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Double signal phase conjugation with a Cat conjugator
Optics & Laser Technology 33 (2001) 435–438
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Double signal phase conjugation with a Cat conjugator Xiudong Sun ∗ , Yongyuan Jiang, Zhongxiang Zhou Department of Physics, Harbin Institute of Technology, Harbin 150001, China Received 6 March 2001; received in revised form 12 June 2001; accepted 15 June 2001
Abstract The phase conjugate re4ection of double signals, induced by the self-pumped phase conjugation, is demonstrated in a 16◦ cut Cu-doped potassium sodium strontium barium niobate (KNSBN) photorefractive crystal. The phase conjugate re4ectivities of signals were measured versus the pump-signal beam ratio. A comparison was made between the signal’s re4ectivity with and without the presence of the other signal beam. The multi-region four-wave mixing model within the same crystal has been employed to explain the geometry performance c 2001 Elsevier Science Ltd. All rights reserved. and the experimental results. Keywords: Phase conjugation; Four-wave mixing; Photorefractive e>ect
1. Introduction Optical phase conjugation (OPC) in photorefractive crystals has attracted great attention because of its numerous potential applications in information processing, optical communications and neural network, etc. [1]. The self-pumped phase conjugator (Cat conjugator) [2,3] involves a single illuminating incident beam which is phase conjugated via the four-wave mixing interaction through total internal re4ection from the surfaces of the crystal. The pumping beams needed for producing the phase conjugation of the incident beam are derived from the incident wave itself so that the phase conjugate re4ectivity cannot exceed unity. One interesting approach is to use the self-pumped phase conjugation process to generate automatically self-aligned counter-propagating pump beams for four-wave mixing in the same nonlinear medium. It was Crst shown by Feinberg [3] that when a signal beam is incident on a continuous wave self-pumped crystal of BaTiO3 , the four-wave mixing interaction can occur and it might be expected to obtain the phase conjugate re4ectivity of the signal beam greater than unity. Zhao and Yamaguchi [4] reported dynamic four-wave mixing induced by self-pumped phase conjugation in Cu : KNSBN crystal and compared ∗ Corresponding author. Tel.: +86-451-641-4129; fax: +86-451622-1048. E-mail address: [email protected] (X. Sun).
the response time scale of the self-pumping process and the induced four-wave mixing process. Troth et al. [5] obtained pulsed phase conjugate re4ectivities of a signal in excess of 500% in a single BaTiO3 crystal. Sun et al. [6,7] investigated the beam ratio dependence of the re4ectivity of the signal and applied the geometry to the holographic associative memory. It is demonstrated in this paper that double signals may be phase conjugated simultaneously by the aid of the self-pumping of the pumping beam in a photorefractive crystal. The phase conjugate re4ectivities of signal beams were studied experimentally. On various experiment conditions, the re4ectivity of each signal was measured versus the pump-signal ratio with and without the other signal beam. The multi-region four-wave mixing processes within the same crystal have been employed to explain the experimental results. 2. Geometry The experimental scheme is shown in Fig. 1. A laser beam is split into two parts by a beam splitter. Then these two parts, mutually coherent and e polarized with respect to the c-axis of the crystal, are directed through mirrors and beam splitters into the crystal, respectively. Beam 1, called the pumping, is positioned at an incident angle of to su>er asymmetric self-defocusing toward one corner of the crystal,
c 2001 Elsevier Science Ltd. All rights reserved. 0030-3992/01/$ - see front matter PII: S 0 0 3 0 - 3 9 9 2 ( 0 1 ) 0 0 0 5 5 - X
436
X. Sun et al. / Optics & Laser Technology 33 (2001) 435–438
Fig. 1. Experimental geometry for individual signal.
Fig. 3. ConCguration showing the incident angles and incident positions of the pump beam and signal beams.
Fig. 2. Schematic setup for producing the phase conjugate re4ection of double signals IS1 and IS2 , induced by the self-pumped phase conjugate process of the pump IP within the same crystal.
