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Measurements of phonon lifetimes by two successive light pulses
Volume 27A. number 6
PHYSICS LETTERS
any s t r u c t u r e . T h i s c o n f i r m s o u r p r e v i o u s c o n clusi on that a s e c o n d and b r o a d conduction band is e x i s t i n g in a n t h r a c e n e s e p a r a t e d f r o m the f i r s t conduction band by an e n e r g y gap of 0.6 eV. We g r a t e f u l l y ack n o w le d g e s t i m u l a t i n g d i s c u s s ions with P r o f e s s o r N. Riehl. 1. M. Pope. J. Burgos and J.Giachino. J. Chem. Phys. 43 (1965) 3367.
12 August 1968
2. G. Castro and J. F. Hornig, J. Chem. Phys. 42 (1965) 1459. 3. H. Baessler and G. Vaubel. Solid State Comm. 6 (1968) 97. 4. G. Vaubel and H. Baessler. Phys. Stat. Sol. 26 (1968) 599. 5. R. Williams and J. Dresner. J. Chem. Phys. 46 (1967) 2133. 6. R.Silbey. J . J o r t n e r , S.A.Rice and M.T.Vala. J. Chem. Phys. 42 (1965) 733. 7. H. Baessler. N. Riehl and G. Vaubel. Phys. Stat. Sol. 26 (1968) 607.
MEASUREMENTS OF PHONON LIFETIMES TWO SUCCESSIVE LIGHT PULSES
BY
G. WINTERLING and W. HEINICKE Physik-Department der Technischen Hochschule, M~nchen, Germany Received 27 May 1968
By generating phonons with an intense light pulse and observing these phonons with a second delayed one we measured very short lifetimes of longitudinal hypersonic phonons in the previously inaccessible range of 10 -7 to 10 -8 see. The lifetimes of 29 GHz phonons in z-cut quartz were determined from 60°K up to 150°K.
Today v a r i o u s m e t h o d s a r e c o m m o n l y u s e d to m e a s u r e the a b s o r p t i o n of h y p e r s o n i c w a v e s at f r e q u e n c i e s of about 5 GHz to 70 GHz. With e l e c t r i c a l g e n e r a t i o n and d e t e c t i o n [1] r e l a t i v e l y low a b s o r p t i o n s c o r r e s p o n d i n g to phonon l i f e t i m e s g r e a t e r than 10 -7 s e c can be d e t e r m i n e d . L i f e t i m e s s h o r t e r than about 10 -9 s e c can be s e e n in spontaneous B r i l l o u l n s c a t t e r i n g [2], t h o s e about 10 -9 s e c in s t i m u l a t e d B r i l l o u i n a m p l i f i e r s [3]. H o w e v e r t i l l now it has not been p o s s i b l e to o b s e r v e l i f e t i m e s in the r a n g e between 10 -7 s e c and 10 -8 s e c . In this p a p e r a new optical m e t h o d i s p r e s e n t e d which g i v e s d i r e c t a c c e s s to this i n t e r v a l . Its u s e f u l n e s s f o r longitudinal h y p e r s o n i c w a v e s is d e m o n s t r a t e d f o r 29 GHz phonons in z cut q u a r t z . Our e x p e r i m e n t a l a r r a n g e m e n t i s shown in fig. l a . T h e f o c u s e d b e a m of a Q - s w i t c h e d ruby l a s e r (peak p o wer 15 MW, half width t i m e 16 n s e c ) g e n e r a t e s in a q u a r t z s a m p l e (without da ma ge ) a v e r y l a r g e population of c o h e r e n t a c o u s t i c phonons by s t i m u l a t e d B r i l l o u i n s c a t t e r ing [4]. S i m u l t a n e o u s l y a s m a l l p a r t of the s a m e l a s e r p u l s e i s s p l i t off. A f t e r p a s s i n g an o p ti c a l delay l i n e of 48 n s e c this p a r t e n t e r s e x a c tl y the
