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Four wave mixing in the picosecond range: Intensities, durations, wave front reconstruction
Volume 41, number 3
OPTICS COMMUNICATIONS
1 April 1982
FOUR WAVE MIXING IN THE PICOSECOND RANGE: INTENSITIES, DURATIONS, WAVE FRONT RECONSTRUCTION J.L. FERRIER, Z. WU *, X. NGUYEN PHU and G. RIVOIRE Fluid Optics Laboratory, University of Angers, France Received 10 July 1981 Revised manuscript received 12 November 1981 Degenerate four wave mixing is produced by the single pulse of a mode locked laser (duration 25 ps). The intensities are measured. The feasibility of image reconstruction is proved, and methods for time measurements (pulse durations, relaxation times) are proposed.
1. Introduction
2. Experimental set up and measurement methods
Phase conjugation by four wave mixing has been proposed by Hellwarth [ 1], theoretically studied and produced in nanosecond excitation by Yariv [2,3]. For the degenerate situation, three waves at the same frequency co are mixed in a medium characterized by a non linear susceptibility tensor X3 . Two intense wave A 1 and A 2 travel in opposite directions (wave vectors k 1 = - k 2 ) and a probe wave a 3 (wave vector k3) meet the intense waves in the medium. A fourth wave a 4 is produced in the direction k 4 = ~ 3 (fig. 1). In the picosecond range, phase conjugate reflection was demonstrated when produced by saturable absorbers [4] and by scattering [5]. Optical wavefront conjugation by four wave mixing in CS 2 was used by Bloom et al. [6] to produce sub-picosecond gating in an experiment where the exciting pulse duration was 0.5 ps and the length L = 50/am. To our knowledge, no quantitative study of wave front reconstruction by four wave mixing in the picosecond range has been published. We present a study of four wave mixing produced by the single pulse o f a mode locked laser (duration 25 ps). We propose methods to measure relaxation times by four wave mixing and demonstrate the feasibility of image reconstruction.
The experimental set up is shown in fig. 1. As light source, we use the second harmonic generation of a YAG laser: this laser delivers a pulse of 25 ps duration at 5320 A, with a typical power of 2 GW/cm 2, linearly polarized. A quarter wave plate gives a circular polarization in order to obtain the same energy on both outputs o f the prism P. By calibrated Wratten filters F1, 2 and F3, the thickness of which (0.1 mm) is small enough to minimize optical path changes, we can vary energy on beams 1,2 and 3. The arrival times of the three beams in the cell C are controlled by VL1, VL2, VL 3 which are water cells or glass plates. The cell C, currently used in our experiments, is only 1 cm long because the maximum interaction duration between the three beams is limited by the duration of the pulse (25 ps). Several liquids will be studied: CS2, C 6 H6, C 6 H 5 NO2, Rh6G etc. M 1, M2, M3 are totally reflective mirrors; to eliminate parasitic interference fringes, every beam splitter used in our set up is thick. The energies of the exciting laser and of the beams 2, 3 and 4 are measured by detectors Enc , En2 , En3 , En4 constituted of a photoelectric cell associated with an integrating filter [7]. In order to minimize the effect o f spatial fluctuations of the laser, a lens is disposed in front of every detector. The energy E i of the ith beam is connected to the amplitude A i of the electric field by the relation:
* On study leave from the Wu Han Institute of Building Materials, People Republic of China. 0 030-4018/82/0000--0000/$ 02.75 O 1982 North-Holland
Ei = pA27"iSi,
207
Volume 41, number 3
OPTICS COMMUNICATIONS
1 April 1982
N~ 44 Co,,,ero
"\"
",/ / I Z ~
/
I/+
/
- _ #
I
VL 5 ~
t
0 v
IZL.I
Eric
Jt
r3
J i i
I
1
Y.
//
~L.2
£'.!.
