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Stimulated backward Raman scattering excited in the picosecond range: high efficiency conversions
Volume 82, number 1,2
OPTICS COMMUNICATIONS
1 April 1991
Stimulated backward Raman scattering excited in the picosecond range: high efficiency conversions R. Chevalier, A. Sokolovskaia 1, N. Tcherniega ~ and G. Rivoire Laboratory Properties Optiques des Materiaux et Applications, Unit# Associ#e CNRS D0780, 4 Boulevard Lavoisier BP 2018, 49016 Angers Cedex, France Received 16 July 1990; revised manuscript received 13 December 1990
Stimulated backward Raman scattering (SBRS) excited by picosecond laser pulses is produced with high efficiency conversion in materials displaying large Raman gain and small Kerr constants. A constant energy efficiency of 40% is obtained in aceton for a wide range of the exciting laser energy. The spatial, spectral and temporal structure of the backscattering beam is studied.
1. Introduction Stimulated scattering excited by laser beams has a wide range of applications: production of light generators at new wavelengths [ 1 ], phase conjugation [2,3 ] and image reconstruction [4,5 ]. Studies on stimulated scattering have more concerned the nanosecond than the picosecond range of excitation. For instance, the experimental conditions leading to a high efficiency of stimulated backward Brillouin scattering (SBBS), and to a good quality of its phase conjugation properties have been ascertained. In the picosecond range, SBBS is not produced because of its long relaxation time: only Raman and Rayleigh wing scattering can be amplified. We" have shown that these scatterings used in their backward direction - stimulated backward Raman scattering (SBRS) and stimulated backward Rayleigh wing scattering (SBWRS) - excited by 25 ps laser pulses can be used for image reconstruction [ 6 ]. However, the efficiencies obtained in our first experiments were low, on the order of 10 -2. In order to realise applications, larger efficiencies are necessary and the knowledge of the spatial, temporal and energetic properties of the backscattering is required. In this article, we present the results concerning SBRS excited by picosecond pulses in different maOn study leave from Lebedev Institute of Moscow, USSR.
terials, with various geometrical exciting configurations. We give the conditions necessary for obtaining high efficiency and stability simultaneously.
2. Experimental conditions SBRS is excited by a modelocked Nd:YAG laser, delivering single pulses of a duration zv=25 ps at 2 = 532 nm. The laser presents temporal and spatial gaussian structures. The set up is shown in fig. I. The laser beam is focused either inside or outside the Raman active medium by lens L~ (focusing length f~ ). The distance d B..~.
B. ~'.
B.5.
L1
B.S.
B.$.
beam--I cGmero Spe¢rrogroph
Fig. I. Set up used for the study of SBRS. L~, L2, L3: lenses, BS: beamsplitters, Pht, Ph2: calibrated photodiodes or Joulemeters.
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d between lens Lt and the entrance window of the Raman material, as well as the radius ¢~ of the laser beam on L~, significantly influence the backscattering. The input and backscattered energies are controlled by calibrated photodiodes associated with neutral optical filters. The spatial structures of the transmitted and backscattered beams are registered simultaneously by a numerical camera, linked to a computer. They are displayed on the computer screen with a magnification 20. The image of the Raman medium output window Wo is made on the camera by lens L2, with a magnification 10. The backscattered Raman beam structure, recorded at the distance D from lens L1, can be directly compared with the structure of the exciting beam. The image of the entrance window We is produced by the backscattered beam, using lens L3, o n the slit of an Ebert Fastie spectrograph, with a magnification 10. The temporal impulse response of this spectrograph is 130 ps, larger than Tp: this allows the resolution of the temporal details of the Raman spectrum, and enables the user to determine the duration of the backscattering [ 8 ]. The backscattered beam is amplified in the Raman medium only on a length of the order of lp = W p - 5 mm, where v is the light phase velocity in this medium [ 6 ]. We thus use short lengths l for the Raman medium. In order to have a strong Raman amplification with these small values of 1, large Raman gain g and high values of the laser intensity IL are required, according to the formula IR= IRo exp (glL l), where I~ is the Raman intensity. Most of the materials displaying large Raman gain also have large nonlinear refractive index changes AnNL=7IL. A strong Raman conversion will thus often be associated with the self-focusing of the laser and scattered beams. In most of the experiments described below, more than 90% of the backscattered energy is concentrated in the first Stokes line, characterized by a frequency OgR= 09L--09V, where are and - o ~ are respectively the laser and molecular vibration frequencies. The Raman active liquids studied are excited in a steady state situation: their dephasing time 7"2 w h i c h describes the damping of the molecular vibration - is much smaller than Zp [ 10 ]. For instance, in aceton, T2=0.34 ps. 118
1 April 1991
The results obtained are presented in three sections: - Spatial structures of the backscattered beams. - Energies and efficiencies. - Temporal structures.
