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−C curve configuration (−C3) photorefractive self-pumped phase conjugator
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EISEVIER
15 March 1996 OPTICS COMMUNICATIONS Optics Communications 124 (1996) 481-487
- C curve configuration ( - C”) photorefractive self-pumped phase conjugator Chi Ching Chang a, David R. Selviah b ” Department of Applied Physics, Chung Cheng Institute of Technology, Tahsi, Taoyuan 33509, Taiwan, ROC h Department of Electronic and Electrical Engineering, University College London, Torrington Place, London WCIE 7JE. UK
Received 19 September1995;accepted2 November 1995
Abstract A novel configuration for a self-pumped phase conjugator has either only one internal loop, or beam path, which curves into one corner or two loops of similar form or two loops of quite different form depending on the exact geometry when the incident beam enters the barium titanate crystal at an acute angle to the C axis. Phase conjugation is demonstrated over a wide range (30 degrees) of incident angles and over a range of 4 mm in lateral position with efficiencies up to 30%. We characterise the dynamic response, compare our configuration with that of the “Cat” and propose a tentative four-interaction region mechanistic model.
-
A variety of arrangements for photorefractive optical phase conjugation (OPC) , by means of four-wave mixing (FWM) , have been proposed and demonstrated in several phase conjugators such as the self-pumped phase conjugator (SPPC) (or “Cat” conjugator) [ 11, several kinds of mutually pumped phase conjugator (MPPC) [2--S], the induced self-pumped phase conjugator (ISPPC) [ 9,101, and the multi-beam induced phase conjugator [ 111. Recently, a 2-D model proposed by Zozulya et al. [ 121 can numerically analyse the propagation of Iight and formation of complex structures of light in photorefractive crystal, Theoretical predictions for certain types of SPPC and MPPC have a nice agreement with experimental results [ 131. The SPPC is distinct from other phase conjugators (such as the externally pumped FWM and the mutually pumped types) in that only one beam enters the crystal which generates its own pump beams from itself to generate the phase conjugate of the beam. The SPPCs have found applications in optical signal and image 0030-4018/96/$12.00 0 1996Elsevier Science B.V. All rights reserved SSDf0030-4018(95)00720-2
processing [ 141, optical pattern recognition [ 15,161, and multimodal self-pumped phase-conjugate resonators [ 171. In the last 13 years four configurations have been discovered for SPPC. The various geometries can be classified according to the number of internal reflections and the direction of the incident beam relative to the c-axis (defined here as pointing along the spontaneous polarization direction) which is the direction into which any beam or beams entering the crystal in any orientation would tend to bend. No internal reflections appear to occur in the “Stimulated Photorefractive Backscattering” [ 1S-201 configuration (the beam is incident at an acute angle to the + C direction of both BaTi03 and BaTiO,:Ce crystals) or in the “Stimulated Photorefractive Backscattering and FWM” [ 211 configuration (the beam is incident at an acute angle to the + C direction of both KTN:Fe and BaTiO,:Co crystals an to the -C direction of KNSBN:Cu crystal), in both of these the phase-conjugate beam is generated by stimulated backward scattering in the volume of the crystal;
482
C.C. Chang, D.R. S&ah/
Optics Communications
Two internal reflections occur in the popular “Cat” [ 1] configuration (the beam is incident at an acute angle to the +C direction of BaTiO, crystal or to the - C direction of an SBN crystal) ; Six internal reflections appeared to occur in a configuration mentioned briefly in Ref. [ 181 (the incident beam traveled at an acute angle to the -C direction of a O”-cut undoped BaTiO, crystal). In this paper we report the discovery of new configurations (the incident beam travels at an acute angle to the -C direction of a O”-cut undoped BaTi03 crystal) for SPPC, in which several distinguishable spatial features of the beam path or loop were observed within the BaTi03 crystal. We also demonstrate