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Multiple forward phase conjugation in a photorefractive bismuth silicate crystal
Optics Communications 93 ( 1992) 223-226 North-Holland
OPTICS COMMUNICATIONS
Multiple forward phase conjugation in a photorefractive bismuth silicate crystal J. Takacs, H . C . EUin a n d L. S o l y m a r Holography Group, Department of Engineering Science, University of Oxford, Parks Road, Oxford, UK Received 22 May 1992
The geometrical configuration in which two pump beams and one non coplanar signal beam are incident upon the same side of a bismuth silicate crystal is investigated. It is shown that a strong interaction giving rise to a multiplicity of output beams (three of them phase conjugate) may be obtained when the pump beams are detuned in the opposite directions by the same amount. The phase conjugate images obtained are analysed.
1. Introduction Forward phase-conjugate imaging using a signal beam and a p u m p beam, both incident from the same side o f the nonlinear material (sodium vapour), was first demonstrated by Heer and Griffin [ 1 ] in 1979. The phase conjugate image appeared in a higher order output beam. A different kind of forward phase conjugation with perfect phase matching o f the wave x~ectors was demonstrated by Khyzniak et al. [2 ] by using thermal nonlinearity in absorbing liquids, and the photorefractive effect in LiNbO3. A third method o f forward phase conjugation was reported more recently by Jones et al. [ 3 ] who used three coplanar beams in Bi~2SiO2o. In the present Letter we shall introduce some modification o f the geometry used in ref. [ 2 ] which leads to enhanced interaction and to multiple phase conjugate images.
PM2
P2
Fig. 1. Experimental arrangement. face o f a Bil2SiO2o crystal in the horizontal plane at angles of + 1 ° and - 1 ° to the normal, producing a grating with spacing o f 15 lxm. The signal beam having also vertical polarization is incident on the crystal front surface in the vertical plane. The inclination of this beam to the horizontal (~ in fig. l ) was adjustable between 0 and l °. The crystal used for the
2. Experimental arrangement o
The experimental arrangement shown in fig. 1 is similar to that reported in ref. [ 3 ] but for the signal beam which is now directed out o f the horizontal plane. A laser beam from an argon ion laser (wavelength o f 514.5 n m ) is split into three beams, expanded and spatially filtered. Two o f the beams, both with vertical polarization, are incident upon the 1 l0
PC3 o
o
PC2 P2
0
o
PC1 P1
Q
0
S-I
0
So
o
o
S-~
o
Fig. 2. Schematic diagram of the output beams.
0030-4018/92/$05.00 © 1992 Elsevier Science Publishers B.V. All rights reserved.
223
Volume 93, n u m b e r 3,4
OPTICS COMMUNICATIONS
1 O c t o b e r 1992
o.4E=7 4
c
E =
3
02
=--
KV/cm •
o
.m
.c
-
03
E 0.1
al
1 a. 0.0
0 0.2
04
06
08
12
10
J
10
20
i
30
•
i
i
40
50
•
60
Detuning In Hz
O degrees
Fig. 4. Power in the PC2 phase conjugate b e a m as a function of detuning.
Fig. 3. Intensity of PC2 versus the vertical inclination.
Ill
•
"
B
400pm Fig. 5. R e c o n s t r u c t e d
224
(a)
/400 um
phase conjugate images of part of USAF
(b)
L00/am
1951 r e s o l u t i o n t a r g e t . ( a ) P C 1 , ( b ) P C 2 , ( c ) P C 3 .
(c)
Volume 93, number 3,4
OPTICS COMMUNICATIONS
experiment was grown by Sumitomo and had dimensions of 10 X 10 X 10 m m 3. The two horizontal pump beams Were deflected by two piezo-electric mirrors driven in opposite phase by the same triangular wave of variable frequency producing equal but opposite detuning in their frequencies relative to that of the signal beam. The intensities of the two pump beams both flooding the front of the crystal were kept the same at 5.5 m W / c m 2 each, during the experiment. The size of the circular signal beam was restricted to 2.5 m m in diameter with an intensity of 0.75 m W / c m 2. A dc electric field of 7 k V / c m was applied to the crystal in the 001 direction. The emerging beam pattern was observed on a screen behind the crystal.