intensities, i.e. IS1 = IS2 = IS . During the measurement, the pump–signal intensity ratio = IP =IS is varied when Cxing the values of ; ’; ; x; y1 , and y2 . 3. Experiments and discussion
being able to generate stable self-pumped phase conjugate output. On the other hand, beam 2, called the signal, is directed into the same facet of the crystal. In this scheme, the signal beam is conjugated in the presence of the self-pumped phase conjugation of the pumping beam, and almost all of the energy of its conjugation stemmed from the pumping, especially when the intensity of the pumping is quite larger than that of the signal. According to the detailed study in Ref. [6], one feature of this scheme is that the signal beam has 4exible incident angle and incident position. Moreover, the phase conjugate re4ectivity of the signal beam is related to the intensity ratio and the relative position of the signal beam and pumping beam and is maximized when it is close to but not intersecting with the pumping beam. Another feature of the conjugator is its extremely large dynamic range of the input intensity ratio. These two properties allow it to simultaneously perform phase conjugation of multiple weak signals. The schematic setup for phase conjugating two signals is shown in Fig. 2. An input beam from an argon-ion laser at 488 nm is split into three extraordinarily polarized beams. One of them is designated as the pumping beam, IP . Two other signal beams, IS1 and IS2 , enter the crystal at different angles and positions. All the geometry parameters are described with values of ; ’; ; x; y1 , and y2 , respectively, as shown in Fig. 3. The crystal used in our experiment is a 16◦ cut Cu-doped potassium sodium niobate strontium barium crystal with dimensions of 7:2 mm × 7:0 mm × 5:7 mm. These three beams are mutually coherent and extraordinarily polarized to maximize the di>raction eMciency by taking advantage of the largest electro-optic coeMcient in KNSBN, r33 . In order to compare the phase conjugate re4ectivities of these two signals, we let them have identical
After the pump beam established the self-pumped phase conjugate re4ection, the two signal beams would be phase conjugated immediately and have the energy coming from the pump, at least majority. The conjugates of the two sigc c nals are IS1 and IS2 , respectively. The phase conjugate rec =IS1 4ectivities of the signal beams are deCned as R1 = IS1 c for the signal beam IS1 and R2 = IS2 =IS2 for the signal beam IS2 , respectively. We measured the phase conjugate re4ectivities of both signal beams at di>erent situations as indicated in Fig. 4(a)(b). It can be seen that in the situation (a) the re4ectivity of signal beam 2 was higher than that of signal beam 1, but the reverse happened in the situation (b). We also measured the signal’s re4ectivity when it is incident without the other, which is named as R1 and R2 for two signal beams, respectively. Fig. 5 shows the comparison of the signal’s phase conjugate re4ectivity between the cases with and without the other signal beam. It is seen that the signal’s re4ectivity without the presence of the other signal is always higher than that in the presence of the other signal. Here we use an existing four-wave mixing model [8] to describe the e>ect of introducing signal beams into a self-pumping geometry in photorefractive crystals. We take the example of one signal beam. As shown in Fig. 6, the formation of the phase conjugation of signal beams involves at least two four-wave mixing interaction regions when the signal does not intersect directly with the pump. In region A, the signal IS interferes with its scattered beam ISS and writes a real-time grating via the photorefractive e>ect. Owing to the two-beam coupling, the scattered signal ISS is ampliCed and directed into the region B, where it overlaps any of the pumping-beam loops that the pump beam generated. A four-wave mixing process occurs in the region B, while the pump and its phase conjugate or the loops it
X. Sun et al. / Optics & Laser Technology 33 (2001) 435–438
437
Fig. 4. Phase conjugate re4ectivities of signal beams versus the pump-signal beam ratio when two signals are incident simultaneously. (a) = 36◦ ; ’ = 11◦ ; = 7◦ ; X = 2 mm; Y1 = 3:3 mm; Y2 = 3:5 mm. (b) = 30◦ ; ’ = 25◦ ; = 5◦ ; X = 3 mm; Y1 = 1:5 mm; Y2 = 2 mm.
Fig. 5. Signals’ re4ectivities with and without the other signal beam incidence on the condition = 30◦ ; ’ = 25◦ ; = 5◦ ; X = 3 mm; Y1 = 1:5 mm; Y2 = 2 mm.
Establishing the coupled wave equations describing the four-wave interaction in a photorefractive crystal and using non-depleted pump approximation, an expression describing the phase conjugate re4ectivity of a four-wave mixing geometry is given from Cronin-Golomb et al. as [8] RS = P
exp(−l2 ) − 1 exp(−l2 ) + P
2 ;
(1)
where the ratio of the counter-propagating pumps, P , is given by Fig. 6. Schematic representation of two four-wave mixing interaction regions in the photorefractive crystal showing the performance of the signal’s phase conjugate induced by the self-pumping of the pump beam.
formed, such as IP and IPC , provide the counter-propagating pumping beams for any scattered signal beams from region A.
