- Email: [email protected]
Stimulated scattering in the far wing of the rayleigh line and low-frequency raman lines in liquids
Volume 4, number 1
STIMULATED
OPTICS COMMUNICATIONS
SCATTERING AND
IN
THE
LOW-FREQUENCY
FAR
WING
RAMAN
September 1971
OF
LINES
THE IN
RAYLEIGH
LINE
LIQUIDS*
C. A. S A C C H I Laboratorio di Fisica del Plasma ed Elettronica Quantistica del Consiglio Nazionale delle Ricerche, Istituto di Fisiea del Politecnico, Milano, Italy
Received 31 July 1971
The observation is reported of new stimulated inelastic scattering phenomena which occur in liquids under picosecond l a s e r excitation. The new observed lines can be divided into three classes and be i n t e r preted as due to: (i) scattering in the far wing of the Rayleigh line; (ii) librations of molecules in m o l e c ular complexes; (iii) intermolecular vibrations in quasi-crystalline structures. These last lines have previously been observed only in crystals.
T h i s l e t t e r r e p o r t s t h e o b s e r v a t i o n of new s t i m u l a t e d light s c a t t e r i n g p h e n o m e n a which o c c u r in a v a r i e t y of l i q u i d s . T h e o b s e r v a t i o n s h e r e r e p o r t e d h a v e b e e n o b t a i n e d by (1) the u s e of p i c o s e c o n d l a s e r p u l s e s which m a k e s the o b s e r v a t i o n of f a s t n o n - l i n e a r i t i e s p o s s i b l e by s u p p r e s s i n g s l o w e r n o n - l i n e a r e f f e c t s and (2) by s t u d y i n g the s p e c t r u m of the f a r - f i e l d p a t t e r n , i.e. by o b s e r v i n g n o n - c o l l i n e a r s c a t t e r e d light. The n e w l i n e s , which a p p e a r a s s a t e l l i t e s of the R a m a n - S t o k e s (RS) l i n e , can be d i v i d e d into t h r e e c l a s s e s . (i) L i n e s due to s c a t t e r i n g in the f a r wing of t h e R a y l e i g h line. T h i s e f f e c t i s r e l a t e d to a n o n - l i n e a r r e f r a c t i v e i n d e x with a s h o r t (a few t e n t h s of p i c o s e c o n d ) r e l a x a t i o n t i m e T. T h e i r f r e q u e n c y shift ~ a l l o w s d i r e c t m e a s u r e m e n t of T = I/~.
(ii) L o w - f r e q u e n c y R a m a n l i n e s p r e v i o u s l y o b s e r v e d in s p o n t a n e o u s s c a t t e r i n g e x p e r i m e n t s in l i q u i d s . T h e s e l i n e s h a v e b e e n a t t r i b u t e d , in t h e l i t e r a t u r e , to l i b r a t i o n s of m o l e c u l e s in molecular complexes. (iii) L o w - f r e q u e n c y R a m a n l i n e s p r e v i o u s l y o b s e r v e d only in c r y s t a l s . T h e s e l i n e s h a v e b e e n a t t r i b u t e d , in the l i t e r a t u r e , to i n t e r m o l e c u l a r v i b r a t i o n s . T h e i r o b s e r v a t i o n in t h i s w o r k i n d i c a t e s that the e x c i t i n g f i e l d s i n t e r a c t with q u a s i - c r y s t a l l i n e s t r u c t u r e s p r e s e n t in the l i q u i d s . A mode-locked ruby laser generating ~ 5 psec p u l s e s with a p o w e r d e n s i t y of ~ 1 G W / c m 2 h a s b e e n u s e d . T h e u n f o c u s e d b e a m of the l a s e r h a s b e e n s e n t t h r o u g h a 12 c m long l i q u i d c e l l . T h e
liquids investigated were carbon disulphide, benzene, toluene, nitrobenzene and brornobenzene. The spectra of both the near-field pattern and the far-field pattern have been studied using a grating spectrograph with a resolving power of 0.5 crn -1. The near-field spectrum shows that the laser b e a m undergoes self-focusing with the formation of small-scale filaments of light. At the input power used here, only a few filaments are formed with a diameter d which ranges from 15~ to 25~. The filaments exhibit the regular broad spectra typical of the self-phase modulation, which have already been observed [1] and which span 200-300 c m -1. S o m e of these filaments contain radiation at the R S frequency. The R S radiation, which is generated only in these filaments, presents a smaller diameter (12-18~) and a narrower spectrum (7-8 c m -1). This bandwidth corresponds to a duration of ~ 2 psec for a gaussian pulse. A weaker spectral structure spanning several tens of c m -I can also be observed, around the RS frequency, in s o m e filaments. With higher input powers the spectral broadening of the filaments exceeds the R a m a n shift and the spectra around the R S frequency present the broadening typical of the selfphase modulation. The far-field spectrum, which allows a study of the angularTversus-frequency distribution of the light, reveals the presence of weak lines around the exciting laser frequency. H o w ever the presence of a very intense background * Work supported by Italian Consiglio Nazionale delle Ricerche. 83
m
L
RS
~oL
RS
~9
rad)
a)
b)
R:3
44
RS
c)
RS
73
Fig. 1. Example of spectra of the far-field pattern given by CS2. L: laser frequency; RS: Raman-Stokes frequency. The laser light is strongly attenuated by an infrared filter (Corning Glass 7-69). The frequency shifts (cm-1) from the RS line are indicated. The continuous background is due to the flashlamp of the laser. due to the untrapped beam and its own frequency broadening probably due to self-phase modulation make the identification of the lines difficult. On the other hand some lines appear very clearly around the RS line. Three examples of such lines for CS2 are shown in fig. I. Here the l a s e r light has been strongly attenuated by an infrared glass filter. The intensity and the spectral broadening (7-8 em - I ) of the new lines are comparable to that of the RS line. This indicates that they a r e due to stimulated effects. These lines extend along the angular axis (~) axis) up to 10-15 mrad. The RS line extends up to ~ 20 mrad, which agrees well with the diffraction angle given by the observed 13~ average diameter of the 84