1 October 1992
(a)
255
A
1000
2000
B jJm
(b)
255
3. Results Our first measurements were aimed at finding the pattern of output beams. Without detuning the pump beams the interaction was very weak, no extra beams appeared at the output. In the presence of detuning however a quite definite output pattern consisting of a large number of beams could be seen (fig. 2). The mechanism of the interaction is clear. The signal beam and each of the pump beams record a grating which is then read by the pump beams giving rise to the multiplicity of output beams. In order to obtain further information about the beams we made, in the second set of experiments, the signal beam divergent. The corresponding output pattern is shown schematically in fig. 2. Besides the signal beam (denoted by S°) two further higher order beams (denoted by S- t and S + ~) diverged whereas three beams above the crystal (denoted by PC1, PC2 and PC3) were found to be convergent indicating that they represented phase conjugates of the signal beam. In our third set of experiments the signal beam was made plane again and we varied 0, the elevation angle of the signal beam. At each angle we varied the detuning and measured the intensity of the PC2 beam. The maximum intensity obtained at optimum detuning is plotted in fig. 3 as a function of 0. It may be clearly seen that the intensity declines as the angle increases. The conclusion appears to be that there is no advantage associated with the angle 0 = 1 ° where
/ I
I
1000
2000
255
B pm
(c)
I
A
1000
2000
B ~m
Fig. 6. Histograms along the AB line on the reconstructed images. (a) PCI, (b) PC2, (c) PC3.
phase matching occurs, i.e. when the wave vectors of the relevant beams satisfy the equality k l - l - k 2 = k 3 d-kPC2. In fact, the smaller is the angle the larger is the phase conjugate intensity. Of course, 0 cannot be arbitrarily small since the signal and phase conjugate beams need to be separated. In addition, depending on the detuning, a subharmonic may also 225
Volume 93, number 3,4
OPTICS COMMUNICATIONS
!:
1 October 1992
the object the three phase conjugate images m a y be seen in figs. 5a, b and c, respectively. The reconstructed images were analysed on a S U N workstation for 'darkness' along the AB line, shown in fig. 5, where the bars are 400 lam wide. The relative darkness o f the bars on a gray scale o f 255 levels is plotted for all three images in figs. 6a, b and c. It is interesting to note that the m a x i m u m 'grayness' in PC2 and PC3 are quite close to each other whereas the bars in PC 1 are less 'gray'. We recorded also the special i n f o r m a t i o n in the signal b e a m at distance d b e h i n d the crystal. As m a y be seen in fig. 7, the original picture is considerably distorted.
4. Conclusions
~ 7
~!:
We have shown that a signal b e a m and two p u m p b e a m s incident from the same side o f the crystal m a y give rise to multiple phase conjugate images by wave interaction in the photorefractive b i s m u t h silicate crystal p r o v i d e d the p u m p b e a m s are d e t u n e d by the right amount.
Fig. 7. The reconstructed scrambled image in the signal beam. a p p e a r between the p u m p b e a m s [5] which would again interfere with the phase conjugate b e a m unless the elevation angle is high enough. F o r the next set o f experiments we took 0 = 0 . 5 ° . First, we m e a s u r e d the o u t p u t o f the PC2 b e a m as a function o f detuning (see fig. 4) noting that the o p t i m u m detuning is about 22 Hz. Then we put some spatial i n f o r m a t i o n in the signal b e a m by inserting a slide at a distance d = 700 m m in front o f the crystal and detuned the p u m p beams by the same a m o u n t o f 22 Hz again. The phase conjugate images were then displayed on a screen at the same distance d b e h i n d the crystal a n d recorded by a video camera. Using a p o r t i o n o f the U S A F 1951 resolution test target as
226
Acknowledgements The authors wish to thank the Science and Engineering Research Council for support.
References [ 1 ] C.V. Heer and N.G. Griffin, Optics Len. 4 (1979) 239.
[2] A. Khyzniak, V. Kondilenko, Tu. Kuchernov, S. Lesnik, S. Odulov and M.S. Soskin, J, Opt. Soc. Am. A 1 (1984) 169. [ 3 ] D.C. Jones, S.F. Lyuksyutov and L. Solymar, Optics Lett. 15 (1990) 935. [4] S. Mallick, B. Imbert, H. Picollet, J.P. Herriau and J.P. Huignard, J. Appl. Phys. 63 (1988) 5660.