phase conjugation in these configurations over a large range of lateral positions and angles of the incident beam. This provides a large effective numerical aperture giving high-resolution imaging which is important for transmission of detailed images within or between slowly vibrating systems or those suffering from dynamic random spatial phase variations. In free space optical communications, for example, the lateral position and incident angle of the arriving beam may vary with time due to convection currents in the intervening air. In the “Cat” configuration shown in schematic form in Fig. la and experimentally in a barium titanate crystal in Fig. 2a, the beam enters a crystal face, a, which lies parallel to the c-axis and, thereupon, begins to diverge or fan out, bending as it does so, into the +C direction. After about 10 seconds (with an incident beam power of 25 mW illuminating an area of -0.2 mm2 on the crystal face and with an incident angle, 0, of 45”) a single loop of light (or closed beam path) is observed to form involving two internal reflections from two orthogonal adjacent faces and at this time the phase-conjugate reflected image is observed. In our configuration the beam is incident (Figs. 1b, 2c) at an angle onto the crystal face normal to the c-axis at its most positive end ( +c face) and travels at an acute angle, 4, to the -C direction. We observed that the incident beam begins almost immediately to fan-out towards one of the opposite corners (Fig. 2b). The angular range of beams within the fan appear to be larger than that in the “Cat”. After 15 seconds (with an incident power of 2.5 mW illuminating an area of - 0.2 mm2 on the crystal face at an incident angle, $, of 45”) one or more loops of light are observed to form depending upon the incident angle and position and at
124 (1996) 481X37
(a>
a
(b)
a
a
Fig. 1. Schematics of a two-interaction region and a four-interaction region models in BaTi03 crystals for (a) the “Cat” and (b) the “ - C3” self-pumped phase conjugator.
this time the phase-conjugate reflection is observed to occur. Since the beam enters close to the - C direction and curves towards one corner we refer to it as the “ -C Curve Configuration (or - C3) ” SPPC. In Fig. lb we show a schematic of what appears to be taking place within the crystal using a mechanism with fourinteraction regions. Our experiment consisted of an argon ion laser with multilongitudinal modes operating at 488 nm in the blue without intracavity etalon giving a coherence length of - 3 cm. We used two crystals of undoped barium titanate with dimensions (a X b X c = 5.16 mmX4.74 mrnX5.00 mm and 5.00 mmX5.00 mm X 5.00 mm) having six polished faces. The laser was extraordinarily polarized and illuminated the entrance face in an ellipse of area -0.2 mm2 and approximate diameter 0.5 mm with a power in the range 25 mW to 150 mW. The beam was focused by a lens
C. C. Chang, D. R. Selviah / Optics Communications
124 (1996) 481487
483
0a
0c Fig. 2. The optical path inside the BaTiO, crystal for (a) the “Cat” during phaseconjugation,(b) and (c) the “ - C”’ SPPC during phase conjugation showing the presence of two loops of light.
to a point about 2 cm outside of the crystal so that the beam diverged into the crystal. This increased the intensity inside the crystal and the angular spread of the incident beam to ensure an even larger angular spread of beams within the fan generated. The gratings formed by the fan can diffract the incident beam into a larger angular range and create multiple interaction regions
the “ -C3” SPPCbefore phase conjugation,
which can provide more effective interaction length for beam coupling. Our lateral alignment and angular tolerance experiments reported later were carried out using an incident beam power of 40 mW. Using a power of 25 mW we measured the dynamic increase in power with time in the phase-conjugate beam, I,,, and the consequent decrease in power of the
484
C.C. Chang, D.R. Selviah /Optics
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Time (see) Fig. 3. Time evolution of the phase conjugate reflectivity in the “ -C”’ SPPC (solid line) and the decay of the transmitted beam power (dashed line) after the incident beam is tamed on.