September 1971
OPTICS COMMUNICATIONS
Volume 4, n u m b e r l
Raman spot in the near-field. Both the RS line and the new lines have the same linear polarization as the l a s e r light. All the new lines have only clearly been observed very near the threshold for the Raman effect. At increasing input powers the RS line becomes much broader and the new lines cannot be distinguished any more. An interesting interpretation of the new observed lines can be given assuming the RS line as the "reference line". This requires one or both of the following assumptions: (1) the RS radiation itself generates its satellite lines: (2) the RS radiation is parametrically modulated by a process driven by fields near the l a s e r frequency [2}. As far as the first assumption is concerned. it has already been observed [3] that the RS line is more efficient than the laser line at producing stimulated low-frequency lines in crystalline CS2. In the present experiment this can be justified by the reason explained below and by the fact that the RS pulses, being generated in a transient regime themselves, can be shorter and less phase modulated than the laser pulses [4]. Therefore they can be more efficient at producing other transient effects than the l a s e r pulses. The frequency shifts of the new lines from the RS frequency are listed in tables 1,2 and 3. The uncertainty of the measurements is about ± 2 cm -I. With the input l a s e r power used here, one or two of the lines listed in the tables appear. At slightly higher input powers, many lines, eventually with overtones and combinations, appear. Table 1 gives the frequency shift i'~ of the
Table 1 Stimulated lines o b s e r v e d in the l o w - f r e q u e n c y side of the s p e c t r u m . The f r e q u e n c y shift ~2 f r o m the R a m a n Stokes (RS) line, the r e l a x a t i o n t i m e 7 = 1 / ~ and, f o r c o m p a r i s o n , the v a l u e s of T found by o t h e r a u t h o r s a r e listed Liquid
~
~ = 1/~(psec)
(cm -1)
this w o r k
other works
c a r b o n disulphide
19 25
0.28 0.21
0.36 - 0.85 [1] 0.21 [8]
benzene
17 22
0.31 0.24
0.24 [8]
toluene
16
0.33
0.38-0.3911]
nitrobenzene
17
0.31
bromobenzene
18 27
0.29 0.19
0.19-0.4911]
Volume 4, number 1
September 1971
OPTICS COMMUNICATIONS
l i n e s o b s e r v e d in the l o w - f r e q u e n c y s i d e of the s p e c t r u m with an i n t e n s i t y c o m p a r a b l e to that of the RS line. T h e s e l i n e s h a v e n e v e r b e e n o b s e r v e d in s p o n t a n e o u s s c a t t e r i n g e x p e r i m e n t s . B e i n g s h i f t e d by 16-27 c m -1, t h e y can b e due to a s t i m u l a t e d s c a t t e r i n g in the f a r wing of the R a y l e i g h line. T h i s p r o c e s s can be due to a n o n l i n e a r r e f r a c t i v e index with a s h o r t r e l a x a t i o n t i m e 7. T h i s has b e e n t h e o r e t i c a l l y t r e a t e d [5] and e x p e r i m e n t a l l y o b s e r v e d with n a n o s e c o n d l a s e r p u l s e s in the n e a r wing (a few c m -1) of the R a y l e i g h l i n e [6]. In the n e a r - f o r w a r d d i r e c t i o n t h e d o m i n a t i n g p r o c e s s is the d e g e n e r a t e l i g h t b y - l i g h t s c a t t e r i n g w h i c h i n v o l v e s no f r e q u e n c y shift of the s c a t t e r e d light and is r e s p o n s i b l e f o r s e l f - f o c u s i n g . At l a r g e a n g l e s the R a y l e i g h s c a t t e r i n g o c c u r s with a Stokes g a i n at a f r e q u e n c y shift ~2 = 1/~-. T h e l a s e r light, b e i n g t r a p p e d in the f i l a m e n t s , d i f f r a c t s at a m a x i m u m a n g l e 0cr = ( 1 / 2 . 8 8 ) ( ~ / d ) [7] which e q u a l s the
a n g l e 0 opt of m a x i m u m g a i n f o r the l i g h t - b y - l i g h t s c a t t e r i n g . T h e RS p u l s e s h a v e a d u r a t i o n s h o r t e r t h a n the l a s e r p u l s e s and a s m a l l e r d i a m e t e r , b e i n g g e n e r a t e d , n e a r the R a m a n t h r e s h o l d , only in the c e n t r a l p a r t of the f i l a m e n t s . In c o n s e q u e n c e t h e y c a n h a v e a h i g h e r p o w e r d e n s i t y than the l a s e r p u l s e s at the a n g l e s (8 > 2 0 o p t ) and at the f r e q u e n c y ( ~2 = l / T ) at which the R a x l e i g h s c a t t e r ing o c c u r s . T h e light s c a t t e r e d by t h i s p r o c e s s a r o u n d the RS f r e q u e n c y e m e r g e s f r o m the f i l a m e n t s and can be d e t e c t e d in the f a r - f i e l d s p e c t r u m . F o r e x a m p l e , t h e light s c a t t e r e d at an a n g l e ~ = 20op t would e m e r g e f r o m the f i l a m e n t s at an a n g l e which is, t a k i n g a c c o u n t of the w e a k w a v e r e t a r d a t i o n [5] and of S n e l l ' s l a w , 0 = f 2 0 o p t. A s s u m i n g 0opt = ( 1 / 2 . 8 8 ) ( ~ . / d ) , one g e t s , in the p r e s e n t c a s e , 0 = 13 - 2 2 m r a d in a g r e e m e n t with t h e e x p e r i m e n t a l v a l u e s . F r o m the f r e q u e n c y s h i f t ~2 one can d e d u c e the v a l u e of the r e l a x a t i o n t i m e 7. T h e v a l u e s of T found in t h i s w o r k a r e