path of the p r i m a r y b e a m s e r v i n g a s an useful o p t i cal p r o b l e f o r the r e m a i n i n g a c o u s t i c phonons. Its i n t e n s i t y i s s m a l l e r than that of the p r i m a r y p u l s e by m o r e than one o r d e r of m a g nitude so that it cannot p r o d u c e f u r t h e r s t i m u l at ed s c a t t e r i n g . In o r d e r to r e c o r d the r e l a t i v ely weak b a c k s c a t t e r e d s i g n a l of the d el ay ed p u l s e t o g e t h e r with the s t r o n g s t i m u l a t e d B r i l louln i n t e n s i t y of the f i r s t p u l s e p o l a r i s a t i o n o p t i c s (see fig. 1) w e r e u s e d to e q u a l i z e both s i g nals f o r detection. If the a c o u s t i c phonons l i v e c o n s i d e r a b l y l o n g e r than the d e l a y t i m e of 48 n s e c t h e d e l a y e d p r o b e light m e e t s s t i l l a l m o s t al l g e n e r a t e d phonons s u f f e r i n g t h e r e f o r e g r e a t e s t b a c k s c a t t e r i n g . In q u a r t z this happens at t e m p e r a t u r e s below 35°K [5]. With i n c r e a s i n g t e m p e r a t u r e t h e phonon l i f e t i m e b e c o m e s s h o r t e r . T h e r e f o r e the p r o b e light will s e e f e w e r phonons and the b a c k s c a t t e r e d p r o b e intensity d e c r e a s e s a c c o r d i n g l y (see fig. lb). F r o m this d e c r e a s e the a b s o l u t e magnitude of the phonon l i f e t i m e can be d e t e r m i n e d within ± 10%. T h e s h o r t e s t l i f e t i m e which can be m e a s u r e d in this way d e pends on t h e t i m e d u r a t i o n of t h e l a s e r pulse, the l o n g e s t on the d e l a y t i m e b et w een both p u l s e s .
329
Volume 27A. n u m b e r 6
PHYSICS
LETTERS
12 August 1968 ,
I
|
¢#?'-extrapolation
~e
~1~/BRE'WSTER Z-QUARTZ
,00
I"--/--'1
LASER
:i: •-
i i
f=25cm : . . . . .j CRYOSTAT
: 7, _ -
|
f
g
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/
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w
~o-7
DELAY LINE (48nsec)
U_
10 a_ UJ
I-UJ
(48 nsec)
-J
T2/~/
Z
o
dA /
bZ
32°K
10-6
/
O.
/
Z-CUT QUARTZ
/
@. 0::
o 1 tn .Om
o,,,,.o.-,.''°~°'
~_~. ~ 1 4 3
OK
10-5 30
oo z _o
1GHz
I
I
I
50
100
150
TEMPERATUREPK] Fig. 1 a) Schematic of the e x p e r i m e n t a l set up. The points and a r r o w s on the optical path indicate p o l a r i s a tion v e c t o r s p e r p e n d i c u l a r and p a r a l l e l to the drawing plane. The quartz sample in a c r y o s t a t could be held at any t e m p e r a t u r e between 5°K and 300°K. b) Oscilloscope t r a c e s ( r i s e time 7 nsec) of the b a c k s c a t t e r e d light at various sample t e m p e r a t u r e s v e r s u s t i m e . c: undelayed stimulated Brillouin pulse, d: d e layed probe light, b a c k s c a t t e r e d f r o m the r e m a i n i n g
phonons. T h e m e a s u r e d l i f e t i m e s f o r l o n g i t u d i n a l 29 G H z p h o n o n s i n z - c u t q u a r t z a r e s h o w n i n fig. 2. It is obvious that around 100°K the absorption varies as T 2 and does not yet reach any temperature independent plateau in contrast to the k n o w n a b s o r p t i o n d a t a of 1 G H z p h o n o n s [1] w h i c h are also shown for comparison. Assuming an absorption due to collisions with thermal phonons w e m u s t c o n c l u d e 00~-ther m >/ 1 f o r 29 G H z p h o n o n s u p to 1 5 0 ° K c o r r e s p o n d i n g t o a t h e r m a l phonon lifetime (inclu!!ing U- and N-processes) of T t h e r m >/ 0 . 5 " 10 - t l s e c . I t s h o u l d b e n o t e d t h a t h e a t c o n d u c t i v i t y m e a s u r e m e n t s [6] l e a d to a similar value for U-processes only.