3. S p a t i a l structures of t h e b a e k s c a t t e r e d b e a m s
In order to produce a high value of the laser intensity in the Raman medium, it is necessary to obtain a small beam waist radius r~ =2f~/nCh~ after the focusing of the laser beam by L~. The observations described below show that in materials with a large value of y it is interesting to achieve rE-----rf, where rf is the radius of the filaments built by self focusing. In these conditions, for all the geometrical configurations (focusing inside or outside the cell with different values off~ and d), the same evolution of the spatial structure of the backscattered beam is observed with increasing laser energy EL. This is illustrated in fig. 2: for small values of EL, a diffuse structure (fig. 2a) is observed, becoming more and more intense and symmetrical, progressively acquiring the shape of a circular diffraction pattern, which is centered on the axis of the system (fig. 2b). For a critical value of the laser energy E L = E L o the image breaks up in several spots having the same size (fig.
Fig. 2. Spatial structure o f SBRS in aceton with the conditions: f l = 10cm, l = 5 cm, d = 7 cm, rL=80 ttm. (a) E L f 2 × 10-s J, (b) EL=ELC=3 X 10 - s J, (c) ELffi4X 10 .5 J, (d) EL----4X 10 -4 J.
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Table 1 Characteristics of different Raman active materials and values of the measured critical energy. Raman material
Aceton Cyclohexane Carbon tetrachioride Benzene
Raman frequency shift toy (cm -I )
Rarnan gain g [9,10] ( 10 tl m / W )
Constant 7 [ 11 ] ( 10 - i s m 2 / W )
Ratio g/7
2921 2850 460
1 1 0.85
0.059 0.053 0.050
16.9 18.9 17
3×10 -~ 4×10 -5 3×10 -5
3
0.29
10
10-5
990, 3064
2c). For large values o f EL, the individual spots become more numerous and they overlap, producing a large and fairly non-homogeneous image (fig. 2d). Steps 2b and 2c are related to the existence o f a nonlinearity AnNL in the refractive index, and to the correlated self-focusing phenomenon. Several features prove this conclusion: - T h e same kind o f shapes are obtained in cyclohexane, chloroform, carbon tetrachloride and benzene, but with different values o f ELc (table 1 ). In calcite, where y-~0, steps 2b and 2c do not exist: the spatial structure o f SBRS, diffuse when EL is small, breaks up at high laser energies into several irregular areas. Large values o f the constant y (table 1 ) are thus connected with the presence o f circular spots. We note here that we have not used carbon disulphide: in spite o f a high R a m a n gain and a high Kerr constant, the amplification o f SBRS is limited by the presence o f a strong Rayleigh wing scattering [12,13]. - The break up o f the scattered beam into several spots is connected with the same phenomenon on the exciting beam, as illustrated in fig. 3. The radius OR o f the R a m a n spots measured on the camera is quasi independent o f the distance D between the camera and the lens LI. This observation can be understood as resulting from a scattering created near the focus o f L~, on a radius rg connected to ~R by the relation: -
20R =f~A/2rR.
Measured value of ELC (J)
Fig. 3. Spatial structures of SBRS (a) and transmitted laser light (b) obtained in aceton, with ft=10 cm, l=5 cm, d=7 cm, EL= 1.2X 10-4 J.
~tm. The size o f the laser filaments measured in the same experimental conditions (on fig. 3) is r f = 5 0 ~tm. Therefore, we can deduce from these measurements that the backward R a m a n light is generated in the laser filaments. To our knowledge, it is the first time that the evolution o f a self-focusing structure is observed in SBRS. The creation o f a first stable filament in the central part o f the laser beam (fig. 2b) is connected with the small size o f the laser beam waist. When the laser energy is increased, lateral scatterings filaments (seen on fig. 2c) can develop (fig. 4).
( 1)
From the measurements o f ~ , we can deduce rR using formula ( 1 ). U n d e r the experimental conditions of fig. 2, we measure 0R=0.25 mm; this yields rg--- 50
Fig. 4. Scheme describing the creation of the self focusing filaments in the Raman active medium. 119
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4. Energies and efficiencies The curve representing the total backscattered energy ER versus the laser energy EL has the same shape in all the geometric configurations, and for all the Kerr active materials studied. This behaviour is illustrated in fig. 5, still given for the same experimental conditions (aceton, 1= 5 cm, f~ = 10 cm, L = 7 cm): for EL < ELC, ER grows exponentially. Then, for ELcELmax, the efficiency of SBRS tends to decrease and strong fluctuations are observed: they are due to the amplification of the forward Raman scattering, and to the presence of other nonlinear effects. In the range ELc
og~" R o.u.
0 0
/.
P
5,
o
O
1 April 1991
When the laser power reaches a critical value PLC, the propagation becomes unstable, leading to the formation of filaments [ 14-17 ]. If the material length l is larger than the Fresnel length IF of the beam, the value of PLC is
P° c =2 2/8no7 .
(2)
In our experiments, we generally have l< IF, hence
& c -~P°c lF/l. The corresponding critical energy is
ELc=P~_c ( lv/l) rp.