Fig. 1. Phase conjugation by four wave mixing. Experimental set up.
where r i is the duration of the pulse, S i the area of the beam and/a a constant connected with the unit system used in the numerical calculations. To have the best spatial covering for beams 1 and 3 in the cell C, the angle between both beams is chosen to be about 5 degrees. In sect. 5 of this publication we will study the influence of the presence o f an object O on beam 3. With picosecond pulses, there are two major difficul tie s : -- first is how to get interaction of beams 1,2 and 3 in the cell, and stability of the different lengths; - second is how to have a good spatial covering with beams o f about 2 mm diameter. We note that in our experimental set up, because of polarization phenomena, iX31 = gXxxxx, 7 d• - we suppose that molecular reorientation is the principal phenomenon responsible o f four wave mixing.
3. Intensities
3.1. btfluence o f the intensity o f the probe beam a 3
The energy E 3 is varied using the filters F3, while the energies E 1 and E 2 are k e p t constant, under the stimulated Raman threshold. The mininmm value of E 3 is chosen in order to obtain a value o f E 4 just above the noise of the detector, estimated at E4t h 10 _7 J ; i n these conditions E3min = 8 × 10 6 j for E1E 2 = 0.35 X 10 . 3 J (corresponding to a density power ~0.7 GW/cm2). The ratio E3max/E3min ~ 14 is connected with the maximum energy provided by our laser. The results are displayed in fig. 2 where the curves E 4 = f ( E 3 ) are drawn for two different values of E l E 2. These curves demonstrate - with a correlation coefficient 0.9 - the linearity o f the relation E 4 = f ( E 3 ) for ~ kept constant. The slope of the straight line E 4 = f ( E 3 ) i s 0.04 for a pumping energy X / E l f 2 ~ 0 . 4 5 X10 - 3 J. 3.2. Influence o f the intensities o f the exciting beams E 1 and E ,
We measured the energy o f the wave 4 created in CS 2 as a function of the energies of the probe beam 3
and of the intense beams 1 and 2. (We verify first that the beam 4 disappears when one of the three beams 1, 2 and 3 is hidden).
208
The energies E 1 and E 2 are simultaneously varied by the filter F 1 2 (El =E2 = E ) , while E 3 is constant. We choose E 3 ~ 6 × 10 -5 J, and we vary E from the minimum value Emi n = 0.10 X l 0 - 3 j corresponding to the detection threshold for E4, to the maximmn value Ema x = 4 Emi n allowed by the laser. The results are displayed in fig. 3. The nraximum
E4 (.lO-3mj)
x x
/
4--
/ X 3 --
x Sj X
~/x ./" / /.
2 -X X
i
X•
X
X
x "'/i
1 --
x~
te
le
et• I
I
I
I
20
40
60
80
I
I
100
120
E L3 (. 10
-3
mj)
Fig. 2. Energ y of the created beam a 4 versus energy o f the p robe b e a m a 3 for constant energies of the p u m p i n g b e a m s in 1 cm long CS2 cell.
.004--
x
o003--
7
.002--
X
o 0 0 1 --
X
X
X X X X X
X
X X
X X
"¢" 0
I .1
X
X XXX
X
X
X~X X XX
O--
X X
I .2
XX
X
I .3
I .4
mj
Fig. 3. Ratio E4/E 3 versus energy o f the p u m p i n g be a m E 1 = E 2 = E in a 1 cm long CS 2 cell.
V o l u m e 41, n u m b e r 3
OPTICS COMMUNICATIONS
response obtained in our set up is R = E4/E 3 = (A4/ A 3) 2 r4S4/r3S 3 = 0.04 for an input energy E = 0.4 mJ, i.e. a power density 0.80 GW/cm 2 . In the nanosecond range, the efficiency E4/E 3 ~ (.44/.43 )2 obtained [3] is o f the order of 1 for an i n p u t energy E 11 mJ i.e. a power density of the order of 10 MW/ cm 2. Therefore, the efficiency R = E4/E 3 at 25 ps is far smaller than in the n a n o s e c o n d range for the same density power. Transient effects can be responsible o f this result. To our knowledge, n o theoretical work exists describing the calculation A4/A 3 = f ( E ) in the transient situation. Even the m e a s u r e m e n t s of l X31 at 25 ps present some disagreements: for instance, the measurements of rio and Alfano [8] lead to the same values Of Xxxxx in pico and n a n o s e c o n d excitations while our o w n m e a s u r e m e n t s show that the value of Xxyyx at 25 ps is far smaller t h a n the stationary one. F r o m the shape o f the curve (fig. 3) a rapid increase of R can be expected for a rather small increase of E. The comparison b e t w e e n the experimental curve and a f u n c t i o n 3' tan2(crow) shows a possible agreement - w i t h a correlation coefficient 0.87 - i t ' 7 = 2.9 X 10 3 and a = 3.2 X 103 rad/J.