330
Fig. 2. Lifetimes of longitudinal acoustic phonons in z - c u t quartz v e r s u s t e m p e r a t u r e . The t r i a n g l e s show our optical m e a s u r e m e n t s at 29 GHz and the pointdashed line an wE-extrapolation for 29 GHz f r o m p r e vious 1 GHz data [1] included for c o m p a r i s o n . W e a r e t h a n k f u l t o K. D r a n s f e l d f o r m u c h i n terest in this work especially for suggesting this method.
References 1. H . E . B ~ m m e l and K . D r a n s f e l d . Phys. Rev. 177 (1960) 1245. 2. R.Y. Chiao and P.A. Fleury. in Physics of quantum electronics, eds. P.Kelley et al. (McGraw-Hill Book Company, New York. 1966) p. 241. 3. D. Pohl, M. M a i e r and W. Kaiser. Phys. Rev. L e t t e r s 20 (1968) 366. 4. R . Y . Chiao. C.H. Townes and B. P. Stoicheff. Phys. Rev. L e t t e r s 12 (1964) 592. 5. M . F . Lewis and E. P a t t e r s o n . Phys. Rev. 159 (1967) 703; W. Heinicke and G. Winterling. Appl. Phys. L e t t e r s 11 (1967) 231. 6. H . J . M a r i s . Phil. Mag. 9 (1964) 901.
PHYSICS LETTERS
any s t r u c t u r e . T h i s c o n f i r m s o u r p r e v i o u s c o n clusi on that a s e c o n d and b r o a d conduction band is e x i s t i n g in a n t h r a c e n e s e p a r a t e d f r o m the f i r s t conduction band by an e n e r g y gap of 0.6 eV. We g r a t e f u l l y ack n o w le d g e s t i m u l a t i n g d i s c u s s ions with P r o f e s s o r N. Riehl. 1. M. Pope. J. Burgos and J.Giachino. J. Chem. Phys. 43 (1965) 3367.
12 August 1968
2. G. Castro and J. F. Hornig, J. Chem. Phys. 42 (1965) 1459. 3. H. Baessler and G. Vaubel. Solid State Comm. 6 (1968) 97. 4. G. Vaubel and H. Baessler. Phys. Stat. Sol. 26 (1968) 599. 5. R. Williams and J. Dresner. J. Chem. Phys. 46 (1967) 2133. 6. R.Silbey. J . J o r t n e r , S.A.Rice and M.T.Vala. J. Chem. Phys. 42 (1965) 733. 7. H. Baessler. N. Riehl and G. Vaubel. Phys. Stat. Sol. 26 (1968) 607.
MEASUREMENTS OF PHONON LIFETIMES TWO SUCCESSIVE LIGHT PULSES
BY
G. WINTERLING and W. HEINICKE Physik-Department der Technischen Hochschule, M~nchen, Germany Received 27 May 1968
By generating phonons with an intense light pulse and observing these phonons with a second delayed one we measured very short lifetimes of longitudinal hypersonic phonons in the previously inaccessible range of 10 -7 to 10 -8 see. The lifetimes of 29 GHz phonons in z-cut quartz were determined from 60°K up to 150°K.