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Communications
124 (1996) 48Id87
incident beam, Ii,, after transmission through the crystal (Fig. 3) until a steady state response was achieved. The phase-conjugate signal was found to begin to develop 15 seconds after the incident beam began to illuminate the crystal. This phase-conjugate beam then grew over the next 10 seconds, as the loops were observed forming in the crystal, to reach a more stable value. The transmitted beam appeared to decrease very quickly (during the first 3 s) while the beam was developing into a fan within the crystal. The intensity remained constant for about a further 15 s before again decreasing, as the loops formed within the crystal, to reach a lower, more stable level. All experiments were performed at a room temperature of 26.0 k 0.2”C. Figs. 4 and 5 show the dependence of the phaseconjugate reflectivity on the lateral position and angular orientation of the incident beam. Phase-conjugate signals could be observed over a wide range of angles of the incident beam of at least 30 degrees and over a range of about 4 mm in lateral positioning. The maximum phase-conjugate reflectivity in the “ - C Curve Configuration” was observed to be about 30% for z = 2 mm and 4 = 64”. Similar results were obtained using two crystals one grown in the USA and the other in China. We verified that phase conjugation was indeed taking place by placing a resolution target (US Airforce chart) object in the incident beam. In addition a phase distorting plastic screen (which also caused some scattering) was placed between the object and the crystal. Fig. 6a shows the seriously distorted image appearing after the phase distorting screen just before the beam entered the crystal. Fig. 6b shows the very clear phaseconjugate image of the resolution target using our “ - C3” phase-conjugate geometry. For comparison we show in Fig. 6c a similar reconstructed image resulting from the “Cat” phase-conjugate geometry formed in the same crystal. Our - C3 geometry gives a better resolution of 12.7 lp/mm (39 pm) while the Cat gives 7.13 lp/mm (70 pm). We have observed that by slightly altering the angle of incidence and lateral position at which the beam illuminates the first crystal ( + c) face we can induce either one loop of light (such as the central loop in Fig. lb) (when z = 2.2 mm, #J= 5 1”) or more often, two loops of light (as shown in Fig. 1b) (when z = 1.7 mm, + = 5 1” and 60”). When larger changes of angle and lateral position are made we can induce BOTH one loop of the new “ - C Curve Configuration” AND one
C.C. Chang, D.R. Selviah /Optics Communications 124 (1996) 481-487
0a
485
loop of the six internal reflection configuration (mentioned in Ref. [ 181) as shown in Fig. 7a. This appears to be the first time to the authors knowledge that two quite different phase conjugation loops, each of which can exist independently, have been reported to occur at the same time. For the sake of clarity we will refer to the six internal reflection configuration as the “J configuration” as the beam path appears to form a J shape within the crystal. We observed that over a range of angles and positions the J and -C3 phase-conjugate loops coexist (for a range from z = 2.9 mm and 3.3 mm with 4 = 5 1”). It would appear that the conventional two-interaction-region mechanism [ 1,221 would have difficulty in explaining these phenomena and that a more advanced mechanism may be required. We suggest one such mechanism, in which transitions occur instead between four interaction regions. In our experimental configurations (Figs. 2c and 7b) the incident beam initially propagates at an acute angle to the -C direction of the barium titanate crystal. This causes a fan to develop which has constituent beams over a wide range of angles. This gives rise to a large range of gratings, formed as the beams in the fan interact with each other, having a wide range of angles and periodicities. Therefore, there is a high change of mutual scattering occurring from these fanning gratings via the process of simultaneous degenerate four-wave mixing (DFWM) . Unlike the two-interaction-region mechanism exploited in the “cat” configuration, here four interaction regions give rise to the two loops of the “ -C3” configuration (Fig. lb) and both the “ - C3” and “J” coexisting loops configuration (Fig. 7a). In “ -C3” with two stable loops it appears that the outer loop forms between regions I and IV while the inner between regions II and III. When the incident beam enters close to the edge of the crystal (larger z) several of the beams in the fan can be internally reflected from adjacent crystal faces to give rise to the “J” loop with six internal reflections. To obtain phase conjugation we again make recourse to the four-interaction-region mechanism (Fig. 7a). Two stable loops, “ -C3” and “J” (Fig. 7a),canform and coexist as the loops form between regions I and II
Fig. 6. (a) Phase distorted resolution target input to BaTiO, crystal, (b) phase-conjugate reconstructed image using “ - C”’ SPPC, and (c) phase-conjugate reconstructed image using “Cat” SPPC. ~=50°andz=2.5mm.
486
C.C. Gang,
a
D.R. SelviahlOptics
a
Communications
124 (1996) 481487
this remains to be fully confirmed. In conclusion, we have demonstrated a self-pumped phase conjugator using novel configurations: “ - C3’ ’ and “J” configurations and we compare these to the popular “Cat” phase conjugator. A very wide angular and lateral positional acceptance was obtained which will make this more suitable for practical applications requiring free space transmission of high resolution images. We have suggested tentative mechanisms to explain the spatial features of the optical path observed in the BaTiO, crystals. The authors wish to thank the National Science Council, Taiwan, ROC, the Chung Cheng Institute of Technology, Taiwan, ROC, and the University College London, UK for supporting this project.