4. Temporal applications The four wave mixing process can be considered as a d y n a m i c holography: the interference o f the waves 1 and 3 creates in the cell an hologram which is " r e c o r d e d " b y X3 [2]. When illuminated b y the wave 2, this hologram diffracts the field a 4. Two conditions are necessary, in the picosecond range, in order to o b t a i n a 4 : - A 1 and a 3 must have in the cell a recovering time 7"h :¢: 0 (fig. 4a). e = or h is varied b y VL 1 and VL 3. - A 2 must read the hologram before the end o f the relaxation of X3. Using VL2, we can vary the delay o f A 2 and find a temporal w i d t h for which a 4 exists. We calculate, for square pulses: r 2 = 2 r c + rp + r h + rr
(1)
where r c = L/u and r r is the relaxation time o f X3.
The four wave mixing method can be used to measure the pulse duration rp, the length rh o f the hologram and the relaxation time rr" Measurement o f the hologram length: Fig. 4a represents a typical i n s t a n t a n e o u s configuration o f the 210
1 A p r i l 1982
(a)
2
L
J
lt3
lt3 al, 2
i
Co)
Fig. 4. Four wave mixing process considered as a dynamic holography: recovering of the three beams mixed in a cell. ///: hologram (due to the interference of 1 and 3). (a): a typical mean situation, (b) : an extreme situation a small hologram read only at the entrance of the cell. pulses 1 , 2 and 3 in the cell. We have neglected the small angle b e t w e e n 1 and 3 to simplify the scheme. If a delay 7 h is added with VL 3 b e t w e e n a 3 and A 1, a 4 disappears. This allows the m e a s u r e m e n t of r h. Measurement o f the pulse duration: Using the configuration described in fig. 4b, where the hologram size is very small and illuminated only by the end o f the pulse 2, if we increase the delay o f A 1 with regard to a3, a 4 disappears when the delay added b e t w e e n A 1 a n d a 3 is rp. Measurement o f the relaxation time: r 2 being measured (see above) and r c calculated, r r can be deduced from (1). We measured, in the experimental conditions previously indicated, r 2 , 7 h and 7-p for a typical position of the cell (L = 1 cm, 2 r c = 108.5 ps) filled with CS 2 We found r 2 = 153 ps, r h = 11 ps and rp = 15 ps. The value r r = 18 ps deduced from (1) is only an indication :~, since first, the errors made are i m p o r t a n t due to three successive time measurements, and moreover formula (1) is valid for square pulses only. The set up described above can be used in b e t t e r c o n d i t i o n s for mediums displaying larger relaxation times, such as high pressure gases. We measured the ratio E4/E 3 as a f u n c t i o n o f the 4 r r in CS 2 e s t i m a t e d b y o t h e r m e t h o d s is 2 ps [11].
Volume 41, number 3
OPTICS COMMUNICATIONS
1 April 1982
F-4/~a 2 arbi~'rary unil'~
E~- . ~ Gw /cm ~
1
o
i/
~
2
3
~
33
66
I0o
135
"~'~ ~ 2 ~s
Fig. 5. Ratio E4/E3 versus delay time z2 of the beam A 2 with regard to A 1 and a 3 (Acre = C72)for two different values of E 1 = E 2 =E. delay o f A 2 w i t h regard to A 1 and a3, for constant values o f E 1 and E 2. The results (fig. 5) first give the value o f 7"2 (see above), but lead to m o r e i n f o r m a t i o n s : w i t h the help o f the curves, we can select the delay o f A 2 in order to have the m a x i m u m efficiency E4/ E 3. We can also observe directly the influence o f the relaxation p h e n o m e n a : the a s y m m e t r y o f the curves is visible even for CS2, in spite o f the small value o f
5. Image reconstruction In the d y n a m i c h o l o g r a p h y processes, the image o f an object illuminated b y the b e a m 3 can be transferred on the b e a m 4. We proved t h a t image r e c o n s t r u c t i o n was possible in the picosecond range b y four wave mixing: with the set up described in fig. 1, we inserted an object
7"4 .