Today v a r i o u s m e t h o d s a r e c o m m o n l y u s e d to m e a s u r e the a b s o r p t i o n of h y p e r s o n i c w a v e s at f r e q u e n c i e s of about 5 GHz to 70 GHz. With e l e c t r i c a l g e n e r a t i o n and d e t e c t i o n [1] r e l a t i v e l y low a b s o r p t i o n s c o r r e s p o n d i n g to phonon l i f e t i m e s g r e a t e r than 10 -7 s e c can be d e t e r m i n e d . L i f e t i m e s s h o r t e r than about 10 -9 s e c can be s e e n in spontaneous B r i l l o u l n s c a t t e r i n g [2], t h o s e about 10 -9 s e c in s t i m u l a t e d B r i l l o u i n a m p l i f i e r s [3]. H o w e v e r t i l l now it has not been p o s s i b l e to o b s e r v e l i f e t i m e s in the r a n g e between 10 -7 s e c and 10 -8 s e c . In this p a p e r a new optical m e t h o d i s p r e s e n t e d which g i v e s d i r e c t a c c e s s to this i n t e r v a l . Its u s e f u l n e s s f o r longitudinal h y p e r s o n i c w a v e s is d e m o n s t r a t e d f o r 29 GHz phonons in z cut q u a r t z . Our e x p e r i m e n t a l a r r a n g e m e n t i s shown in fig. l a . T h e f o c u s e d b e a m of a Q - s w i t c h e d ruby l a s e r (peak p o wer 15 MW, half width t i m e 16 n s e c ) g e n e r a t e s in a q u a r t z s a m p l e (without da ma ge ) a v e r y l a r g e population of c o h e r e n t a c o u s t i c phonons by s t i m u l a t e d B r i l l o u i n s c a t t e r ing [4]. S i m u l t a n e o u s l y a s m a l l p a r t of the s a m e l a s e r p u l s e i s s p l i t off. A f t e r p a s s i n g an o p ti c a l delay l i n e of 48 n s e c this p a r t e n t e r s e x a c tl y the
path of the p r i m a r y b e a m s e r v i n g a s an useful o p t i cal p r o b l e f o r the r e m a i n i n g a c o u s t i c phonons. Its i n t e n s i t y i s s m a l l e r than that of the p r i m a r y p u l s e by m o r e than one o r d e r of m a g nitude so that it cannot p r o d u c e f u r t h e r s t i m u l at ed s c a t t e r i n g . In o r d e r to r e c o r d the r e l a t i v ely weak b a c k s c a t t e r e d s i g n a l of the d el ay ed p u l s e t o g e t h e r with the s t r o n g s t i m u l a t e d B r i l louln i n t e n s i t y of the f i r s t p u l s e p o l a r i s a t i o n o p t i c s (see fig. 1) w e r e u s e d to e q u a l i z e both s i g nals f o r detection. If the a c o u s t i c phonons l i v e c o n s i d e r a b l y l o n g e r than the d e l a y t i m e of 48 n s e c t h e d e l a y e d p r o b e light m e e t s s t i l l a l m o s t al l g e n e r a t e d phonons s u f f e r i n g t h e r e f o r e g r e a t e s t b a c k s c a t t e r i n g . In q u a r t z this happens at t e m p e r a t u r e s below 35°K [5]. With i n c r e a s i n g t e m p e r a t u r e t h e phonon l i f e t i m e b e c o m e s s h o r t e r . T h e r e f o r e the p r o b e light will s e e f e w e r phonons and the b a c k s c a t t e r e d p r o b e intensity d e c r e a s e s a c c o r d i n g l y (see fig. lb). F r o m this d e c r e a s e the a b s o l u t e magnitude of the phonon l i f e t i m e can be d e t e r m i n e d within ± 10%. T h e s h o r t e s t l i f e t i m e which can be m e a s u r e d in this way d e pends on t h e t i m e d u r a t i o n of t h e l a s e r pulse, the l o n g e s t on the d e l a y t i m e b et w een both p u l s e s .