Table 2 Stimulated low-frequency Raman lines observed predominantly in the high-frequency side of the spectrum. The f r e quency shifts observed here are compared to the values found by other authors from spontaneous scattering experiments in liquids. Some of these lines, which have been observed also in c r y s t a l s , are listed also in table 3 Liquid
Frequency shift (cm -1) this work
other works
carbon disulphide
34, 44
35 [9], 45 [10]
benzene
15,50,61,74
50,58 [11], 71 [12], 75 [9]
toluene
13, 19,22,29 66,218
13,21 [11], 66 [12], 215 [13] 219 [12]
nitrobenzene
24, 56 ± 4,186
56, 186 [12]
bromobenzene
24, 40 - 45, 59,185
63, 183 [12]
Table 3 Stimulated low-frequency Raman lines observed either in the low or in the high-frequency side of the spectrum. The frequency shifts here observed in liquids are compared to those found by other authors from spontaneous scattering experiments in crystalline solids Material
Frequency shift (cm "1) this work (liquids)
other works (crystals)
carbon disulphide
7 0 - 73, 83
69 [10], 73 [14], 75 [3], 83 [14]
benzene
34, 50- 53, 61 7 4 - 7 7 , 80, 99, 105-107, 115, 134
35 [15], 53 [16], 55 [15], 73, 84, 119 [16]
toluene
4 5 - 5 0 , 66, 88, 100, 123-127, 218
47, 66, 86. 108, 127, 220 [13]
bromobenzene
75, 88, 97, 185
85
Volume 4, number 1
OPTICS
COMMUNICATIONS
c o m p a r e d in table 1 with the v a l u e s found in o t h e r works. V e r y good a g r e e m e n t is found with (i) the v a l u e s obtained by F a b e l i n s k i i [8] f r o m spontaneous s c a t t e r i n g e x p e r i m e n t s in the f a r wing of the R a y l e i g h line and (ii) with the v a l u e s d e r i v e d in ref. [1] f r o m the s p e c t r a of the f i l a m e n t s u n d e r identical e x c i t a tion*. F o r carbon disulphide, b e n z e n e and b r o m o b e n z e n e two s t i m u l a t e d li n e s have been o b s e r v e d . This m ay be due to the fact that m o r e than one p h y s i c a l p r o c e s s can o c c u r , as d i s c u s s e d below. In table 2 the f r e q u e n c y shifts of o t h e r s t i m u l a t e d l i n es a r e listed. T h e s e lines have been p r e d o m i n a n t l y o b s e r v e d in the h i g h - f r e q u e n c y side of the s p e c t r u m . T h e i r i n t e n s it y is u s u a ll y w e a k e r , by one o r d e r of magnitude, than the RS intensity. Most of t h e s e l in e s have been obs e r v e d in spontaneous s c a t t e r i n g e x p e r i m e n t s in liquids [9-13], as indicated in table 2. T h e s e l i n e s have been a t t r i b u t e d , in the l i t e r a t u r e [11,12] to m o l e c u l a r l i b r a t i o n s in t r a n s i e n t c o m pl e xe s. F i n a l l y in table 3 a list is given of o t h e r lowf r e q u e n c y R a m a n l i n e s o b s e r v e d in the low or in the h i g h - f r e q u e n c y side of the s p e c t r u m . T h e i r i n t e n s i t y is u s u al l y one o r d e r of magnitude w e a k e r t h a n ' t h e RS intensity, although h i g h e r i n t e n s i t i e s have o c c a s i o n a l l y been o b s e r v e d . Most of t h e s e l i n e s have been ")bserved in spontaneous s c a t t e r i n g e x p e r i m e n t s by a u t h o r s who use d, i n s t ead of liquids, the c o r r e s p o n d i n g c r y s t a l l i n e s o l i d s and have been a t t r i b u t e d to i n t e r m o l e c u l a r v i b r a t i o n s [10, 13-16]. The f r e quency shifts of t h e s e lines a r e l i s t e d for c o m p a r i s o n in table 3. Although, as indicated in tables 2 and 3, most of the lines o b s e r v e d h e r e a g r e e well with the l i ne s p r e v i o u s l y o b s e r v e d in liquids and c r y s t a l s , s o m e i m p o r t a n t a s p e c t s of t h e i r g e n e r a t i o n d e s e r v e f u r t h e r i n v e s t i g a t i o n . F o r e x a m p l e , the a p p e a r a n c e of the li n es of table 2 and of s o m e l i n e s of table 3 only in the h i g h - f r e q u e n c y side of the f a r - f i e l d s p e c t r u m , could be explained by the s u r f a c e - p h a s e m a t c h i n g conditions for the a n t i - S t o k e s g e n e r a t i o n in f i l a m e n t s [17]. H o w e v e r t h e s e conditions can only c o r r e c t l y be applied to the g e n e r a t i o n in f i l a m e n t s c o n s i d e r a b l y s m a l l e r then those observed here. A q u a l i t a t i v e d i s c u s s i o n only is now p r e s e n t e d about the p h y s i c a l p r o c e s s e s which may o c c u r in t h e s e e x p e r i m e n t a l conditions. Many m e c h a n i s m s , * In ref. [1] a second order differential equation has been assumed for 6n. However the term ~-2b~ of e q . (3) does not affect the measurement of ~-1. 86
September 1971