Fig. 6. Images in the beam 4 of a grid inserted in the beam 3. (a) Image obtained in CS2, grid 1 : wire thickness of the grid 0.25 mm, distance between wires 1 mm. (b) Image obtained in CS2, grid 2 : wire thickness 0.18 mm, distance between wires 0.63 mm. (c) linage obtained in C6H s NO2, grid 2, with a deformed part. 211
Volume 41, number 3
OPTICS COMMUNICATIONS
(periodical or not) in the beam 3. Fig. 6 presents the corresponding images on the beam 4. Good images were obtained on the laser frequency in CS 2 and, with more difficulties, in C6H6NO2, C6H 6 and Rhodamine 6 G. In all the experiments, the magnification is 1. Thus we can conclude that degenerate four wave mixing in the picosecond range allows wave front reconstruction. This phenomenon has interesting applications, especially to observe rapid changes in the objects, for instance during the passage of an intense and short light pulse. The authors are grateful to R. Chevalier and J.P. Lecoq for their valuable help during the experiments.
212
1 April 1982
References [1] R.W. Hellwarth, J. Opt. Soc. Amer. 67 (1977) 1. [2] A. Yariv, IEEE J. Quant. Electr. QE-14 (1978) 650. [3] D.M. Pepper, D. I:ekete and A. Yariv, Appl. Phys. Lctt. 33 (1978) 41. [4] J.O. Tocho, W. Sibbett and D.J. Bradley, Optics Comm. 34 (1980) 122. [5 ] A.D. Kudriavtseva, A.I. Sokolovskaia, J. Gazengel, N. Phu Xuan and G. Rivoire, Optics Comm. 26 (1978) 446. [6] D.M. Bloom, C.V. Shank, R.L. Fork and O. Teschke, Springer series in Chemical physics, Vol. 4, Picosecond phenomena (1978) p. 96. [7] J.L. Ferrier, N. Phu Xuan and G. Rivoire, Mesures, regulation, automatismes 1 (1980) 5 3. {8] P.P. tto and S.L. Alfano, Phys. Rev. A 20 (1979) 2170.
OPTICS COMMUNICATIONS
1 April 1982
FOUR WAVE MIXING IN THE PICOSECOND RANGE: INTENSITIES, DURATIONS, WAVE FRONT RECONSTRUCTION J.L. FERRIER, Z. WU *, X. NGUYEN PHU and G. RIVOIRE Fluid Optics Laboratory, University of Angers, France Received 10 July 1981 Revised manuscript received 12 November 1981 Degenerate four wave mixing is produced by the single pulse of a mode locked laser (duration 25 ps). The intensities are measured. The feasibility of image reconstruction is proved, and methods for time measurements (pulse durations, relaxation times) are proposed.
1. Introduction
2. Experimental set up and measurement methods
Phase conjugation by four wave mixing has been proposed by Hellwarth [ 1], theoretically studied and produced in nanosecond excitation by Yariv [2,3]. For the degenerate situation, three waves at the same frequency co are mixed in a medium characterized by a non linear susceptibility tensor X3 . Two intense wave A 1 and A 2 travel in opposite directions (wave vectors k 1 = - k 2 ) and a probe wave a 3 (wave vector k3) meet the intense waves in the medium. A fourth wave a 4 is produced in the direction k 4 = ~ 3 (fig. 1). In the picosecond range, phase conjugate reflection was demonstrated when produced by saturable absorbers [4] and by scattering [5]. Optical wavefront conjugation by four wave mixing in CS 2 was used by Bloom et al. [6] to produce sub-picosecond gating in an experiment where the exciting pulse duration was 0.5 ps and the length L = 50/am. To our knowledge, no quantitative study of wave front reconstruction by four wave mixing in the picosecond range has been published. We present a study of four wave mixing produced by the single pulse o f a mode locked laser (duration 25 ps). We propose methods to measure relaxation times by four wave mixing and demonstrate the feasibility of image reconstruction.
