of B. The v a l u e of x f o r t h e s e calcu- l a t i o n s i s 0 . 5 mm, which corresponds t o a t l e a s t 5 a b s o r p t i o n l e n g t h s f o r each value of 6; t h u s , t h e e v e n t u a l p u l s e shape should be w e l l approximated. I t should be n o t i c e d t h a t t h e s t r a i n amplitude i n c r e a s e s with i n c r e a s i n g 6 over t h i s

TIME CNANOSEcomS)

Fig. 2. T h e o r e t i c a l s t r a i n v s . time f o r s e v e r a l v a l u e s of x , 6 = 100 cm-I, peak absorbed l i g h t i n t e n s i t y = 1 . 0 w/m2, ^.c = 10 n s , sample = water, backing = q u a r t z .

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JOURNAL DE PHYSIQUE

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F i g . 3 . T h e o r e t i c a l s t r a i n / B v s . t i m e f o r s e v e r a l v a l u e s o f B i n cm-l, x = 0 . 5 mm, peak a b s o r b e d l i g h t i n t e n s i t y = 1 . 0 h'/m2, ~ = 1 0 n s , s a m p l e = w a t e r , b a c k i n g = q u a r t z .

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F i g . 4 . T h e o r e t i c a l s t r a i n v s . t i m e f o r s e v e r a l v a l u e s o f B i n cm-l, x = 0 . 1 mm, peak a b s o r b e d l i g h t i n t e n s i t y = l . O w / r n 2 , ~ = 1 0 n s , s a m p l e = w a t e r , b a c k i n g = a i r .

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r a n g e o f 6. F u r t h e r m o r e , t h e pulsi: w i d t h d e c r e a s e s a s 6 i n c r e a s e s . For t h e p u l s e s shown, t h e f u l l - w i d t h a t o n e - h a l f t h e maximal s t r a i n i s o f t h e o r d e r o f

(BV) l , where v i s t h e c o m p r e s s i o n a l wave v e l o c i t y o f t h e sample.

The e f f e c t o f d i f f e r e n t boundary c o n d i t i o n s i s shown i n F i g . 4 , where s t r a i n i s shown a s a f u n c t i o n o f t i m e f o r 4 v a l u e s o f B . I n t h i s c a s e , t h e b a c k i n g m a t e r i a l i s assumed t o b e a i r , which i s a l a r g e a c o u s t i c impedance mismatch f o r w a t e r .

The p h o t o e l a s t i c a l l y - d e f l e c t e d probe-beam s i g n a l shown i n F i g . 1 h a s a f u l l - w i d t h a t o n e - h a l f t h e maximum a m p l i t u d e (FWHM) o f a b o u t 80 n s . The e x c i t i n g l a s e r p u l s e had a FWHM o f 8 n ? . Thus, t h e r e i s s u b s t a n t i a l b r o a d e n i n g o f t h e e l a s t i c p u l s e r e l a t i v e t o t h e h e a t i n g p u l s e , a s p r e d i c t e d by t h e t h e o r y . A c c u r a t e q u a n t i t a t i v e comparison o f e x p e r i m e n t a l and t h e o r e t i c a l e l a s t i c p u l s e s h a p e s i s hampered a t t h e moment by a l a c k o f p r e c i s e knowledge o f t h e B o f t h e sample.

F u r t h e r m o r e , one must b e c a r e f u l t o e l i m i n a t e t h e e f f e c t o f t h e d e t e c t i o n geometry on d e t e c t e d p u l s e s h a p e .

I n c o n c l u s i o n , we have developed a o n e - d i m e n s i o n a l model o f p h o t o t h e r m a l g e n e r a t i o n o f s h o r t e l a s t i c p u l s e s i n t h e t i m e domain. The t h e o r y p r e d i c t s t h a t t h e p u l s e s h a p e changes a s it p r o p a g a t e s from t h e p h o t o t h e r m a l g e n e r a t i o n volume, o b t a i n i n g i t s e v e n t u a l s h a p e i n a b o u t 5 a b s o r p t i o n l e n g t h s , and o b t a i n i n g a n e v e n t u a l FWHM o f t h e o r d e r o f (vB) l . The s h a p e and w i d t h o f t h e e l a s t i c p u l s e a l s o depends on t h e boundary c o n d i t i o n s a t t h e sample-backing i n t e r f a c e . P h o t o e l a s t i c l a s e r - b e a m d e f l e c t i o n a p p e a r s t o be a good t e c h n i q u e f o r e x p e r i m e n t a l s t u d y of p h o t o t h e r m a l e l a s t i c - w a v e g e n e r a t i o n / 9 / .

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on A c o u s t i c Imaging, Plenum, London (1982).

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9 . D e t e c t i o n o f c o m p r e s s i o n a l waves i n l i q u i d s by t h i s method h a s a l s o

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