References [l] [2] [3] [4] [5]
m Fig. 7. Schematic of a four-interaction region model for the SPPC (b) the optical path with both “ - C3” and “.I” configurations, inside the BaTiO? crystal during phase conjugation.
for the “J” and between III and IV regions for the “ - Ca” configuration. It appears that the presence of two loops may improve the efficiency, angular range, lateral range and temporal stability as only the most efficient loops are self sustaining and may erase other gratings preventing other loops being formed although
J. Feinberg, Optics Len. 7 (1982) 486. Weiss, S. Sternklar and B. Fischer, Optics Lett. 12 ( 1987) 114. A.M.C. Smount and R.W. Eason, Optics Lett. 12 (1987) 498. M.D. Ewbank, Optics Lett. 13 (1988) 47. M.D. Ewbank, R.A. Vazquez, R.R. Neurgaonkar and J. Feinberg, J. Opt. Sot. Am. B 7 (1990) 2306. [ 61 D. Wang, Z. Zhang, Y. Zhu, S. Zhang and P. Ye, Optics Comm. 73 (1989) 495. [7] E.J. Sharp, W.W. Clark III, M.J. Miller, G.L. Wood, B.D. Monson, G.J. Salamo and R.R. Neurgaonkar, Appl. Optics 29 (1990) 743. [ 81 C.C. Chang and D.R. Selviah, Optics Lett. 20 ( 1995) 677. [9] H.F. Yau, Y.P. Tong, C.C. Chang and N.C. Wang, Optics Comm. 89 (1992) 457. [lo] Y.S. Riu, T.S. Lu, J. Zhuang and X.C. Gao, Optics Lett. 18 (1993) 143. [ 1 l] D.R. Selviah and C.C. Chang, OSA Photorefractive materials, Effects, and Devices Conference Proc., Kiev, Ukraine (1993) pp. PD6.1-PD6.4. [ 121 A.A. Zozulya, M. Saffman and D.Z. Anderson, Phys. Rev. Lett. 73 (1994) 818; OSA Photorefractive materials, Effects, and Devices Conference, TPC 29 ( 1995) 375. [ 131 A.A. Zozulya, M. Saffman and D.Z. Anderson, J. Opt. Sot. Am. B 12 (1995) 255. [ 141 P. Gtinter and J-P. Huignard, eds., Photorefractive Materials and Their Application (Springer, Berlin, 1988). [ 151 D.Z. Anderson, Optics Lett. 11 (1986) 56. [ 161 Y. Owechko, G.J. Dunning, E. Marom and B.H. Soffer, Appl. Optics 26 (1987) 1900. [ 171 D.R. Selviah and C.C. Chang, Opt. Lasers in Eng. (1995), to be published. [ 181 T.Y. Chang and R.W. Hellwatth, Optics L&t. 10 (1985) 408. [ 191 G.C. Valley, J. Opt. Sot. Am. B 9 (1992) 1440.
C. C. Chang, D.R. Selvialz / Optics Communications
201 Y. Zhu, C. Yang, M. Hui, X. Niu, J. Zhang, T. Zhou and X. Wu, Appl. Phys. Lett. 64 (1994) 2341. 211 Y. Liau, H. Gao, P. Ye, Q. Guan and J. Wang, Appl. Phys. Lett. 63 ( 1993) 1745; Y. Lian, S.X. Dou, H. Dao, Y. Zhu, X. Wu, C. Yang and P. Ye, Optics Lett. 19 (1993) 610;
I24 (1996) 481-487
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Y. Lian, H. Gao, S.X. Dou, H. Wang, P. Ye, Q. Guan and J. Wang, Appl. Phys. B 59 (1994) 655; X. Gao, Sasaki A. and Zheng Y., Jpn. J. Appl. Phys. 33 (1994) 5565. [22] K.R. MacDonald and J. Feinberg, J. Opt. Sot. Am. 73 (1983) 548.