The experimental set up is shown in fig. 1. As light source, we use the second harmonic generation of a YAG laser: this laser delivers a pulse of 25 ps duration at 5320 A, with a typical power of 2 GW/cm 2, linearly polarized. A quarter wave plate gives a circular polarization in order to obtain the same energy on both outputs o f the prism P. By calibrated Wratten filters F1, 2 and F3, the thickness of which (0.1 mm) is small enough to minimize optical path changes, we can vary energy on beams 1,2 and 3. The arrival times of the three beams in the cell C are controlled by VL1, VL2, VL 3 which are water cells or glass plates. The cell C, currently used in our experiments, is only 1 cm long because the maximum interaction duration between the three beams is limited by the duration of the pulse (25 ps). Several liquids will be studied: CS2, C 6 H6, C 6 H 5 NO2, Rh6G etc. M 1, M2, M3 are totally reflective mirrors; to eliminate parasitic interference fringes, every beam splitter used in our set up is thick. The energies of the exciting laser and of the beams 2, 3 and 4 are measured by detectors Enc , En2 , En3 , En4 constituted of a photoelectric cell associated with an integrating filter [7]. In order to minimize the effect o f spatial fluctuations of the laser, a lens is disposed in front of every detector. The energy E i of the ith beam is connected to the amplitude A i of the electric field by the relation:
* On study leave from the Wu Han Institute of Building Materials, People Republic of China. 0 030-4018/82/0000--0000/$ 02.75 O 1982 North-Holland
Ei = pA27"iSi,
207
Volume 41, number 3
OPTICS COMMUNICATIONS
1 April 1982
N~ 44 Co,,,ero
"\"
",/ / I Z ~
/
I/+
/
- _ #
I
VL 5 ~
t
0 v
IZL.I
Eric
Jt
r3
J i i
I
1
Y.
//
~L.2
£'.!.
Fig. 1. Phase conjugation by four wave mixing. Experimental set up.
where r i is the duration of the pulse, S i the area of the beam and/a a constant connected with the unit system used in the numerical calculations. To have the best spatial covering for beams 1 and 3 in the cell C, the angle between both beams is chosen to be about 5 degrees. In sect. 5 of this publication we will study the influence of the presence o f an object O on beam 3. With picosecond pulses, there are two major difficul tie s : -- first is how to get interaction of beams 1,2 and 3 in the cell, and stability of the different lengths; - second is how to have a good spatial covering with beams o f about 2 mm diameter. We note that in our experimental set up, because of polarization phenomena, iX31 = gXxxxx, 7 d• - we suppose that molecular reorientation is the principal phenomenon responsible o f four wave mixing.
3. Intensities
3.1. btfluence o f the intensity o f the probe beam a 3
The energy E 3 is varied using the filters F3, while the energies E 1 and E 2 are k e p t constant, under the stimulated Raman threshold. The mininmm value of E 3 is chosen in order to obtain a value o f E 4 just above the noise of the detector, estimated at E4t h 10 _7 J ; i n these conditions E3min = 8 × 10 6 j for E1E 2 = 0.35 X 10 . 3 J (corresponding to a density power ~0.7 GW/cm2). The ratio E3max/E3min ~ 14 is connected with the maximum energy provided by our laser. The results are displayed in fig. 2 where the curves E 4 = f ( E 3 ) are drawn for two different values of E l E 2. These curves demonstrate - with a correlation coefficient 0.9 - the linearity o f the relation E 4 = f ( E 3 ) for ~ kept constant. The slope of the straight line E 4 = f ( E 3 ) i s 0.04 for a pumping energy X / E l f 2 ~ 0 . 4 5 X10 - 3 J. 3.2. Influence o f the intensities o f the exciting beams E 1 and E ,
We measured the energy o f the wave 4 created in CS 2 as a function of the energies of the probe beam 3
and of the intense beams 1 and 2. (We verify first that the beam 4 disappears when one of the three beams 1, 2 and 3 is hidden).