OPTICS COMMUNICATIONS
Multiple forward phase conjugation in a photorefractive bismuth silicate crystal J. Takacs, H . C . EUin a n d L. S o l y m a r Holography Group, Department of Engineering Science, University of Oxford, Parks Road, Oxford, UK Received 22 May 1992
The geometrical configuration in which two pump beams and one non coplanar signal beam are incident upon the same side of a bismuth silicate crystal is investigated. It is shown that a strong interaction giving rise to a multiplicity of output beams (three of them phase conjugate) may be obtained when the pump beams are detuned in the opposite directions by the same amount. The phase conjugate images obtained are analysed.
1. Introduction Forward phase-conjugate imaging using a signal beam and a p u m p beam, both incident from the same side o f the nonlinear material (sodium vapour), was first demonstrated by Heer and Griffin [ 1 ] in 1979. The phase conjugate image appeared in a higher order output beam. A different kind of forward phase conjugation with perfect phase matching o f the wave x~ectors was demonstrated by Khyzniak et al. [2 ] by using thermal nonlinearity in absorbing liquids, and the photorefractive effect in LiNbO3. A third method o f forward phase conjugation was reported more recently by Jones et al. [ 3 ] who used three coplanar beams in Bi~2SiO2o. In the present Letter we shall introduce some modification o f the geometry used in ref. [ 2 ] which leads to enhanced interaction and to multiple phase conjugate images.
PM2
P2
Fig. 1. Experimental arrangement. face o f a Bil2SiO2o crystal in the horizontal plane at angles of + 1 ° and - 1 ° to the normal, producing a grating with spacing o f 15 lxm. The signal beam having also vertical polarization is incident on the crystal front surface in the vertical plane. The inclination of this beam to the horizontal (~ in fig. l ) was adjustable between 0 and l °. The crystal used for the
2. Experimental arrangement o
The experimental arrangement shown in fig. 1 is similar to that reported in ref. [ 3 ] but for the signal beam which is now directed out o f the horizontal plane. A laser beam from an argon ion laser (wavelength o f 514.5 n m ) is split into three beams, expanded and spatially filtered. Two o f the beams, both with vertical polarization, are incident upon the 1 l0
PC3 o
o
PC2 P2
0
o
PC1 P1
Q
0
S-I
0
So
o
o
S-~
o
Fig. 2. Schematic diagram of the output beams.
0030-4018/92/$05.00 © 1992 Elsevier Science Publishers B.V. All rights reserved.
223
Volume 93, n u m b e r 3,4
OPTICS COMMUNICATIONS
1 O c t o b e r 1992
o.4E=7 4
c
E =
3
02
=--
KV/cm •
o
.m
.c
-
03
E 0.1
al
1 a. 0.0
0 0.2
04
06
08
12
10
J
10
20
i
30
•
i
i
40
50
•
60
Detuning In Hz
O degrees
Fig. 4. Power in the PC2 phase conjugate b e a m as a function of detuning.
Fig. 3. Intensity of PC2 versus the vertical inclination.
Ill
•
"
B
400pm Fig. 5. R e c o n s t r u c t e d
224
(a)
/400 um
phase conjugate images of part of USAF
(b)
L00/am
1951 r e s o l u t i o n t a r g e t . ( a ) P C 1 , ( b ) P C 2 , ( c ) P C 3 .
(c)
Volume 93, number 3,4
OPTICS COMMUNICATIONS
experiment was grown by Sumitomo and had dimensions of 10 X 10 X 10 m m 3. The two horizontal pump beams Were deflected by two piezo-electric mirrors driven in opposite phase by the same triangular wave of variable frequency producing equal but opposite detuning in their frequencies relative to that of the signal beam. The intensities of the two pump beams both flooding the front of the crystal were kept the same at 5.5 m W / c m 2 each, during the experiment. The size of the circular signal beam was restricted to 2.5 m m in diameter with an intensity of 0.75 m W / c m 2. A dc electric field of 7 k V / c m was applied to the crystal in the 001 direction. The emerging beam pattern was observed on a screen behind the crystal.