P =
IPC IP
(2)
and the coupling constant, , is given by =
n3e> re> ESC ; 4
(3)
438
X. Sun et al. / Optics & Laser Technology 33 (2001) 435–438
where ne> is the e>ective refractive index of the crystal, re> is the e>ective electro-optic coeMcient, + re> = n4o r13 cos cos + 2n2o n4e r42 cos2 2
+
n4e r33
+ sin sin sin 2
(ne n3o );
and ESC is the space-charge Celd in the crystal, kg kB T ; ESC = m q 1 + (kg =k0 )2
(4)
(5)
where ne is the refractive index of the crystal for e-polarized light, no is the refractive index of the crystal for o-polarized light, r13 ; r33 and r42 = r51 are the non-zero electro-optic coeMcients of the photorefractive crystal, and are the angles included between the writing beams of the grating and the positive c-axis, respectively, m is the modulation index, kB is Boltzmann’s constant, T is temperature and q is the charge of the carriers. The grating wave-vector and the space-charge screening wave-vector are given by − 4ne> sin ; (6) kg = 2 and k0 =
Ne> q2 ; 0 kB T
(7)
respectively, where Ne> is the e>ective trap density. Due to the presence of two-beam coupling between the incident signal and its scattered beam and of the four-wave mixing interaction, the scattered beam is ampliCed in region A and phase conjugated in region B successively. The phase conjugated beam then di>racts o> the grating written by the incident signal and its scattered beam, resulting Cnally in the phase conjugate of the incident signal via a four-wave mixing process in region A. As discussed above, the phase conjugate re4ectivity of the signal beam is dependent on the coupling strengths in regions A and B as well as the angular and spatial distribution of the fanned signal beam. The dominant parameters are the incident angle and position of the signal. Changing both the incident angle and position would cause the shift of the four-wave interaction region sequentially causing the change of the coupling strength. Additionally, it should be noted that all the incident beams are mutually coherent; coupling among various beams made it diMcult to analyze the geometry quantitatively while making it feasible to use it to realize phase conjugate of multiple weak signals. In our experiment, as shown in Fig. 4(a) and (b), the various experimental conditions lead to reversed results. It indicates that the phase conjugate re4ectivities of two
signals depend not only on the relative positions to the pump beam but also on the consideration of all the parameters. The results shown in Fig. 5 can be explained by the competition between two signals because the energy of the signals comes from the pump beam.
4. Conclusion The generation of phase conjugation of double incident signals in a photorefractive crystal is investigated while the self-pumped phase conjugation acts as a predetermination. The phase conjugation has been realized when double signals were incident on a 16◦ cut Cu-doped KNSBN crystal. Changing the experimental conditions, the phase conjugate re4ectivities of signals were measured versus the pump– signal beam ratio. It has been found that the phase conjugate re4ectivities of two signals depend not only on their relative positions to the pump beam but also on the consideration of all the parameters. The experimental results implied the existence of a competition between the signal beams, which made the re4ectivity of an individual signal larger than that with two signals incident.
Acknowledgements The authors thank Dr. Q. Jiang and Prof. H. Chen for providing the photorefractive crystal. This work was supported by the National Natural Science Foundation of China. References [1] Gunter P, Huignard J-P. Photorefractive materials and their applications I. Berlin: Springer, 1989. [2] Feinberg J. Self-pumped, continuous-wave phase conjugator using internal re4ection. Opt Lett 1982;7:486–8. [3] Lam JF. Origin of phase conjugate waves in self-pumped photorefractive mirrors. Appl Phys Lett 1985;46:909–11. [4] Zhao M, Yamaguchi I. Dynamic four-wave mixing induced by self-pump phase conjugation in Cu : KNSBN crystal. Opt Commun 1994;112:163–8. [5] Troth RC, Ramos-Garcia R, Damzen MJ. Greater than unity pulsed phase conjugate re4ectivities using self-pumped four-wave mixing in a single BaTiO3 crystal. Opt Commun 1994;109:472–6. [6] Sun X, Zhang J, Zhou Z, Xu K, Hong J. Coherent mutually pumped phase conjugation induced with high-eMciency by self-pumped phase conjugate re4ection. Chin Phys Lett 1995;12:533–6. [7] Sun X, Zhou Z, Li Y, Jiang Y, Xu K. Holographic associative memory using a coherently induced double phase conjugate mirror. Opt Eng 1996;35:2153–7. [8] Cronin-Golomb M, Fischer B, White JO, Yariv A. Theory and applications of four-wave mixing in photorefractive media. IEEE J Quantum Electron 1984;QE-20:12–29.