208
The energies E 1 and E 2 are simultaneously varied by the filter F 1 2 (El =E2 = E ) , while E 3 is constant. We choose E 3 ~ 6 × 10 -5 J, and we vary E from the minimum value Emi n = 0.10 X l 0 - 3 j corresponding to the detection threshold for E4, to the maximmn value Ema x = 4 Emi n allowed by the laser. The results are displayed in fig. 3. The nraximum
E4 (.lO-3mj)
x x
/
4--
/ X 3 --
x Sj X
~/x ./" / /.
2 -X X
i
X•
X
X
x "'/i
1 --
x~
te
le
et• I
I
I
I
20
40
60
80
I
I
100
120
E L3 (. 10
-3
mj)
Fig. 2. Energ y of the created beam a 4 versus energy o f the p robe b e a m a 3 for constant energies of the p u m p i n g b e a m s in 1 cm long CS2 cell.
.004--
x
o003--
7
.002--
X
o 0 0 1 --
X
X
X X X X X
X
X X
X X
"¢" 0
I .1
X
X XXX
X
X
X~X X XX
O--
X X
I .2
XX
X
I .3
I .4
mj
Fig. 3. Ratio E4/E 3 versus energy o f the p u m p i n g be a m E 1 = E 2 = E in a 1 cm long CS 2 cell.
V o l u m e 41, n u m b e r 3
OPTICS COMMUNICATIONS
response obtained in our set up is R = E4/E 3 = (A4/ A 3) 2 r4S4/r3S 3 = 0.04 for an input energy E = 0.4 mJ, i.e. a power density 0.80 GW/cm 2 . In the nanosecond range, the efficiency E4/E 3 ~ (.44/.43 )2 obtained [3] is o f the order of 1 for an i n p u t energy E 11 mJ i.e. a power density of the order of 10 MW/ cm 2. Therefore, the efficiency R = E4/E 3 at 25 ps is far smaller than in the n a n o s e c o n d range for the same density power. Transient effects can be responsible o f this result. To our knowledge, n o theoretical work exists describing the calculation A4/A 3 = f ( E ) in the transient situation. Even the m e a s u r e m e n t s of l X31 at 25 ps present some disagreements: for instance, the measurements of rio and Alfano [8] lead to the same values Of Xxxxx in pico and n a n o s e c o n d excitations while our o w n m e a s u r e m e n t s show that the value of Xxyyx at 25 ps is far smaller t h a n the stationary one. F r o m the shape o f the curve (fig. 3) a rapid increase of R can be expected for a rather small increase of E. The comparison b e t w e e n the experimental curve and a f u n c t i o n 3' tan2(crow) shows a possible agreement - w i t h a correlation coefficient 0.87 - i t ' 7 = 2.9 X 10 3 and a = 3.2 X 103 rad/J.
4. Temporal applications The four wave mixing process can be considered as a d y n a m i c holography: the interference o f the waves 1 and 3 creates in the cell an hologram which is " r e c o r d e d " b y X3 [2]. When illuminated b y the wave 2, this hologram diffracts the field a 4. Two conditions are necessary, in the picosecond range, in order to o b t a i n a 4 : - A 1 and a 3 must have in the cell a recovering time 7"h :¢: 0 (fig. 4a). e = or h is varied b y VL 1 and VL 3. - A 2 must read the hologram before the end o f the relaxation of X3. Using VL2, we can vary the delay o f A 2 and find a temporal w i d t h for which a 4 exists. We calculate, for square pulses: r 2 = 2 r c + rp + r h + rr
(1)
where r c = L/u and r r is the relaxation time o f X3.