i n t r o d u c e d to i n t e r p r e t the f ar wing of the spont a n e o u s Rayleigh line, can give a n o n - l i n e a r r e f r a c t i v e index with a r e l a x a t i o n t i m e of a few tenths of a picosecond. A model i n t r o d u c e d by L e v i n e and B i r n b a u m [18] is b a s e d on the change of a n i s o t r o p i c p o l a r i z a b i l i t y p r o d u c e d in p a i r s of m o l e c u l e s during c o l l i s i o n s . Another model, d ev el o p ed by Thibeau et al. [19] c o n s i d e r s the s c a t t e r i n g due to a " d i p o l e - i n d u c e d d i p o l e" effect. Although i n t r o d u c e d f o r light s c a t t e r i n g in g a s e s of s p h e r i c a l l y s y m m e t r i c m o l e c u l e s , the two m e c h a n i s m s a r e of i m p o r t a n c e also in liquids [20,21]. In this c a s e the f o r m e r m e c h a n i s m is m o r e i m p o r t a n t due to the density dependence [22]. It has also been o b s e r v e d [20] that m a n y p a r t i c l e c o r r e l a t i o n s can be i m p o r t a n t to produce intermolecular light scattering in liquids. Namely it has been shown by Hellwarth [23] that a local spatial redistribution of molecules in the p r e s ence of a strong electric field, can be as important, in producing a non-linear refractive index, as the effects of molecular reorientation. This process should have a relaxation time comparable to the molecular diffusion time which is a few tenths of a picosecond, at least for simple dense fluids [20]. Transient complexes formed during collisions of two or more molecules are also expected to give librations or intermolecular vibrations [12]. Instead of a manyparticle problem, one can take a different point of view and consider the librations of a molecule in the field of the neighboring ones. This has been done by Starunov [24] to interpret the far wing of the spontaneous Rayleigh line and by Hahn et al. [25] who observed a stimulated librational scattering in water. The same point of view has also been assumed by Hill [26] to explain the second dispersion of polar liquids. In particular the last author calculated some resonance frequencies which agree well with some of the lines reported in table 2. The following conclusions may be drawn. The lines reported in table 1 suggest that under ultrashort excitation a non-linear refractive index with a short relaxation time is formed. All the processes previously considered may occur although to different extents. Moreover, the lines reported in table 2 suggest that the exciting fields stimulate resonant oscillations which occur in molecular complexes existing in the liquid. Finally the lines reported in table 3 indicate the presence, recognized long ago [27], of quasicrystalline structures in the liquids. Since these lines have never been observed before in liquids it is suggested that the ultrashort exciting field may have the following effect:
Volume 4, number 1
OPTICS COMMUNICATIONS
(1) to f a v o r t h e f o r m a t i o n of o r d e r e d m o l e c u l a r complexes and/or (2) to e x c i t e o s c i l l a t i o n s in q u a s i - c r y s t a l l i n e s t r u c t u r e s a l r e a d y e x i s t i n g in t h e l i q u i d s . T h e s e o s c i l l a t i o n s c o u l d not e a s i l y be o b s e r v e d w i t h l o n g e r p u l s e s o r in s p o n t a n e o u s s c a t t e r i n g e x p e r i m e n t s due to a b r o a d s p o n t a n e o u s b a n d w i t h of t h e o r d e r of 1/~'. F i n a l l y it m u s t b e p o i n t e d out t h a t t h e p r e s e n c e of m o l e c u l a r c o m p l e x e s a n d q u a s i crystalline structures may significantly influenc e t h e f i l a m e n t s ' p r o p e r t i e s [28]. V e r y helpful d i s c u s s i o n s with P r o f e s s o r O. S v e l t o , Dr. R. C u b e d d u a n d D r . F. Z a r a g a and t h e t e c h n i c a l a s s i s t a n c e of M r . S B r u g h e r a and M r . M. S c a t t o r i n a r e a c k n o w l e d g e d .
REFERENCES [1] R. Polloni, C. A. Sacehi and O. Svelto, Phys. Rev. L e t t e r s 23 (1969) 690. [2] J. A. Giordmaine and W. K a i s e r . Phys. Rev. 144 (1966) 676; N. Bloembergen and P. Lallemand, Phys. Rev. L e t t e r s 16 (1966) 81. [3] Ya. S. Bobovieh and A. V. Borktevich, Opt. Spectry. 27 (1969) 373. [4] R. L. Carman, F. Shimizu, C. S. Wang and N. Bloembergen, Phys. Rev. 2A (1970) 60. [5] R. Y. Chiao, P. L. Kelley and E. G a r m i r e , Phys. Rev. L e t t e r s 17 (1966) 1158. [6] G. I. Zaitsev, Yu. I. Kyzylasov, V. S. Starunov and I. L. Fahelinskii, J E T P L e t t e r s 6 (1967) 180.
September 1971
[7] R. G. B r e w e r , J. R. Lifsitz, E. G a r m i r e , R.Y. Chiao and C. H. Townes, Phys. Rev. 166 (1968) 326. [8] I. L. Fabelinskii, Molecular s c a t t e r i n g of light (Plenum P r e s s , New York, 1968) table 32, p. 413. [9] L. A. Blatz, J. Chem. Phys. 47 (1967) 841. [10] N. C. Majumdar, Indian J. Phys. 23 (1959) 253. [11] B. Simic-Glavaski, D. A. Jackson and J. G. Powles, Phys. L e t t e r s 32A (1970) 329. [12] N. T. McDevitt and W. G. Fateley, J. Mol. Struct. 5 (1970) 477. [13] A.K. Ray, Indian J. Phys. 24 (1950) 111. [14] M. Ito, J. Chem. Phys. 42 (1965) 815. [15] A. K a s t l e r and A. Fruhling, Compt. Rend. Acad. Sci. (Paris) 218 (1944) 997. [16] M. Ito and T. Shigeoka, Spectrochim. Acta 22 (1966) 1029. [17] C. A. Sacchi, C. H Townes and J. R. Lifsitz, Phys. Rev. 174 (1968) 439. [18] H. B. Levine and G. Birnbaum, Phys. Rev. L e t t e r s 20 (1968) 439. [19] M. Thibeau, B. Oksengorn and V. Vodar, J. Phys. (Paris) 29 (1968) 287. [20] P. Mc Tague, P. A. Fleury and D. B. DuPrg, Phys. Rev. 188 (1969) 303. [21] W. S. Gornall, H. E. Howard-Lock and B. P. Stoicheff, Phys. Rev. A1 (1970) 1288. [22] V. V o l t e r r a , J. A. Bucaro and T. A. Litovitz, Phys. Rev. L e t t e r s 26 (1971) 55. [23] R. V. Hellwarth, Phys. Rev. 152 (1966) 156. [24] V. S. Starunov, Opt. Spectry. 18 (1965) 165. [25] O. Rahn, M. Maier and W. K a i s e r , Opt. Commun. 1 (1969) 109. [26] N. Hill, P r o e . Phys. Soc. (London) 82 (1963) 723. [27] E. Gross and M.Vuks, Nature 135 (1935) 100. [28] A. H. P i e k a r a , Sixth Intern. Quantum Electron. Conf., Digest of Technical P a p e r s , Kyoto, Japan (1970).