__ BB
EISEVIER
15 March 1996 OPTICS COMMUNICATIONS Optics Communications 124 (1996) 481-487
- C curve configuration ( - C”) photorefractive self-pumped phase conjugator Chi Ching Chang a, David R. Selviah b ” Department of Applied Physics, Chung Cheng Institute of Technology, Tahsi, Taoyuan 33509, Taiwan, ROC h Department of Electronic and Electrical Engineering, University College London, Torrington Place, London WCIE 7JE. UK
Received 19 September1995;accepted2 November 1995
Abstract A novel configuration for a self-pumped phase conjugator has either only one internal loop, or beam path, which curves into one corner or two loops of similar form or two loops of quite different form depending on the exact geometry when the incident beam enters the barium titanate crystal at an acute angle to the C axis. Phase conjugation is demonstrated over a wide range (30 degrees) of incident angles and over a range of 4 mm in lateral position with efficiencies up to 30%. We characterise the dynamic response, compare our configuration with that of the “Cat” and propose a tentative four-interaction region mechanistic model.
-
A variety of arrangements for photorefractive optical phase conjugation (OPC) , by means of four-wave mixing (FWM) , have been proposed and demonstrated in several phase conjugators such as the self-pumped phase conjugator (SPPC) (or “Cat” conjugator) [ 11, several kinds of mutually pumped phase conjugator (MPPC) [2--S], the induced self-pumped phase conjugator (ISPPC) [ 9,101, and the multi-beam induced phase conjugator [ 111. Recently, a 2-D model proposed by Zozulya et al. [ 121 can numerically analyse the propagation of Iight and formation of complex structures of light in photorefractive crystal, Theoretical predictions for certain types of SPPC and MPPC have a nice agreement with experimental results [ 131. The SPPC is distinct from other phase conjugators (such as the externally pumped FWM and the mutually pumped types) in that only one beam enters the crystal which generates its own pump beams from itself to generate the phase conjugate of the beam. The SPPCs have found applications in optical signal and image 0030-4018/96/$12.00 0 1996Elsevier Science B.V. All rights reserved SSDf0030-4018(95)00720-2
processing [ 141, optical pattern recognition [ 15,161, and multimodal self-pumped phase-conjugate resonators [ 171. In the last 13 years four configurations have been discovered for SPPC. The various geometries can be classified according to the number of internal reflections and the direction of the incident beam relative to the c-axis (defined here as pointing along the spontaneous polarization direction) which is the direction into which any beam or beams entering the crystal in any orientation would tend to bend. No internal reflections appear to occur in the “Stimulated Photorefractive Backscattering” [ 1S-201 configuration (the beam is incident at an acute angle to the + C direction of both BaTi03 and BaTiO,:Ce crystals) or in the “Stimulated Photorefractive Backscattering and FWM” [ 211 configuration (the beam is incident at an acute angle to the + C direction of both KTN:Fe and BaTiO,:Co crystals an to the -C direction of KNSBN:Cu crystal), in both of these the phase-conjugate beam is generated by stimulated backward scattering in the volume of the crystal;
482
C.C. Chang, D.R. S&ah/
Optics Communications
Two internal reflections occur in the popular “Cat” [ 1] configuration (the beam is incident at an acute angle to the +C direction of BaTiO, crystal or to the - C direction of an SBN crystal) ; Six internal reflections appeared to occur in a configuration mentioned briefly in Ref. [ 181 (the incident beam traveled at an acute angle to the -C direction of a O”-cut undoped BaTiO, crystal). In this paper we report the discovery of new configurations (the incident beam travels at an acute angle to the -C direction of a O”-cut undoped BaTi03 crystal) for SPPC, in which several distinguishable spatial features of the beam path or loop were observed within the BaTi03 crystal. We also demonstrate phase conjugation in these configurations over a large range of lateral positions and angles of the incident beam. This provides a large effective numerical aperture giving high-resolution imaging which is important for transmission of detailed images within or between slowly vibrating systems or those suffering from dynamic random spatial phase variations. In free space optical communications, for example, the lateral position and incident angle of the arriving beam may vary with time due to convection currents in the intervening air. In the “Cat” configuration shown in schematic form in Fig. la and experimentally in a barium titanate crystal in Fig. 2a, the beam enters a crystal face, a, which lies parallel to the c-axis and, thereupon, begins to diverge or fan out, bending as it does so, into the +C direction. After about 10 seconds (with an incident beam power of 25 mW illuminating an area of -0.2 mm2 on the crystal face and with an incident angle, 0, of 45”) a single loop of light (or closed beam path) is observed to form involving two internal reflections from two orthogonal adjacent faces and at this time the phase-conjugate reflected image is observed. In our configuration the beam is incident (Figs. 1b, 2c) at an angle onto the crystal face normal to the c-axis at its most positive end ( +c face) and travels at an acute angle, 4, to the -C direction. We observed that the incident beam begins almost immediately to fan-out towards one of the opposite corners (Fig. 2b). The angular range of beams within the fan appear to be larger than that in the “Cat”. After 15 seconds (with an incident power of 2.5 mW illuminating an area of - 0.2 mm2 on the crystal face at an incident angle, $, of 45”) one or more loops of light are observed to form depending upon the incident angle and position and at
124 (1996) 481X37
(a>
a
(b)
a
a
Fig. 1. Schematics of a two-interaction region and a four-interaction region models in BaTi03 crystals for (a) the “Cat” and (b) the “ - C3” self-pumped phase conjugator.