(3)
The numerical calculations lead to P ° z p = 10 -5 J for aceton, and to ELC--4× 10 -5 J for the geometrical situation described in figure captions, 2, 3 and 5. This value is in agreement with the measurements (table I ). We notice that ELC is inversely proportional to y: this is the reason why, with the small values of l imposed by the picosecond excitation, the backward Raman threshold is not reached in liquids displaying a large Raman gain, as well as a large Kerr constant. This is the case for nitrobenzene. In the filaments, the laser intensity IL has a maximum value:
o
0
O
o
o
/o
0
(4)
In the amplification formula,
0
o
ELC /~2 IF 1 ILmax-- TpTtrf2 -- 8no) ~ l rtr 2 "
O0
IR = IRo exp (glL IR) ,
(5)
00
where IR is the length of the material active in SBRS, the maximum value of the gain G=glL is
g2 21v 1 Gm~=gIL~x= 8no~ 1 ttr 2"
r/ (
Gm,~ depends on the Raman material, and is roughly proportional to g/y (if the variations of the filament radius rf with the material are neglected [ 18 ] ). In aceton, for the experimental conditions described in fig. 2,
I. IOggLC"
to~lELMAX
I L ~ = 15 G W / c m 2 and Gm~,lp = 10.5. log
EL
Fig. 5. Raman energy E• versus laser energy EL, obtained in aceton, with f t = 1 0 cm, / = 5 cm, d = 7 cm, ELC=3×10 -s J, ELm~= 10 -3 J-
120
(6)
In one filament the Raman energy is 1 1 2 ER=IRZRTrrf =lRoexp(glLm~lg) rRnr~ ,
(7)
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where ZR is the Raman pulse duration. In N filaments, if ZR and IR are presumed to be the same in all the filaments (this hypothesis will be discussed later), the total energy is
! April 1991
duce a strong amplification of the forward Raman wave, and thus there is less competition with the backward Raman amplification.
E R ,~ N E ff I .
5. S p e c t r a l a n d t e m p o r a l s t r u c t u r e s
The number N is the related to the laser energy by EL "" NEI-c ,
and the scattered energy is thus ER = ( E L / ELc ) E L .
(8)
Formula (8) shows a linear relation between the backscattered and laser energies, in agreement with the experimental curves (fig. 5). From (8), (4) and (7), the energy efficiency r/of the SBRS process is obtained ER
EL
--
r / = El- -- E L f
-
IR0 exp(GmaxlR) ZR IL max Tp
The evolution of the Raman spectrum with the laser energy EL, and therefore with the Raman spatial structure, is illustrated in fig. 6. For EL << ELc, when the spatial SBRS structure is diffuse, the spectrum contains only one line (fig. 6a). Its width is the same as that of the laser line (1.5 c m - l ) , indicating that the Raman and laser pulses have the same duration % = 2 5 ps. Then, for EL -----ELc, in the spatial location where the first filament is built, this line becomes larger, and a structure begins to appear (fig. 6b). The width
(9)
When IR et ZR have their maximum values lp and % (9) yields t/m~x=IR0 exp ( glm~x lR ) .
(10)
lLmax
From formula (10) we deduce the conditions leading to the best efficiency: (i) The material is chosen in order to obtain a maximum value of g/y: aceton, cyclohexane, carbon tetrachloride are among the best materials (table 1 ). A convenient polarization of the laser beam can increase the ratio g/y: if g is independent of the polarization state, y can be decreased in some materials by the use of a circular polarization instead of a linear one [ 19 ]. (ii) The geometrical configuration has to maximize the ratio lF/r~. We have obtained the best efficiency ~/=40% in aceton excited in circular polarization, withfl = 5 cm, d = 2 cm, l= 5 cm. The efficiency is the same for f~ = 10 cm, d = 7 cm, l = 5 cm. However, we have observed that the limit El-~= for the stability of the Raman energy (fig. 5 ) is higher for ft = 5 cm than for f~ = 10 cm. This fact can be interpreted as follows: the size of the laser beam on the entrance window W, is larger forf~ = 5 cm than forf~ = 10 cm. Therefore several lateral filaments are created (fig. 4), for f~ = 5 cm. These filaments remain too short to pro-
Fig. 6. Spectrum of the SBRS obtained in aceton with ft = 10 cm, l = 5 cm, d = 7 cm, (a) E L = 2 × 10-s J, (b) E L ~ - - E L c = 3 X 10-5 J, (c) 7X 104J.