87
STIMULATED
OPTICS COMMUNICATIONS
SCATTERING AND
IN
THE
LOW-FREQUENCY
FAR
WING
RAMAN
September 1971
OF
LINES
THE IN
RAYLEIGH
LINE
LIQUIDS*
C. A. S A C C H I Laboratorio di Fisica del Plasma ed Elettronica Quantistica del Consiglio Nazionale delle Ricerche, Istituto di Fisiea del Politecnico, Milano, Italy
Received 31 July 1971
The observation is reported of new stimulated inelastic scattering phenomena which occur in liquids under picosecond l a s e r excitation. The new observed lines can be divided into three classes and be i n t e r preted as due to: (i) scattering in the far wing of the Rayleigh line; (ii) librations of molecules in m o l e c ular complexes; (iii) intermolecular vibrations in quasi-crystalline structures. These last lines have previously been observed only in crystals.
T h i s l e t t e r r e p o r t s t h e o b s e r v a t i o n of new s t i m u l a t e d light s c a t t e r i n g p h e n o m e n a which o c c u r in a v a r i e t y of l i q u i d s . T h e o b s e r v a t i o n s h e r e r e p o r t e d h a v e b e e n o b t a i n e d by (1) the u s e of p i c o s e c o n d l a s e r p u l s e s which m a k e s the o b s e r v a t i o n of f a s t n o n - l i n e a r i t i e s p o s s i b l e by s u p p r e s s i n g s l o w e r n o n - l i n e a r e f f e c t s and (2) by s t u d y i n g the s p e c t r u m of the f a r - f i e l d p a t t e r n , i.e. by o b s e r v i n g n o n - c o l l i n e a r s c a t t e r e d light. The n e w l i n e s , which a p p e a r a s s a t e l l i t e s of the R a m a n - S t o k e s (RS) l i n e , can be d i v i d e d into t h r e e c l a s s e s . (i) L i n e s due to s c a t t e r i n g in the f a r wing of t h e R a y l e i g h line. T h i s e f f e c t i s r e l a t e d to a n o n - l i n e a r r e f r a c t i v e i n d e x with a s h o r t (a few t e n t h s of p i c o s e c o n d ) r e l a x a t i o n t i m e T. T h e i r f r e q u e n c y shift ~ a l l o w s d i r e c t m e a s u r e m e n t of T = I/~.
(ii) L o w - f r e q u e n c y R a m a n l i n e s p r e v i o u s l y o b s e r v e d in s p o n t a n e o u s s c a t t e r i n g e x p e r i m e n t s in l i q u i d s . T h e s e l i n e s h a v e b e e n a t t r i b u t e d , in t h e l i t e r a t u r e , to l i b r a t i o n s of m o l e c u l e s in molecular complexes. (iii) L o w - f r e q u e n c y R a m a n l i n e s p r e v i o u s l y o b s e r v e d only in c r y s t a l s . T h e s e l i n e s h a v e b e e n a t t r i b u t e d , in the l i t e r a t u r e , to i n t e r m o l e c u l a r v i b r a t i o n s . T h e i r o b s e r v a t i o n in t h i s w o r k i n d i c a t e s that the e x c i t i n g f i e l d s i n t e r a c t with q u a s i - c r y s t a l l i n e s t r u c t u r e s p r e s e n t in the l i q u i d s . A mode-locked ruby laser generating ~ 5 psec p u l s e s with a p o w e r d e n s i t y of ~ 1 G W / c m 2 h a s b e e n u s e d . T h e u n f o c u s e d b e a m of the l a s e r h a s b e e n s e n t t h r o u g h a 12 c m long l i q u i d c e l l . T h e
liquids investigated were carbon disulphide, benzene, toluene, nitrobenzene and brornobenzene. The spectra of both the near-field pattern and the far-field pattern have been studied using a grating spectrograph with a resolving power of 0.5 crn -1. The near-field spectrum shows that the laser b e a m undergoes self-focusing with the formation of small-scale filaments of light. At the input power used here, only a few filaments are formed with a diameter d which ranges from 15~ to 25~. The filaments exhibit the regular broad spectra typical of the self-phase modulation, which have already been observed [1] and which span 200-300 c m -1. S o m e of these filaments contain radiation at the R S frequency. The R S radiation, which is generated only in these filaments, presents a smaller diameter (12-18~) and a narrower spectrum (7-8 c m -1). This bandwidth corresponds to a duration of ~ 2 psec for a gaussian pulse. A weaker spectral structure spanning several tens of c m -I can also be observed, around the RS frequency, in s o m e filaments. With higher input powers the spectral broadening of the filaments exceeds the R a m a n shift and the spectra around the R S frequency present the broadening typical of the selfphase modulation. The far-field spectrum, which allows a study of the angularTversus-frequency distribution of the light, reveals the presence of weak lines around the exciting laser frequency. H o w ever the presence of a very intense background * Work supported by Italian Consiglio Nazionale delle Ricerche. 83
m
L
RS
~oL
RS
~9
rad)
a)
b)
R:3
44
RS
c)
RS
73
Fig. 1. Example of spectra of the far-field pattern given by CS2. L: laser frequency; RS: Raman-Stokes frequency. The laser light is strongly attenuated by an infrared filter (Corning Glass 7-69). The frequency shifts (cm-1) from the RS line are indicated. The continuous background is due to the flashlamp of the laser. due to the untrapped beam and its own frequency broadening probably due to self-phase modulation make the identification of the lines difficult. On the other hand some lines appear very clearly around the RS line. Three examples of such lines for CS2 are shown in fig. I. Here the l a s e r light has been strongly attenuated by an infrared glass filter. The intensity and the spectral broadening (7-8 em - I ) of the new lines are comparable to that of the RS line. This indicates that they a r e due to stimulated effects. These lines extend along the angular axis (~) axis) up to 10-15 mrad. The RS line extends up to ~ 20 mrad, which agrees well with the diffraction angle given by the observed 13~ average diameter of the 84