this time the phase-conjugate reflection is observed to occur. Since the beam enters close to the - C direction and curves towards one corner we refer to it as the “ -C Curve Configuration (or - C3) ” SPPC. In Fig. lb we show a schematic of what appears to be taking place within the crystal using a mechanism with fourinteraction regions. Our experiment consisted of an argon ion laser with multilongitudinal modes operating at 488 nm in the blue without intracavity etalon giving a coherence length of - 3 cm. We used two crystals of undoped barium titanate with dimensions (a X b X c = 5.16 mmX4.74 mrnX5.00 mm and 5.00 mmX5.00 mm X 5.00 mm) having six polished faces. The laser was extraordinarily polarized and illuminated the entrance face in an ellipse of area -0.2 mm2 and approximate diameter 0.5 mm with a power in the range 25 mW to 150 mW. The beam was focused by a lens
C. C. Chang, D. R. Selviah / Optics Communications
124 (1996) 481487
483
0a
0c Fig. 2. The optical path inside the BaTiO, crystal for (a) the “Cat” during phaseconjugation,(b) and (c) the “ - C”’ SPPC during phase conjugation showing the presence of two loops of light.
to a point about 2 cm outside of the crystal so that the beam diverged into the crystal. This increased the intensity inside the crystal and the angular spread of the incident beam to ensure an even larger angular spread of beams within the fan generated. The gratings formed by the fan can diffract the incident beam into a larger angular range and create multiple interaction regions
the “ -C3” SPPCbefore phase conjugation,
which can provide more effective interaction length for beam coupling. Our lateral alignment and angular tolerance experiments reported later were carried out using an incident beam power of 40 mW. Using a power of 25 mW we measured the dynamic increase in power with time in the phase-conjugate beam, I,,, and the consequent decrease in power of the
484
C.C. Chang, D.R. Selviah /Optics
100
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I,
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,
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30
40
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50
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Time (see) Fig. 3. Time evolution of the phase conjugate reflectivity in the “ -C”’ SPPC (solid line) and the decay of the transmitted beam power (dashed line) after the incident beam is tamed on.
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I
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Communications
124 (1996) 48Id87
incident beam, Ii,, after transmission through the crystal (Fig. 3) until a steady state response was achieved. The phase-conjugate signal was found to begin to develop 15 seconds after the incident beam began to illuminate the crystal. This phase-conjugate beam then grew over the next 10 seconds, as the loops were observed forming in the crystal, to reach a more stable value. The transmitted beam appeared to decrease very quickly (during the first 3 s) while the beam was developing into a fan within the crystal. The intensity remained constant for about a further 15 s before again decreasing, as the loops formed within the crystal, to reach a lower, more stable level. All experiments were performed at a room temperature of 26.0 k 0.2”C. Figs. 4 and 5 show the dependence of the phaseconjugate reflectivity on the lateral position and angular orientation of the incident beam. Phase-conjugate signals could be observed over a wide range of angles of the incident beam of at least 30 degrees and over a range of about 4 mm in lateral positioning. The maximum phase-conjugate reflectivity in the “ - C Curve Configuration” was observed to be about 30% for z = 2 mm and 4 = 64”. Similar results were obtained using two crystals one grown in the USA and the other in China. We verified that phase conjugation was indeed taking place by placing a resolution target (US Airforce chart) object in the incident beam. In addition a phase distorting plastic screen (which also caused some scattering) was placed between the object and the crystal. Fig. 6a shows the seriously distorted image appearing after the phase distorting screen just before the beam entered the crystal. Fig. 6b shows the very clear phaseconjugate image of the resolution target using our “ - C3” phase-conjugate geometry. For comparison we show in Fig. 6c a similar reconstructed image resulting from the “Cat” phase-conjugate geometry formed in the same crystal. Our - C3 geometry gives a better resolution of 12.7 lp/mm (39 pm) while the Cat gives 7.13 lp/mm (70 pm). We have observed that by slightly altering the angle of incidence and lateral position at which the beam illuminates the first crystal ( + c) face we can induce either one loop of light (such as the central loop in Fig. lb) (when z = 2.2 mm, #J= 5 1”) or more often, two loops of light (as shown in Fig. 1b) (when z = 1.7 mm, + = 5 1” and 60”). When larger changes of angle and lateral position are made we can induce BOTH one loop of the new “ - C Curve Configuration” AND one