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reached by the spectral line indicates that the R a m a n filament has a short duration, in the range o f a few picoseconds. F o r E L > ELC, the spectrum structure shows a large n u m b e r o f lines (fig. 6c). W h e n EL is increased up to E L = E L. . . . the n u m b e r o f spectral striations a n d the total R a m a n spectral width grow simultaneously. A typical example is given in fig. 6c. It is possible to deduce i n f o r m a t i o n on the temporal structure o f the signal from the frequency spectrum: the F o u r i e r transform o f this spectrum is the autocorrelation function o f the t e m p o r a l intensity I(t). In fig. 6c, the spectrum is roughly described by a c o m b l i m i t e d to p - 10 lines o f width w = i. 5 c m - 1, separated by a p e r i o d J = 2 . 4 cm -~. T h e F o u r i e r transform o f this signal displays t e m p o r a l pulses sepa r a t e d by a delay 1 / p J c = 1.4 ps, inside an envelope whose total d u r a t i o n is 1/wc~-22 ps. Thus, for E L > E L c , the R a m a n signal is m a d e o f several short pulses having a d u r a t i o n on the order o f one picosecond.
6. Conclusion In spite o f a small a m p l i f i c a t i o n length, SBRS excited by picosecond pulses can present interesting energy conversions, particularly in materials displaying large R a m a n gain a n d small K e r r constants. The efficiency ~/= 40% is o b t a i n e d in aceton, where the picosecond b e a m is focused b y a lens with a short focal length ( 5 t o 10 c m ) . A constant efficiency is kept on a wide range o f exciting laser energy, from a m i n i m u m value EL--~ELC corresponding to the beginning o f the self-focusing to a m a x i m u m value E L = E L m ~ corresponding to the c o m p e t i t i o n o f the f o r w a r d R a m a n a m p l i f i c a t i o n with the b a c k w a r d one. In aceton, we have o b t a i n e d ~/=40% in the total range [ E L c = 3 × 1 0 -5 J, Emax = 10 -3 J ] . F o r EL=ELc, the transverse spatial structure o f the S B R S i s m-~o-6-0T~-~i-n~--~i~iillr area. T h e R a m a n spectrum is thin. This corresponds to a scattering d u r a t i o n which is about equal to the laser pulse du-
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ration. F o r EL--~EL m a x , the total size o f the scattering area is equal to the size o f the laser beam. The spatial structure o f the SBRS is fairly non-homogeneous. The t e m p o r a l profile shows sub-structures with d u r a t i o n s o f a p p r o x i m a t e l y 1 ps. In spite o f the complex spatial a n d t e m p o r a l structures o f the SBRS when E L > ELC, we have o b t a i n e d positive results for image reconstruction: the image o f a three-dimensional object placed in the laser b e a m is transferred on the R a m a n b e a m .
References [ 1] J.O. White, J. Opt. Soc. Am. B 7 (1990) 785. [2]B.Ya Zeldovich, N.F. Pilipetski and V.V. Shkunov, Principles of phase conjugation, Springer Series in Optical Sciences, Vol. 42 (Springer Verlaf. 1985). [ 3 ] D.M. Pepper, Laser handbook, Vol. 4, eds. M.L. Stitch and M. Bass (North Holland, Amsterdam, 1985). [4] C. Rivoire and A. Sokolovsaia, Optics Comm. 42 (1982) 138. [ 5 ] A. Sokolovskaia,G.L. Brekhovskikh and A.D. Kudriavtseva, IEEE J. Quant. Elec. QE23 (1987) 1332. [ 6 ] J.L. Ferrier, Z. Wu, J. Gazengel, N.P. Xuan and G. Rivoire, Optics Comm. 41 (1982) 135. [ 7 ] J.P. Lecoq and J.L. Ferrier, Mesures 6 ( 1988 ) 82. [ 8 ] C. Froeihy, B. Colombean and M. Vampouille, Progress in Optics, Vol. XX, ed. E. Wolf (North Holland, Amsterdam, 1983) p. 63. [9] W. Kaiser and M. Maier, Laser Handbook, Vol. 1, eds. Arecchi and Schluz-Dubois (North Holland, Amsterdam, 1972) p. 1078. [10]J. Gazengel, N.P. Xuan and G. Rivoire, Optica Acta 26 (1979) 1245. [ 11 ] N.P. Xuan, J.L. Ferrier, J. Gazengel and G. Rivoire, Optics Comm. 51 (1984) 433. [ 12] J.L. Ferrier, J. Gazengel, N.P. Xuan and G. Rivoire, Optics Comm. 51 (1984) 285. [ 13] G.S. He and P.N. Prasad, Optics Comm. 73 (1989) 161. [ 14 ] P.L. Kelley, Phys. Rev. Lett. 15 (1965) 1005. [ 15] J.H. Marburger, Prof. Quant. Elec. 4 (1975) 35. [ 16] S. Maneuf, Thesis, Limoges, 7 July 1988. [ 17 ] H. Maillotte, Thesis, Besanqon, 8 June 1990. [ 18 ] J. Gazengel and G. Rivoire, Optica Acta 26 (1979) 483. [ 19 ] G. Rivoire, C. Desblancs, J.L. Ferrier, J. Gazengel and N.P. ......Xuan, Op~c~! ~ d Qu~anLE!~. ~1~ 983)_209............................. [20] P.L. Baldeck, P.P. Ho and R.R. Alfano, Revue Phys. 22 (1987) 1677. [21 ] Y.R. Shen, Prof. Quant. Elec. 4 ( 1975 ) 25.