September 1971
OPTICS COMMUNICATIONS
Volume 4, n u m b e r l
Raman spot in the near-field. Both the RS line and the new lines have the same linear polarization as the l a s e r light. All the new lines have only clearly been observed very near the threshold for the Raman effect. At increasing input powers the RS line becomes much broader and the new lines cannot be distinguished any more. An interesting interpretation of the new observed lines can be given assuming the RS line as the "reference line". This requires one or both of the following assumptions: (1) the RS radiation itself generates its satellite lines: (2) the RS radiation is parametrically modulated by a process driven by fields near the l a s e r frequency [2}. As far as the first assumption is concerned. it has already been observed [3] that the RS line is more efficient than the laser line at producing stimulated low-frequency lines in crystalline CS2. In the present experiment this can be justified by the reason explained below and by the fact that the RS pulses, being generated in a transient regime themselves, can be shorter and less phase modulated than the laser pulses [4]. Therefore they can be more efficient at producing other transient effects than the l a s e r pulses. The frequency shifts of the new lines from the RS frequency are listed in tables 1,2 and 3. The uncertainty of the measurements is about ± 2 cm -I. With the input l a s e r power used here, one or two of the lines listed in the tables appear. At slightly higher input powers, many lines, eventually with overtones and combinations, appear. Table 1 gives the frequency shift i'~ of the
Table 1 Stimulated lines o b s e r v e d in the l o w - f r e q u e n c y side of the s p e c t r u m . The f r e q u e n c y shift ~2 f r o m the R a m a n Stokes (RS) line, the r e l a x a t i o n t i m e 7 = 1 / ~ and, f o r c o m p a r i s o n , the v a l u e s of T found by o t h e r a u t h o r s a r e listed Liquid
~
~ = 1/~(psec)
(cm -1)
this w o r k
other works
c a r b o n disulphide
19 25
0.28 0.21
0.36 - 0.85 [1] 0.21 [8]
benzene
17 22
0.31 0.24
0.24 [8]
toluene
16
0.33
0.38-0.3911]
nitrobenzene
17
0.31
bromobenzene
18 27
0.29 0.19
0.19-0.4911]
Volume 4, number 1
September 1971
OPTICS COMMUNICATIONS
l i n e s o b s e r v e d in the l o w - f r e q u e n c y s i d e of the s p e c t r u m with an i n t e n s i t y c o m p a r a b l e to that of the RS line. T h e s e l i n e s h a v e n e v e r b e e n o b s e r v e d in s p o n t a n e o u s s c a t t e r i n g e x p e r i m e n t s . B e i n g s h i f t e d by 16-27 c m -1, t h e y can b e due to a s t i m u l a t e d s c a t t e r i n g in the f a r wing of the R a y l e i g h line. T h i s p r o c e s s can be due to a n o n l i n e a r r e f r a c t i v e index with a s h o r t r e l a x a t i o n t i m e 7. T h i s has b e e n t h e o r e t i c a l l y t r e a t e d [5] and e x p e r i m e n t a l l y o b s e r v e d with n a n o s e c o n d l a s e r p u l s e s in the n e a r wing (a few c m -1) of the R a y l e i g h l i n e [6]. In the n e a r - f o r w a r d d i r e c t i o n t h e d o m i n a t i n g p r o c e s s is the d e g e n e r a t e l i g h t b y - l i g h t s c a t t e r i n g w h i c h i n v o l v e s no f r e q u e n c y shift of the s c a t t e r e d light and is r e s p o n s i b l e f o r s e l f - f o c u s i n g . At l a r g e a n g l e s the R a y l e i g h s c a t t e r i n g o c c u r s with a Stokes g a i n at a f r e q u e n c y shift ~2 = 1/~-. T h e l a s e r light, b e i n g t r a p p e d in the f i l a m e n t s , d i f f r a c t s at a m a x i m u m a n g l e 0cr = ( 1 / 2 . 8 8 ) ( ~ / d ) [7] which e q u a l s the
a n g l e 0 opt of m a x i m u m g a i n f o r the l i g h t - b y - l i g h t s c a t t e r i n g . T h e RS p u l s e s h a v e a d u r a t i o n s h o r t e r t h a n the l a s e r p u l s e s and a s m a l l e r d i a m e t e r , b e i n g g e n e r a t e d , n e a r the R a m a n t h r e s h o l d , only in the c e n t r a l p a r t of the f i l a m e n t s . In c o n s e q u e n c e t h e y c a n h a v e a h i g h e r p o w e r d e n s i t y than the l a s e r p u l s e s at the a n g l e s (8 > 2 0 o p t ) and at the f r e q u e n c y ( ~2 = l / T ) at which the R a x l e i g h s c a t t e r ing o c c u r s . T h e light s c a t t e r e d by t h i s p r o c e s s a r o u n d the RS f r e q u e n c y e m e r g e s f r o m the f i l a m e n t s and can be d e t e c t e d in the f a r - f i e l d s p e c t r u m . F o r e x a m p l e , t h e light s c a t t e r e d at an a n g l e ~ = 20op t would e m e r g e f r o m the f i l a m e n t s at an a n g l e which is, t a k i n g a c c o u n t of the w e a k w a v e r e t a r d a t i o n [5] and of S n e l l ' s l a w , 0 = f 2 0 o p t. A s s u m i n g 0opt = ( 1 / 2 . 8 8 ) ( ~ . / d ) , one g e t s , in the p r e s e n t c a s e , 0 = 13 - 2 2 m r a d in a g r e e m e n t with t h e e x p e r i m e n t a l v a l u e s . F r o m the f r e q u e n c y s h i f t ~2 one can d e d u c e the v a l u e of the r e l a x a t i o n t i m e 7. T h e v a l u e s of T found in t h i s w o r k a r e