1 October 1992
(a)
255
A
1000
2000
B jJm
(b)
255
3. Results Our first measurements were aimed at finding the pattern of output beams. Without detuning the pump beams the interaction was very weak, no extra beams appeared at the output. In the presence of detuning however a quite definite output pattern consisting of a large number of beams could be seen (fig. 2). The mechanism of the interaction is clear. The signal beam and each of the pump beams record a grating which is then read by the pump beams giving rise to the multiplicity of output beams. In order to obtain further information about the beams we made, in the second set of experiments, the signal beam divergent. The corresponding output pattern is shown schematically in fig. 2. Besides the signal beam (denoted by S°) two further higher order beams (denoted by S- t and S + ~) diverged whereas three beams above the crystal (denoted by PC1, PC2 and PC3) were found to be convergent indicating that they represented phase conjugates of the signal beam. In our third set of experiments the signal beam was made plane again and we varied 0, the elevation angle of the signal beam. At each angle we varied the detuning and measured the intensity of the PC2 beam. The maximum intensity obtained at optimum detuning is plotted in fig. 3 as a function of 0. It may be clearly seen that the intensity declines as the angle increases. The conclusion appears to be that there is no advantage associated with the angle 0 = 1 ° where
/ I
I
1000
2000
255
B pm
(c)
I
A
1000
2000
B ~m
Fig. 6. Histograms along the AB line on the reconstructed images. (a) PCI, (b) PC2, (c) PC3.
phase matching occurs, i.e. when the wave vectors of the relevant beams satisfy the equality k l - l - k 2 = k 3 d-kPC2. In fact, the smaller is the angle the larger is the phase conjugate intensity. Of course, 0 cannot be arbitrarily small since the signal and phase conjugate beams need to be separated. In addition, depending on the detuning, a subharmonic may also 225
Volume 93, number 3,4
OPTICS COMMUNICATIONS
!:
1 October 1992
the object the three phase conjugate images m a y be seen in figs. 5a, b and c, respectively. The reconstructed images were analysed on a S U N workstation for 'darkness' along the AB line, shown in fig. 5, where the bars are 400 lam wide. The relative darkness o f the bars on a gray scale o f 255 levels is plotted for all three images in figs. 6a, b and c. It is interesting to note that the m a x i m u m 'grayness' in PC2 and PC3 are quite close to each other whereas the bars in PC 1 are less 'gray'. We recorded also the special i n f o r m a t i o n in the signal b e a m at distance d b e h i n d the crystal. As m a y be seen in fig. 7, the original picture is considerably distorted.
4. Conclusions
~ 7
~!:
We have shown that a signal b e a m and two p u m p b e a m s incident from the same side o f the crystal m a y give rise to multiple phase conjugate images by wave interaction in the photorefractive b i s m u t h silicate crystal p r o v i d e d the p u m p b e a m s are d e t u n e d by the right amount.
Fig. 7. The reconstructed scrambled image in the signal beam. a p p e a r between the p u m p b e a m s [5] which would again interfere with the phase conjugate b e a m unless the elevation angle is high enough. F o r the next set o f experiments we took 0 = 0 . 5 ° . First, we m e a s u r e d the o u t p u t o f the PC2 b e a m as a function o f detuning (see fig. 4) noting that the o p t i m u m detuning is about 22 Hz. Then we put some spatial i n f o r m a t i o n in the signal b e a m by inserting a slide at a distance d = 700 m m in front o f the crystal and detuned the p u m p beams by the same a m o u n t o f 22 Hz again. The phase conjugate images were then displayed on a screen at the same distance d b e h i n d the crystal a n d recorded by a video camera. Using a p o r t i o n o f the U S A F 1951 resolution test target as
226
Acknowledgements The authors wish to thank the Science and Engineering Research Council for support.
References [ 1 ] C.V. Heer and N.G. Griffin, Optics Len. 4 (1979) 239.
[2] A. Khyzniak, V. Kondilenko, Tu. Kuchernov, S. Lesnik, S. Odulov and M.S. Soskin, J, Opt. Soc. Am. A 1 (1984) 169. [ 3 ] D.C. Jones, S.F. Lyuksyutov and L. Solymar, Optics Lett. 15 (1990) 935. [4] S. Mallick, B. Imbert, H. Picollet, J.P. Herriau and J.P. Huignard, J. Appl. Phys. 63 (1988) 5660.