OPTICS COMMUNICATIONS
1 April 1991
Stimulated backward Raman scattering excited in the picosecond range: high efficiency conversions R. Chevalier, A. Sokolovskaia 1, N. Tcherniega ~ and G. Rivoire Laboratory Properties Optiques des Materiaux et Applications, Unit# Associ#e CNRS D0780, 4 Boulevard Lavoisier BP 2018, 49016 Angers Cedex, France Received 16 July 1990; revised manuscript received 13 December 1990
Stimulated backward Raman scattering (SBRS) excited by picosecond laser pulses is produced with high efficiency conversion in materials displaying large Raman gain and small Kerr constants. A constant energy efficiency of 40% is obtained in aceton for a wide range of the exciting laser energy. The spatial, spectral and temporal structure of the backscattering beam is studied.
1. Introduction Stimulated scattering excited by laser beams has a wide range of applications: production of light generators at new wavelengths [ 1 ], phase conjugation [2,3 ] and image reconstruction [4,5 ]. Studies on stimulated scattering have more concerned the nanosecond than the picosecond range of excitation. For instance, the experimental conditions leading to a high efficiency of stimulated backward Brillouin scattering (SBBS), and to a good quality of its phase conjugation properties have been ascertained. In the picosecond range, SBBS is not produced because of its long relaxation time: only Raman and Rayleigh wing scattering can be amplified. We" have shown that these scatterings used in their backward direction - stimulated backward Raman scattering (SBRS) and stimulated backward Rayleigh wing scattering (SBWRS) - excited by 25 ps laser pulses can be used for image reconstruction [ 6 ]. However, the efficiencies obtained in our first experiments were low, on the order of 10 -2. In order to realise applications, larger efficiencies are necessary and the knowledge of the spatial, temporal and energetic properties of the backscattering is required. In this article, we present the results concerning SBRS excited by picosecond pulses in different maOn study leave from Lebedev Institute of Moscow, USSR.
terials, with various geometrical exciting configurations. We give the conditions necessary for obtaining high efficiency and stability simultaneously.
2. Experimental conditions SBRS is excited by a modelocked Nd:YAG laser, delivering single pulses of a duration zv=25 ps at 2 = 532 nm. The laser presents temporal and spatial gaussian structures. The set up is shown in fig. I. The laser beam is focused either inside or outside the Raman active medium by lens L~ (focusing length f~ ). The distance d B..~.
B. ~'.
B.5.
L1
B.S.
B.$.
beam--I cGmero Spe¢rrogroph
Fig. I. Set up used for the study of SBRS. L~, L2, L3: lenses, BS: beamsplitters, Pht, Ph2: calibrated photodiodes or Joulemeters.
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d between lens Lt and the entrance window of the Raman material, as well as the radius ¢~ of the laser beam on L~, significantly influence the backscattering. The input and backscattered energies are controlled by calibrated photodiodes associated with neutral optical filters. The spatial structures of the transmitted and backscattered beams are registered simultaneously by a numerical camera, linked to a computer. They are displayed on the computer screen with a magnification 20. The image of the Raman medium output window Wo is made on the camera by lens L2, with a magnification 10. The backscattered Raman beam structure, recorded at the distance D from lens L1, can be directly compared with the structure of the exciting beam. The image of the entrance window We is produced by the backscattered beam, using lens L3, o n the slit of an Ebert Fastie spectrograph, with a magnification 10. The temporal impulse response of this spectrograph is 130 ps, larger than Tp: this allows the resolution of the temporal details of the Raman spectrum, and enables the user to determine the duration of the backscattering [ 8 ]. The backscattered beam is amplified in the Raman medium only on a length of the order of lp = W p - 5 mm, where v is the light phase velocity in this medium [ 6 ]. We thus use short lengths l for the Raman medium. In order to have a strong Raman amplification with these small values of 1, large Raman gain g and high values of the laser intensity IL are required, according to the formula IR= IRo exp (glL l), where I~ is the Raman intensity. Most of the materials displaying large Raman gain also have large nonlinear refractive index changes AnNL=7IL. A strong Raman conversion will thus often be associated with the self-focusing of the laser and scattered beams. In most of the experiments described below, more than 90% of the backscattered energy is concentrated in the first Stokes line, characterized by a frequency OgR= 09L--09V, where are and - o ~ are respectively the laser and molecular vibration frequencies. The Raman active liquids studied are excited in a steady state situation: their dephasing time 7"2 w h i c h describes the damping of the molecular vibration - is much smaller than Zp [ 10 ]. For instance, in aceton, T2=0.34 ps. 118
1 April 1991
The results obtained are presented in three sections: - Spatial structures of the backscattered beams. - Energies and efficiencies. - Temporal structures.