Table 2 Stimulated low-frequency Raman lines observed predominantly in the high-frequency side of the spectrum. The f r e quency shifts observed here are compared to the values found by other authors from spontaneous scattering experiments in liquids. Some of these lines, which have been observed also in c r y s t a l s , are listed also in table 3 Liquid
Frequency shift (cm -1) this work
other works
carbon disulphide
34, 44
35 [9], 45 [10]
benzene
15,50,61,74
50,58 [11], 71 [12], 75 [9]
toluene
13, 19,22,29 66,218
13,21 [11], 66 [12], 215 [13] 219 [12]
nitrobenzene
24, 56 ± 4,186
56, 186 [12]
bromobenzene
24, 40 - 45, 59,185
63, 183 [12]
Table 3 Stimulated low-frequency Raman lines observed either in the low or in the high-frequency side of the spectrum. The frequency shifts here observed in liquids are compared to those found by other authors from spontaneous scattering experiments in crystalline solids Material
Frequency shift (cm "1) this work (liquids)
other works (crystals)
carbon disulphide
7 0 - 73, 83
69 [10], 73 [14], 75 [3], 83 [14]
benzene
34, 50- 53, 61 7 4 - 7 7 , 80, 99, 105-107, 115, 134
35 [15], 53 [16], 55 [15], 73, 84, 119 [16]
toluene
4 5 - 5 0 , 66, 88, 100, 123-127, 218
47, 66, 86. 108, 127, 220 [13]
bromobenzene
75, 88, 97, 185
85
Volume 4, number 1
OPTICS
COMMUNICATIONS
c o m p a r e d in table 1 with the v a l u e s found in o t h e r works. V e r y good a g r e e m e n t is found with (i) the v a l u e s obtained by F a b e l i n s k i i [8] f r o m spontaneous s c a t t e r i n g e x p e r i m e n t s in the f a r wing of the R a y l e i g h line and (ii) with the v a l u e s d e r i v e d in ref. [1] f r o m the s p e c t r a of the f i l a m e n t s u n d e r identical e x c i t a tion*. F o r carbon disulphide, b e n z e n e and b r o m o b e n z e n e two s t i m u l a t e d li n e s have been o b s e r v e d . This m ay be due to the fact that m o r e than one p h y s i c a l p r o c e s s can o c c u r , as d i s c u s s e d below. In table 2 the f r e q u e n c y shifts of o t h e r s t i m u l a t e d l i n es a r e listed. T h e s e lines have been p r e d o m i n a n t l y o b s e r v e d in the h i g h - f r e q u e n c y side of the s p e c t r u m . T h e i r i n t e n s it y is u s u a ll y w e a k e r , by one o r d e r of magnitude, than the RS intensity. Most of t h e s e l in e s have been obs e r v e d in spontaneous s c a t t e r i n g e x p e r i m e n t s in liquids [9-13], as indicated in table 2. T h e s e l i n e s have been a t t r i b u t e d , in the l i t e r a t u r e [11,12] to m o l e c u l a r l i b r a t i o n s in t r a n s i e n t c o m pl e xe s. F i n a l l y in table 3 a list is given of o t h e r lowf r e q u e n c y R a m a n l i n e s o b s e r v e d in the low or in the h i g h - f r e q u e n c y side of the s p e c t r u m . T h e i r i n t e n s i t y is u s u al l y one o r d e r of magnitude w e a k e r t h a n ' t h e RS intensity, although h i g h e r i n t e n s i t i e s have o c c a s i o n a l l y been o b s e r v e d . Most of t h e s e l i n e s have been ")bserved in spontaneous s c a t t e r i n g e x p e r i m e n t s by a u t h o r s who use d, i n s t ead of liquids, the c o r r e s p o n d i n g c r y s t a l l i n e s o l i d s and have been a t t r i b u t e d to i n t e r m o l e c u l a r v i b r a t i o n s [10, 13-16]. The f r e quency shifts of t h e s e lines a r e l i s t e d for c o m p a r i s o n in table 3. Although, as indicated in tables 2 and 3, most of the lines o b s e r v e d h e r e a g r e e well with the l i ne s p r e v i o u s l y o b s e r v e d in liquids and c r y s t a l s , s o m e i m p o r t a n t a s p e c t s of t h e i r g e n e r a t i o n d e s e r v e f u r t h e r i n v e s t i g a t i o n . F o r e x a m p l e , the a p p e a r a n c e of the li n es of table 2 and of s o m e l i n e s of table 3 only in the h i g h - f r e q u e n c y side of the f a r - f i e l d s p e c t r u m , could be explained by the s u r f a c e - p h a s e m a t c h i n g conditions for the a n t i - S t o k e s g e n e r a t i o n in f i l a m e n t s [17]. H o w e v e r t h e s e conditions can only c o r r e c t l y be applied to the g e n e r a t i o n in f i l a m e n t s c o n s i d e r a b l y s m a l l e r then those observed here. A q u a l i t a t i v e d i s c u s s i o n only is now p r e s e n t e d about the p h y s i c a l p r o c e s s e s which may o c c u r in t h e s e e x p e r i m e n t a l conditions. Many m e c h a n i s m s , * In ref. [1] a second order differential equation has been assumed for 6n. However the term ~-2b~ of e q . (3) does not affect the measurement of ~-1. 86
September 1971