www.elsevier.com/locate/optlastec
Double signal phase conjugation with a Cat conjugator Xiudong Sun ∗ , Yongyuan Jiang, Zhongxiang Zhou Department of Physics, Harbin Institute of Technology, Harbin 150001, China Received 6 March 2001; received in revised form 12 June 2001; accepted 15 June 2001
Abstract The phase conjugate re4ection of double signals, induced by the self-pumped phase conjugation, is demonstrated in a 16◦ cut Cu-doped potassium sodium strontium barium niobate (KNSBN) photorefractive crystal. The phase conjugate re4ectivities of signals were measured versus the pump-signal beam ratio. A comparison was made between the signal’s re4ectivity with and without the presence of the other signal beam. The multi-region four-wave mixing model within the same crystal has been employed to explain the geometry performance c 2001 Elsevier Science Ltd. All rights reserved. and the experimental results. Keywords: Phase conjugation; Four-wave mixing; Photorefractive e>ect
1. Introduction Optical phase conjugation (OPC) in photorefractive crystals has attracted great attention because of its numerous potential applications in information processing, optical communications and neural network, etc. [1]. The self-pumped phase conjugator (Cat conjugator) [2,3] involves a single illuminating incident beam which is phase conjugated via the four-wave mixing interaction through total internal re4ection from the surfaces of the crystal. The pumping beams needed for producing the phase conjugation of the incident beam are derived from the incident wave itself so that the phase conjugate re4ectivity cannot exceed unity. One interesting approach is to use the self-pumped phase conjugation process to generate automatically self-aligned counter-propagating pump beams for four-wave mixing in the same nonlinear medium. It was Crst shown by Feinberg [3] that when a signal beam is incident on a continuous wave self-pumped crystal of BaTiO3 , the four-wave mixing interaction can occur and it might be expected to obtain the phase conjugate re4ectivity of the signal beam greater than unity. Zhao and Yamaguchi [4] reported dynamic four-wave mixing induced by self-pumped phase conjugation in Cu : KNSBN crystal and compared ∗ Corresponding author. Tel.: +86-451-641-4129; fax: +86-451622-1048. E-mail address: [email protected] (X. Sun).
the response time scale of the self-pumping process and the induced four-wave mixing process. Troth et al. [5] obtained pulsed phase conjugate re4ectivities of a signal in excess of 500% in a single BaTiO3 crystal. Sun et al. [6,7] investigated the beam ratio dependence of the re4ectivity of the signal and applied the geometry to the holographic associative memory. It is demonstrated in this paper that double signals may be phase conjugated simultaneously by the aid of the self-pumping of the pumping beam in a photorefractive crystal. The phase conjugate re4ectivities of signal beams were studied experimentally. On various experiment conditions, the re4ectivity of each signal was measured versus the pump-signal ratio with and without the other signal beam. The multi-region four-wave mixing processes within the same crystal have been employed to explain the experimental results. 2. Geometry The experimental scheme is shown in Fig. 1. A laser beam is split into two parts by a beam splitter. Then these two parts, mutually coherent and e polarized with respect to the c-axis of the crystal, are directed through mirrors and beam splitters into the crystal, respectively. Beam 1, called the pumping, is positioned at an incident angle of to su>er asymmetric self-defocusing toward one corner of the crystal,
c 2001 Elsevier Science Ltd. All rights reserved. 0030-3992/01/$ - see front matter PII: S 0 0 3 0 - 3 9 9 2 ( 0 1 ) 0 0 0 5 5 - X
436
X. Sun et al. / Optics & Laser Technology 33 (2001) 435–438
Fig. 1. Experimental geometry for individual signal.
Fig. 3. ConCguration showing the incident angles and incident positions of the pump beam and signal beams.
Fig. 2. Schematic setup for producing the phase conjugate re4ection of double signals IS1 and IS2 , induced by the self-pumped phase conjugate process of the pump IP within the same crystal.