3. S p a t i a l structures of t h e b a e k s c a t t e r e d b e a m s
In order to produce a high value of the laser intensity in the Raman medium, it is necessary to obtain a small beam waist radius r~ =2f~/nCh~ after the focusing of the laser beam by L~. The observations described below show that in materials with a large value of y it is interesting to achieve rE-----rf, where rf is the radius of the filaments built by self focusing. In these conditions, for all the geometrical configurations (focusing inside or outside the cell with different values off~ and d), the same evolution of the spatial structure of the backscattered beam is observed with increasing laser energy EL. This is illustrated in fig. 2: for small values of EL, a diffuse structure (fig. 2a) is observed, becoming more and more intense and symmetrical, progressively acquiring the shape of a circular diffraction pattern, which is centered on the axis of the system (fig. 2b). For a critical value of the laser energy E L = E L o the image breaks up in several spots having the same size (fig.
Fig. 2. Spatial structure o f SBRS in aceton with the conditions: f l = 10cm, l = 5 cm, d = 7 cm, rL=80 ttm. (a) E L f 2 × 10-s J, (b) EL=ELC=3 X 10 - s J, (c) ELffi4X 10 .5 J, (d) EL----4X 10 -4 J.
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Table 1 Characteristics of different Raman active materials and values of the measured critical energy. Raman material
Aceton Cyclohexane Carbon tetrachioride Benzene
Raman frequency shift toy (cm -I )
Rarnan gain g [9,10] ( 10 tl m / W )
Constant 7 [ 11 ] ( 10 - i s m 2 / W )
Ratio g/7
2921 2850 460
1 1 0.85
0.059 0.053 0.050
16.9 18.9 17
3×10 -~ 4×10 -5 3×10 -5
3
0.29
10
10-5
990, 3064
2c). For large values o f EL, the individual spots become more numerous and they overlap, producing a large and fairly non-homogeneous image (fig. 2d). Steps 2b and 2c are related to the existence o f a nonlinearity AnNL in the refractive index, and to the correlated self-focusing phenomenon. Several features prove this conclusion: - T h e same kind o f shapes are obtained in cyclohexane, chloroform, carbon tetrachloride and benzene, but with different values o f ELc (table 1 ). In calcite, where y-~0, steps 2b and 2c do not exist: the spatial structure o f SBRS, diffuse when EL is small, breaks up at high laser energies into several irregular areas. Large values o f the constant y (table 1 ) are thus connected with the presence o f circular spots. We note here that we have not used carbon disulphide: in spite o f a high R a m a n gain and a high Kerr constant, the amplification o f SBRS is limited by the presence o f a strong Rayleigh wing scattering [12,13]. - The break up o f the scattered beam into several spots is connected with the same phenomenon on the exciting beam, as illustrated in fig. 3. The radius OR o f the R a m a n spots measured on the camera is quasi independent o f the distance D between the camera and the lens LI. This observation can be understood as resulting from a scattering created near the focus o f L~, on a radius rg connected to ~R by the relation: -
20R =f~A/2rR.
Measured value of ELC (J)
Fig. 3. Spatial structures of SBRS (a) and transmitted laser light (b) obtained in aceton, with ft=10 cm, l=5 cm, d=7 cm, EL= 1.2X 10-4 J.
~tm. The size o f the laser filaments measured in the same experimental conditions (on fig. 3) is r f = 5 0 ~tm. Therefore, we can deduce from these measurements that the backward R a m a n light is generated in the laser filaments. To our knowledge, it is the first time that the evolution o f a self-focusing structure is observed in SBRS. The creation o f a first stable filament in the central part o f the laser beam (fig. 2b) is connected with the small size o f the laser beam waist. When the laser energy is increased, lateral scatterings filaments (seen on fig. 2c) can develop (fig. 4).
( 1)
From the measurements o f ~ , we can deduce rR using formula ( 1 ). U n d e r the experimental conditions of fig. 2, we measure 0R=0.25 mm; this yields rg--- 50
Fig. 4. Scheme describing the creation of the self focusing filaments in the Raman active medium. 119
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4. Energies and efficiencies The curve representing the total backscattered energy ER versus the laser energy EL has the same shape in all the geometric configurations, and for all the Kerr active materials studied. This behaviour is illustrated in fig. 5, still given for the same experimental conditions (aceton, 1= 5 cm, f~ = 10 cm, L = 7 cm): for EL < ELC, ER grows exponentially. Then, for ELc
og~" R o.u.
0 0
/.
P
5,
o
O
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When the laser power reaches a critical value PLC, the propagation becomes unstable, leading to the formation of filaments [ 14-17 ]. If the material length l is larger than the Fresnel length IF of the beam, the value of PLC is
P° c =2 2/8no7 .
(2)
In our experiments, we generally have l< IF, hence
& c -~P°c lF/l. The corresponding critical energy is
ELc=P~_c ( lv/l) rp.