329
Volume 27A. n u m b e r 6
PHYSICS
LETTERS
12 August 1968 ,
I
|
¢#?'-extrapolation
~e
~1~/BRE'WSTER Z-QUARTZ
,00
I"--/--'1
LASER
:i: •-
i i
f=25cm : . . . . .j CRYOSTAT
: 7, _ -
|
f
g
"G
/
(U
w
~o-7
DELAY LINE (48nsec)
U_
10 a_ UJ
I-UJ
(48 nsec)
-J
T2/~/
Z
o
dA /
bZ
32°K
10-6
/
O.
/
Z-CUT QUARTZ
/
@. 0::
o 1 tn .Om
o,,,,.o.-,.''°~°'
~_~. ~ 1 4 3
OK
10-5 30
oo z _o
1GHz
I
I
I
50
100
150
TEMPERATUREPK] Fig. 1 a) Schematic of the e x p e r i m e n t a l set up. The points and a r r o w s on the optical path indicate p o l a r i s a tion v e c t o r s p e r p e n d i c u l a r and p a r a l l e l to the drawing plane. The quartz sample in a c r y o s t a t could be held at any t e m p e r a t u r e between 5°K and 300°K. b) Oscilloscope t r a c e s ( r i s e time 7 nsec) of the b a c k s c a t t e r e d light at various sample t e m p e r a t u r e s v e r s u s t i m e . c: undelayed stimulated Brillouin pulse, d: d e layed probe light, b a c k s c a t t e r e d f r o m the r e m a i n i n g
phonons. T h e m e a s u r e d l i f e t i m e s f o r l o n g i t u d i n a l 29 G H z p h o n o n s i n z - c u t q u a r t z a r e s h o w n i n fig. 2. It is obvious that around 100°K the absorption varies as T 2 and does not yet reach any temperature independent plateau in contrast to the k n o w n a b s o r p t i o n d a t a of 1 G H z p h o n o n s [1] w h i c h are also shown for comparison. Assuming an absorption due to collisions with thermal phonons w e m u s t c o n c l u d e 00~-ther m >/ 1 f o r 29 G H z p h o n o n s u p to 1 5 0 ° K c o r r e s p o n d i n g t o a t h e r m a l phonon lifetime (inclu!!ing U- and N-processes) of T t h e r m >/ 0 . 5 " 10 - t l s e c . I t s h o u l d b e n o t e d t h a t h e a t c o n d u c t i v i t y m e a s u r e m e n t s [6] l e a d to a similar value for U-processes only.
330
Fig. 2. Lifetimes of longitudinal acoustic phonons in z - c u t quartz v e r s u s t e m p e r a t u r e . The t r i a n g l e s show our optical m e a s u r e m e n t s at 29 GHz and the pointdashed line an wE-extrapolation for 29 GHz f r o m p r e vious 1 GHz data [1] included for c o m p a r i s o n . W e a r e t h a n k f u l t o K. D r a n s f e l d f o r m u c h i n terest in this work especially for suggesting this method.
References 1. H . E . B ~ m m e l and K . D r a n s f e l d . Phys. Rev. 177 (1960) 1245. 2. R.Y. Chiao and P.A. Fleury. in Physics of quantum electronics, eds. P.Kelley et al. (McGraw-Hill Book Company, New York. 1966) p. 241. 3. D. Pohl, M. M a i e r and W. Kaiser. Phys. Rev. L e t t e r s 20 (1968) 366. 4. R . Y . Chiao. C.H. Townes and B. P. Stoicheff. Phys. Rev. L e t t e r s 12 (1964) 592. 5. M . F . Lewis and E. P a t t e r s o n . Phys. Rev. 159 (1967) 703; W. Heinicke and G. Winterling. Appl. Phys. L e t t e r s 11 (1967) 231. 6. H . J . M a r i s . Phil. Mag. 9 (1964) 901.