intensities, i.e. IS1 = IS2 = IS . During the measurement, the pump–signal intensity ratio = IP =IS is varied when Cxing the values of ; ’; ; x; y1 , and y2 . 3. Experiments and discussion
being able to generate stable self-pumped phase conjugate output. On the other hand, beam 2, called the signal, is directed into the same facet of the crystal. In this scheme, the signal beam is conjugated in the presence of the self-pumped phase conjugation of the pumping beam, and almost all of the energy of its conjugation stemmed from the pumping, especially when the intensity of the pumping is quite larger than that of the signal. According to the detailed study in Ref. [6], one feature of this scheme is that the signal beam has 4exible incident angle and incident position. Moreover, the phase conjugate re4ectivity of the signal beam is related to the intensity ratio and the relative position of the signal beam and pumping beam and is maximized when it is close to but not intersecting with the pumping beam. Another feature of the conjugator is its extremely large dynamic range of the input intensity ratio. These two properties allow it to simultaneously perform phase conjugation of multiple weak signals. The schematic setup for phase conjugating two signals is shown in Fig. 2. An input beam from an argon-ion laser at 488 nm is split into three extraordinarily polarized beams. One of them is designated as the pumping beam, IP . Two other signal beams, IS1 and IS2 , enter the crystal at different angles and positions. All the geometry parameters are described with values of ; ’; ; x; y1 , and y2 , respectively, as shown in Fig. 3. The crystal used in our experiment is a 16◦ cut Cu-doped potassium sodium niobate strontium barium crystal with dimensions of 7:2 mm × 7:0 mm × 5:7 mm. These three beams are mutually coherent and extraordinarily polarized to maximize the di>raction eMciency by taking advantage of the largest electro-optic coeMcient in KNSBN, r33 . In order to compare the phase conjugate re4ectivities of these two signals, we let them have identical
After the pump beam established the self-pumped phase conjugate re4ection, the two signal beams would be phase conjugated immediately and have the energy coming from the pump, at least majority. The conjugates of the two sigc c nals are IS1 and IS2 , respectively. The phase conjugate rec =IS1 4ectivities of the signal beams are deCned as R1 = IS1 c for the signal beam IS1 and R2 = IS2 =IS2 for the signal beam IS2 , respectively. We measured the phase conjugate re4ectivities of both signal beams at di>erent situations as indicated in Fig. 4(a)(b). It can be seen that in the situation (a) the re4ectivity of signal beam 2 was higher than that of signal beam 1, but the reverse happened in the situation (b). We also measured the signal’s re4ectivity when it is incident without the other, which is named as R1 and R2 for two signal beams, respectively. Fig. 5 shows the comparison of the signal’s phase conjugate re4ectivity between the cases with and without the other signal beam. It is seen that the signal’s re4ectivity without the presence of the other signal is always higher than that in the presence of the other signal. Here we use an existing four-wave mixing model [8] to describe the e>ect of introducing signal beams into a self-pumping geometry in photorefractive crystals. We take the example of one signal beam. As shown in Fig. 6, the formation of the phase conjugation of signal beams involves at least two four-wave mixing interaction regions when the signal does not intersect directly with the pump. In region A, the signal IS interferes with its scattered beam ISS and writes a real-time grating via the photorefractive e>ect. Owing to the two-beam coupling, the scattered signal ISS is ampliCed and directed into the region B, where it overlaps any of the pumping-beam loops that the pump beam generated. A four-wave mixing process occurs in the region B, while the pump and its phase conjugate or the loops it
X. Sun et al. / Optics & Laser Technology 33 (2001) 435–438
437
Fig. 4. Phase conjugate re4ectivities of signal beams versus the pump-signal beam ratio when two signals are incident simultaneously. (a) = 36◦ ; ’ = 11◦ ; = 7◦ ; X = 2 mm; Y1 = 3:3 mm; Y2 = 3:5 mm. (b) = 30◦ ; ’ = 25◦ ; = 5◦ ; X = 3 mm; Y1 = 1:5 mm; Y2 = 2 mm.
Fig. 5. Signals’ re4ectivities with and without the other signal beam incidence on the condition = 30◦ ; ’ = 25◦ ; = 5◦ ; X = 3 mm; Y1 = 1:5 mm; Y2 = 2 mm.
Establishing the coupled wave equations describing the four-wave interaction in a photorefractive crystal and using non-depleted pump approximation, an expression describing the phase conjugate re4ectivity of a four-wave mixing geometry is given from Cronin-Golomb et al. as [8] RS = P
exp(−l2 ) − 1 exp(−l2 ) + P
2 ;
(1)
where the ratio of the counter-propagating pumps, P , is given by Fig. 6. Schematic representation of two four-wave mixing interaction regions in the photorefractive crystal showing the performance of the signal’s phase conjugate induced by the self-pumping of the pump beam.
formed, such as IP and IPC , provide the counter-propagating pumping beams for any scattered signal beams from region A.