(3)
The numerical calculations lead to P ° z p = 10 -5 J for aceton, and to ELC--4× 10 -5 J for the geometrical situation described in figure captions, 2, 3 and 5. This value is in agreement with the measurements (table I ). We notice that ELC is inversely proportional to y: this is the reason why, with the small values of l imposed by the picosecond excitation, the backward Raman threshold is not reached in liquids displaying a large Raman gain, as well as a large Kerr constant. This is the case for nitrobenzene. In the filaments, the laser intensity IL has a maximum value:
o
0
O
o
o
/o
0
(4)
In the amplification formula,
0
o
ELC /~2 IF 1 ILmax-- TpTtrf2 -- 8no) ~ l rtr 2 "
O0
IR = IRo exp (glL IR) ,
(5)
00
where IR is the length of the material active in SBRS, the maximum value of the gain G=glL is
g2 21v 1 Gm~=gIL~x= 8no~ 1 ttr 2"
r/ (
Gm,~ depends on the Raman material, and is roughly proportional to g/y (if the variations of the filament radius rf with the material are neglected [ 18 ] ). In aceton, for the experimental conditions described in fig. 2,
I. IOggLC"
to~lELMAX
I L ~ = 15 G W / c m 2 and Gm~,lp = 10.5. log
EL
Fig. 5. Raman energy E• versus laser energy EL, obtained in aceton, with f t = 1 0 cm, / = 5 cm, d = 7 cm, ELC=3×10 -s J, ELm~= 10 -3 J-
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(6)
In one filament the Raman energy is 1 1 2 ER=IRZRTrrf =lRoexp(glLm~lg) rRnr~ ,
(7)
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where ZR is the Raman pulse duration. In N filaments, if ZR and IR are presumed to be the same in all the filaments (this hypothesis will be discussed later), the total energy is
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duce a strong amplification of the forward Raman wave, and thus there is less competition with the backward Raman amplification.
E R ,~ N E ff I .
5. S p e c t r a l a n d t e m p o r a l s t r u c t u r e s
The number N is the related to the laser energy by EL "" NEI-c ,
and the scattered energy is thus ER = ( E L / ELc ) E L .
(8)
Formula (8) shows a linear relation between the backscattered and laser energies, in agreement with the experimental curves (fig. 5). From (8), (4) and (7), the energy efficiency r/of the SBRS process is obtained ER
EL
--
r / = El- -- E L f
-
IR0 exp(GmaxlR) ZR IL max Tp
The evolution of the Raman spectrum with the laser energy EL, and therefore with the Raman spatial structure, is illustrated in fig. 6. For EL << ELc, when the spatial SBRS structure is diffuse, the spectrum contains only one line (fig. 6a). Its width is the same as that of the laser line (1.5 c m - l ) , indicating that the Raman and laser pulses have the same duration % = 2 5 ps. Then, for EL -----ELc, in the spatial location where the first filament is built, this line becomes larger, and a structure begins to appear (fig. 6b). The width
(9)
When IR et ZR have their maximum values lp and % (9) yields t/m~x=IR0 exp ( glm~x lR ) .
(10)
lLmax
From formula (10) we deduce the conditions leading to the best efficiency: (i) The material is chosen in order to obtain a maximum value of g/y: aceton, cyclohexane, carbon tetrachloride are among the best materials (table 1 ). A convenient polarization of the laser beam can increase the ratio g/y: if g is independent of the polarization state, y can be decreased in some materials by the use of a circular polarization instead of a linear one [ 19 ]. (ii) The geometrical configuration has to maximize the ratio lF/r~. We have obtained the best efficiency ~/=40% in aceton excited in circular polarization, withfl = 5 cm, d = 2 cm, l= 5 cm. The efficiency is the same for f~ = 10 cm, d = 7 cm, l = 5 cm. However, we have observed that the limit El-~= for the stability of the Raman energy (fig. 5 ) is higher for ft = 5 cm than for f~ = 10 cm. This fact can be interpreted as follows: the size of the laser beam on the entrance window W, is larger forf~ = 5 cm than forf~ = 10 cm. Therefore several lateral filaments are created (fig. 4), for f~ = 5 cm. These filaments remain too short to pro-
Fig. 6. Spectrum of the SBRS obtained in aceton with ft = 10 cm, l = 5 cm, d = 7 cm, (a) E L = 2 × 10-s J, (b) E L ~ - - E L c = 3 X 10-5 J, (c) 7X 104J.
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reached by the spectral line indicates that the R a m a n filament has a short duration, in the range o f a few picoseconds. F o r E L > ELC, the spectrum structure shows a large n u m b e r o f lines (fig. 6c). W h e n EL is increased up to E L = E L. . . . the n u m b e r o f spectral striations a n d the total R a m a n spectral width grow simultaneously. A typical example is given in fig. 6c. It is possible to deduce i n f o r m a t i o n on the temporal structure o f the signal from the frequency spectrum: the F o u r i e r transform o f this spectrum is the autocorrelation function o f the t e m p o r a l intensity I(t). In fig. 6c, the spectrum is roughly described by a c o m b l i m i t e d to p - 10 lines o f width w = i. 5 c m - 1, separated by a p e r i o d J = 2 . 4 cm -~. T h e F o u r i e r transform o f this signal displays t e m p o r a l pulses sepa r a t e d by a delay 1 / p J c = 1.4 ps, inside an envelope whose total d u r a t i o n is 1/wc~-22 ps. Thus, for E L > E L c , the R a m a n signal is m a d e o f several short pulses having a d u r a t i o n on the order o f one picosecond.