C.C. Chang, D.R. Selviah /Optics Communications 124 (1996) 481-487
0a
485
loop of the six internal reflection configuration (mentioned in Ref. [ 181) as shown in Fig. 7a. This appears to be the first time to the authors knowledge that two quite different phase conjugation loops, each of which can exist independently, have been reported to occur at the same time. For the sake of clarity we will refer to the six internal reflection configuration as the “J configuration” as the beam path appears to form a J shape within the crystal. We observed that over a range of angles and positions the J and -C3 phase-conjugate loops coexist (for a range from z = 2.9 mm and 3.3 mm with 4 = 5 1”). It would appear that the conventional two-interaction-region mechanism [ 1,221 would have difficulty in explaining these phenomena and that a more advanced mechanism may be required. We suggest one such mechanism, in which transitions occur instead between four interaction regions. In our experimental configurations (Figs. 2c and 7b) the incident beam initially propagates at an acute angle to the -C direction of the barium titanate crystal. This causes a fan to develop which has constituent beams over a wide range of angles. This gives rise to a large range of gratings, formed as the beams in the fan interact with each other, having a wide range of angles and periodicities. Therefore, there is a high change of mutual scattering occurring from these fanning gratings via the process of simultaneous degenerate four-wave mixing (DFWM) . Unlike the two-interaction-region mechanism exploited in the “cat” configuration, here four interaction regions give rise to the two loops of the “ -C3” configuration (Fig. lb) and both the “ - C3” and “J” coexisting loops configuration (Fig. 7a). In “ -C3” with two stable loops it appears that the outer loop forms between regions I and IV while the inner between regions II and III. When the incident beam enters close to the edge of the crystal (larger z) several of the beams in the fan can be internally reflected from adjacent crystal faces to give rise to the “J” loop with six internal reflections. To obtain phase conjugation we again make recourse to the four-interaction-region mechanism (Fig. 7a). Two stable loops, “ -C3” and “J” (Fig. 7a),canform and coexist as the loops form between regions I and II
Fig. 6. (a) Phase distorted resolution target input to BaTiO, crystal, (b) phase-conjugate reconstructed image using “ - C”’ SPPC, and (c) phase-conjugate reconstructed image using “Cat” SPPC. ~=50°andz=2.5mm.
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this remains to be fully confirmed. In conclusion, we have demonstrated a self-pumped phase conjugator using novel configurations: “ - C3’ ’ and “J” configurations and we compare these to the popular “Cat” phase conjugator. A very wide angular and lateral positional acceptance was obtained which will make this more suitable for practical applications requiring free space transmission of high resolution images. We have suggested tentative mechanisms to explain the spatial features of the optical path observed in the BaTiO, crystals. The authors wish to thank the National Science Council, Taiwan, ROC, the Chung Cheng Institute of Technology, Taiwan, ROC, and the University College London, UK for supporting this project.
References [l] [2] [3] [4] [5]
m Fig. 7. Schematic of a four-interaction region model for the SPPC (b) the optical path with both “ - C3” and “.I” configurations, inside the BaTiO? crystal during phase conjugation.
for the “J” and between III and IV regions for the “ - Ca” configuration. It appears that the presence of two loops may improve the efficiency, angular range, lateral range and temporal stability as only the most efficient loops are self sustaining and may erase other gratings preventing other loops being formed although
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