P =
IPC IP
(2)
and the coupling constant, , is given by =
n3e> re> ESC ; 4
(3)
438
X. Sun et al. / Optics & Laser Technology 33 (2001) 435–438
where ne> is the e>ective refractive index of the crystal, re> is the e>ective electro-optic coeMcient, + re> = n4o r13 cos cos + 2n2o n4e r42 cos2 2
+
n4e r33
+ sin sin sin 2
(ne n3o );
and ESC is the space-charge Celd in the crystal, kg kB T ; ESC = m q 1 + (kg =k0 )2
(4)
(5)
where ne is the refractive index of the crystal for e-polarized light, no is the refractive index of the crystal for o-polarized light, r13 ; r33 and r42 = r51 are the non-zero electro-optic coeMcients of the photorefractive crystal, and are the angles included between the writing beams of the grating and the positive c-axis, respectively, m is the modulation index, kB is Boltzmann’s constant, T is temperature and q is the charge of the carriers. The grating wave-vector and the space-charge screening wave-vector are given by − 4ne> sin ; (6) kg = 2 and k0 =
Ne> q2 ; 0 kB T
(7)
respectively, where Ne> is the e>ective trap density. Due to the presence of two-beam coupling between the incident signal and its scattered beam and of the four-wave mixing interaction, the scattered beam is ampliCed in region A and phase conjugated in region B successively. The phase conjugated beam then di>racts o> the grating written by the incident signal and its scattered beam, resulting Cnally in the phase conjugate of the incident signal via a four-wave mixing process in region A. As discussed above, the phase conjugate re4ectivity of the signal beam is dependent on the coupling strengths in regions A and B as well as the angular and spatial distribution of the fanned signal beam. The dominant parameters are the incident angle and position of the signal. Changing both the incident angle and position would cause the shift of the four-wave interaction region sequentially causing the change of the coupling strength. Additionally, it should be noted that all the incident beams are mutually coherent; coupling among various beams made it diMcult to analyze the geometry quantitatively while making it feasible to use it to realize phase conjugate of multiple weak signals. In our experiment, as shown in Fig. 4(a) and (b), the various experimental conditions lead to reversed results. It indicates that the phase conjugate re4ectivities of two
signals depend not only on the relative positions to the pump beam but also on the consideration of all the parameters. The results shown in Fig. 5 can be explained by the competition between two signals because the energy of the signals comes from the pump beam.
4. Conclusion The generation of phase conjugation of double incident signals in a photorefractive crystal is investigated while the self-pumped phase conjugation acts as a predetermination. The phase conjugation has been realized when double signals were incident on a 16◦ cut Cu-doped KNSBN crystal. Changing the experimental conditions, the phase conjugate re4ectivities of signals were measured versus the pump– signal beam ratio. It has been found that the phase conjugate re4ectivities of two signals depend not only on their relative positions to the pump beam but also on the consideration of all the parameters. The experimental results implied the existence of a competition between the signal beams, which made the re4ectivity of an individual signal larger than that with two signals incident.
Acknowledgements The authors thank Dr. Q. Jiang and Prof. H. Chen for providing the photorefractive crystal. This work was supported by the National Natural Science Foundation of China. References [1] Gunter P, Huignard J-P. Photorefractive materials and their applications I. Berlin: Springer, 1989. [2] Feinberg J. Self-pumped, continuous-wave phase conjugator using internal re4ection. Opt Lett 1982;7:486–8. [3] Lam JF. Origin of phase conjugate waves in self-pumped photorefractive mirrors. Appl Phys Lett 1985;46:909–11. [4] Zhao M, Yamaguchi I. Dynamic four-wave mixing induced by self-pump phase conjugation in Cu : KNSBN crystal. Opt Commun 1994;112:163–8. [5] Troth RC, Ramos-Garcia R, Damzen MJ. Greater than unity pulsed phase conjugate re4ectivities using self-pumped four-wave mixing in a single BaTiO3 crystal. Opt Commun 1994;109:472–6. [6] Sun X, Zhang J, Zhou Z, Xu K, Hong J. Coherent mutually pumped phase conjugation induced with high-eMciency by self-pumped phase conjugate re4ection. Chin Phys Lett 1995;12:533–6. [7] Sun X, Zhou Z, Li Y, Jiang Y, Xu K. Holographic associative memory using a coherently induced double phase conjugate mirror. Opt Eng 1996;35:2153–7. [8] Cronin-Golomb M, Fischer B, White JO, Yariv A. Theory and applications of four-wave mixing in photorefractive media. IEEE J Quantum Electron 1984;QE-20:12–29.