6. Conclusion In spite o f a small a m p l i f i c a t i o n length, SBRS excited by picosecond pulses can present interesting energy conversions, particularly in materials displaying large R a m a n gain a n d small K e r r constants. The efficiency ~/= 40% is o b t a i n e d in aceton, where the picosecond b e a m is focused b y a lens with a short focal length ( 5 t o 10 c m ) . A constant efficiency is kept on a wide range o f exciting laser energy, from a m i n i m u m value EL--~ELC corresponding to the beginning o f the self-focusing to a m a x i m u m value E L = E L m ~ corresponding to the c o m p e t i t i o n o f the f o r w a r d R a m a n a m p l i f i c a t i o n with the b a c k w a r d one. In aceton, we have o b t a i n e d ~/=40% in the total range [ E L c = 3 × 1 0 -5 J, Emax = 10 -3 J ] . F o r EL=ELc, the transverse spatial structure o f the S B R S i s m-~o-6-0T~-~i-n~--~i~iillr area. T h e R a m a n spectrum is thin. This corresponds to a scattering d u r a t i o n which is about equal to the laser pulse du-
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ration. F o r EL--~EL m a x , the total size o f the scattering area is equal to the size o f the laser beam. The spatial structure o f the SBRS is fairly non-homogeneous. The t e m p o r a l profile shows sub-structures with d u r a t i o n s o f a p p r o x i m a t e l y 1 ps. In spite o f the complex spatial a n d t e m p o r a l structures o f the SBRS when E L > ELC, we have o b t a i n e d positive results for image reconstruction: the image o f a three-dimensional object placed in the laser b e a m is transferred on the R a m a n b e a m .
References [ 1] J.O. White, J. Opt. Soc. Am. B 7 (1990) 785. [2]B.Ya Zeldovich, N.F. Pilipetski and V.V. Shkunov, Principles of phase conjugation, Springer Series in Optical Sciences, Vol. 42 (Springer Verlaf. 1985). [ 3 ] D.M. Pepper, Laser handbook, Vol. 4, eds. M.L. Stitch and M. Bass (North Holland, Amsterdam, 1985). [4] C. Rivoire and A. Sokolovsaia, Optics Comm. 42 (1982) 138. [ 5 ] A. Sokolovskaia,G.L. Brekhovskikh and A.D. Kudriavtseva, IEEE J. Quant. Elec. QE23 (1987) 1332. [ 6 ] J.L. Ferrier, Z. Wu, J. Gazengel, N.P. Xuan and G. Rivoire, Optics Comm. 41 (1982) 135. [ 7 ] J.P. Lecoq and J.L. Ferrier, Mesures 6 ( 1988 ) 82. [ 8 ] C. Froeihy, B. Colombean and M. Vampouille, Progress in Optics, Vol. XX, ed. E. Wolf (North Holland, Amsterdam, 1983) p. 63. [9] W. Kaiser and M. Maier, Laser Handbook, Vol. 1, eds. Arecchi and Schluz-Dubois (North Holland, Amsterdam, 1972) p. 1078. [10]J. Gazengel, N.P. Xuan and G. Rivoire, Optica Acta 26 (1979) 1245. [ 11 ] N.P. Xuan, J.L. Ferrier, J. Gazengel and G. Rivoire, Optics Comm. 51 (1984) 433. [ 12] J.L. Ferrier, J. Gazengel, N.P. Xuan and G. Rivoire, Optics Comm. 51 (1984) 285. [ 13] G.S. He and P.N. Prasad, Optics Comm. 73 (1989) 161. [ 14 ] P.L. Kelley, Phys. Rev. Lett. 15 (1965) 1005. [ 15] J.H. Marburger, Prof. Quant. Elec. 4 (1975) 35. [ 16] S. Maneuf, Thesis, Limoges, 7 July 1988. [ 17 ] H. Maillotte, Thesis, Besanqon, 8 June 1990. [ 18 ] J. Gazengel and G. Rivoire, Optica Acta 26 (1979) 483. [ 19 ] G. Rivoire, C. Desblancs, J.L. Ferrier, J. Gazengel and N.P. ......Xuan, Op~c~! ~ d Qu~anLE!~. ~1~ 983)_209............................. [20] P.L. Baldeck, P.P. Ho and R.R. Alfano, Revue Phys. 22 (1987) 1677. [21 ] Y.R. Shen, Prof. Quant. Elec. 4 ( 1975 ) 25.