The four wave mixing method can be used to measure the pulse duration rp, the length rh o f the hologram and the relaxation time rr" Measurement o f the hologram length: Fig. 4a represents a typical i n s t a n t a n e o u s configuration o f the 210
1 A p r i l 1982
(a)
2
L
J
lt3
lt3 al, 2
i
Co)
Fig. 4. Four wave mixing process considered as a dynamic holography: recovering of the three beams mixed in a cell. ///: hologram (due to the interference of 1 and 3). (a): a typical mean situation, (b) : an extreme situation a small hologram read only at the entrance of the cell. pulses 1 , 2 and 3 in the cell. We have neglected the small angle b e t w e e n 1 and 3 to simplify the scheme. If a delay 7 h is added with VL 3 b e t w e e n a 3 and A 1, a 4 disappears. This allows the m e a s u r e m e n t of r h. Measurement o f the pulse duration: Using the configuration described in fig. 4b, where the hologram size is very small and illuminated only by the end o f the pulse 2, if we increase the delay o f A 1 with regard to a3, a 4 disappears when the delay added b e t w e e n A 1 a n d a 3 is rp. Measurement o f the relaxation time: r 2 being measured (see above) and r c calculated, r r can be deduced from (1). We measured, in the experimental conditions previously indicated, r 2 , 7 h and 7-p for a typical position of the cell (L = 1 cm, 2 r c = 108.5 ps) filled with CS 2 We found r 2 = 153 ps, r h = 11 ps and rp = 15 ps. The value r r = 18 ps deduced from (1) is only an indication :~, since first, the errors made are i m p o r t a n t due to three successive time measurements, and moreover formula (1) is valid for square pulses only. The set up described above can be used in b e t t e r c o n d i t i o n s for mediums displaying larger relaxation times, such as high pressure gases. We measured the ratio E4/E 3 as a f u n c t i o n o f the 4 r r in CS 2 e s t i m a t e d b y o t h e r m e t h o d s is 2 ps [11].
Volume 41, number 3
OPTICS COMMUNICATIONS
1 April 1982
F-4/~a 2 arbi~'rary unil'~
E~- . ~ Gw /cm ~
1
o
i/
~
2
3
~
33
66
I0o
135
"~'~ ~ 2 ~s
Fig. 5. Ratio E4/E3 versus delay time z2 of the beam A 2 with regard to A 1 and a 3 (Acre = C72)for two different values of E 1 = E 2 =E. delay o f A 2 w i t h regard to A 1 and a3, for constant values o f E 1 and E 2. The results (fig. 5) first give the value o f 7"2 (see above), but lead to m o r e i n f o r m a t i o n s : w i t h the help o f the curves, we can select the delay o f A 2 in order to have the m a x i m u m efficiency E4/ E 3. We can also observe directly the influence o f the relaxation p h e n o m e n a : the a s y m m e t r y o f the curves is visible even for CS2, in spite o f the small value o f
5. Image reconstruction In the d y n a m i c h o l o g r a p h y processes, the image o f an object illuminated b y the b e a m 3 can be transferred on the b e a m 4. We proved t h a t image r e c o n s t r u c t i o n was possible in the picosecond range b y four wave mixing: with the set up described in fig. 1, we inserted an object
7"4 .
Fig. 6. Images in the beam 4 of a grid inserted in the beam 3. (a) Image obtained in CS2, grid 1 : wire thickness of the grid 0.25 mm, distance between wires 1 mm. (b) Image obtained in CS2, grid 2 : wire thickness 0.18 mm, distance between wires 0.63 mm. (c) linage obtained in C6H s NO2, grid 2, with a deformed part. 211
Volume 41, number 3
OPTICS COMMUNICATIONS
(periodical or not) in the beam 3. Fig. 6 presents the corresponding images on the beam 4. Good images were obtained on the laser frequency in CS 2 and, with more difficulties, in C6H6NO2, C6H 6 and Rhodamine 6 G. In all the experiments, the magnification is 1. Thus we can conclude that degenerate four wave mixing in the picosecond range allows wave front reconstruction. This phenomenon has interesting applications, especially to observe rapid changes in the objects, for instance during the passage of an intense and short light pulse. The authors are grateful to R. Chevalier and J.P. Lecoq for their valuable help during the experiments.
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1 April 1982
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