i n t r o d u c e d to i n t e r p r e t the f ar wing of the spont a n e o u s Rayleigh line, can give a n o n - l i n e a r r e f r a c t i v e index with a r e l a x a t i o n t i m e of a few tenths of a picosecond. A model i n t r o d u c e d by L e v i n e and B i r n b a u m [18] is b a s e d on the change of a n i s o t r o p i c p o l a r i z a b i l i t y p r o d u c e d in p a i r s of m o l e c u l e s during c o l l i s i o n s . Another model, d ev el o p ed by Thibeau et al. [19] c o n s i d e r s the s c a t t e r i n g due to a " d i p o l e - i n d u c e d d i p o l e" effect. Although i n t r o d u c e d f o r light s c a t t e r i n g in g a s e s of s p h e r i c a l l y s y m m e t r i c m o l e c u l e s , the two m e c h a n i s m s a r e of i m p o r t a n c e also in liquids [20,21]. In this c a s e the f o r m e r m e c h a n i s m is m o r e i m p o r t a n t due to the density dependence [22]. It has also been o b s e r v e d [20] that m a n y p a r t i c l e c o r r e l a t i o n s can be i m p o r t a n t to produce intermolecular light scattering in liquids. Namely it has been shown by Hellwarth [23] that a local spatial redistribution of molecules in the p r e s ence of a strong electric field, can be as important, in producing a non-linear refractive index, as the effects of molecular reorientation. This process should have a relaxation time comparable to the molecular diffusion time which is a few tenths of a picosecond, at least for simple dense fluids [20]. Transient complexes formed during collisions of two or more molecules are also expected to give librations or intermolecular vibrations [12]. Instead of a manyparticle problem, one can take a different point of view and consider the librations of a molecule in the field of the neighboring ones. This has been done by Starunov [24] to interpret the far wing of the spontaneous Rayleigh line and by Hahn et al. [25] who observed a stimulated librational scattering in water. The same point of view has also been assumed by Hill [26] to explain the second dispersion of polar liquids. In particular the last author calculated some resonance frequencies which agree well with some of the lines reported in table 2. The following conclusions may be drawn. The lines reported in table 1 suggest that under ultrashort excitation a non-linear refractive index with a short relaxation time is formed. All the processes previously considered may occur although to different extents. Moreover, the lines reported in table 2 suggest that the exciting fields stimulate resonant oscillations which occur in molecular complexes existing in the liquid. Finally the lines reported in table 3 indicate the presence, recognized long ago [27], of quasicrystalline structures in the liquids. Since these lines have never been observed before in liquids it is suggested that the ultrashort exciting field may have the following effect:
Volume 4, number 1
OPTICS COMMUNICATIONS
(1) to f a v o r t h e f o r m a t i o n of o r d e r e d m o l e c u l a r complexes and/or (2) to e x c i t e o s c i l l a t i o n s in q u a s i - c r y s t a l l i n e s t r u c t u r e s a l r e a d y e x i s t i n g in t h e l i q u i d s . T h e s e o s c i l l a t i o n s c o u l d not e a s i l y be o b s e r v e d w i t h l o n g e r p u l s e s o r in s p o n t a n e o u s s c a t t e r i n g e x p e r i m e n t s due to a b r o a d s p o n t a n e o u s b a n d w i t h of t h e o r d e r of 1/~'. F i n a l l y it m u s t b e p o i n t e d out t h a t t h e p r e s e n c e of m o l e c u l a r c o m p l e x e s a n d q u a s i crystalline structures may significantly influenc e t h e f i l a m e n t s ' p r o p e r t i e s [28]. V e r y helpful d i s c u s s i o n s with P r o f e s s o r O. S v e l t o , Dr. R. C u b e d d u a n d D r . F. Z a r a g a and t h e t e c h n i c a l a s s i s t a n c e of M r . S B r u g h e r a and M r . M. S c a t t o r i n a r e a c k n o w l e d g e d .
REFERENCES [1] R. Polloni, C. A. Sacehi and O. Svelto, Phys. Rev. L e t t e r s 23 (1969) 690. [2] J. A. Giordmaine and W. K a i s e r . Phys. Rev. 144 (1966) 676; N. Bloembergen and P. Lallemand, Phys. Rev. L e t t e r s 16 (1966) 81. [3] Ya. S. Bobovieh and A. V. Borktevich, Opt. Spectry. 27 (1969) 373. [4] R. L. Carman, F. Shimizu, C. S. Wang and N. Bloembergen, Phys. Rev. 2A (1970) 60. [5] R. Y. Chiao, P. L. Kelley and E. G a r m i r e , Phys. Rev. L e t t e r s 17 (1966) 1158. [6] G. I. Zaitsev, Yu. I. Kyzylasov, V. S. Starunov and I. L. Fahelinskii, J E T P L e t t e r s 6 (1967) 180.
September 1971
[7] R. G. B r e w e r , J. R. Lifsitz, E. G a r m i r e , R.Y. Chiao and C. H. Townes, Phys. Rev. 166 (1968) 326. [8] I. L. Fabelinskii, Molecular s c a t t e r i n g of light (Plenum P r e s s , New York, 1968) table 32, p. 413. [9] L. A. Blatz, J. Chem. Phys. 47 (1967) 841. [10] N. C. Majumdar, Indian J. Phys. 23 (1959) 253. [11] B. Simic-Glavaski, D. A. Jackson and J. G. Powles, Phys. L e t t e r s 32A (1970) 329. [12] N. T. McDevitt and W. G. Fateley, J. Mol. Struct. 5 (1970) 477. [13] A.K. Ray, Indian J. Phys. 24 (1950) 111. [14] M. Ito, J. Chem. Phys. 42 (1965) 815. [15] A. K a s t l e r and A. Fruhling, Compt. Rend. Acad. Sci. (Paris) 218 (1944) 997. [16] M. Ito and T. Shigeoka, Spectrochim. Acta 22 (1966) 1029. [17] C. A. Sacchi, C. H Townes and J. R. Lifsitz, Phys. Rev. 174 (1968) 439. [18] H. B. Levine and G. Birnbaum, Phys. Rev. L e t t e r s 20 (1968) 439. [19] M. Thibeau, B. Oksengorn and V. Vodar, J. Phys. (Paris) 29 (1968) 287. [20] P. Mc Tague, P. A. Fleury and D. B. DuPrg, Phys. Rev. 188 (1969) 303. [21] W. S. Gornall, H. E. Howard-Lock and B. P. Stoicheff, Phys. Rev. A1 (1970) 1288. [22] V. V o l t e r r a , J. A. Bucaro and T. A. Litovitz, Phys. Rev. L e t t e r s 26 (1971) 55. [23] R. V. Hellwarth, Phys. Rev. 152 (1966) 156. [24] V. S. Starunov, Opt. Spectry. 18 (1965) 165. [25] O. Rahn, M. Maier and W. K a i s e r , Opt. Commun. 1 (1969) 109. [26] N. Hill, P r o e . Phys. Soc. (London) 82 (1963) 723. [27] E. Gross and M.Vuks, Nature 135 (1935) 100. [28] A. H. P i e k a r a , Sixth Intern. Quantum Electron. Conf., Digest of Technical P a p e r s , Kyoto, Japan (1970).
87