Abstract

The fanning behavior of the two interacting laser beams in a double phase-conjugate mirror (DPCM) obviously influences the characteristics of the mirror. We present a two-dimensional experimental study and model of the beam-fanning patterns obtained in nominally undoped and cobalt-doped (20 parts in 106) BaTiO3 samples. We propose a numerical method based on beam coupling theory that allows us to determine, for each crystal, which directions will develop significant fanning. We thus interpret the beam-fanning patterns by focusing on the influence of the incident beam’s width and incidence angle. The time evolution of the intensity in each of these directions is also studied and modeled. This model has been applied to DPCM to enable both incident beams to generate fanning in a common direction, with good results in terms of response time, efficiency, and stability. © 2001 Optical Society of America

© 2001 Optical Society of America

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  24. A. Smout, R. Eason, and M. Gower, “Regular oscillations and self-pulsating in self-pumped BaTiO3,” Opt. Commun. 59, 77–82 (1986).
  25. D. Gauthier, P. Narum, and R. Boyd, “Observation of deterministic chaos in a phase-conjugate mirror,” Phys. Rev. Lett. 58, 1640–1643 (1987).
  26. A. M. Darwish, M. Dokhanian, P. R. K. Rao, M. Curley, and P. Venkateswarlu, “Oscillations in coherent beam pumped mutual phase conjugate emissions,” in Photorefractive Fiber and Crystal Devices: Materials, Optical Properties, and Applications, S. Yin and F. T. Yu, eds., Proc. SPIE 3470, 137–145 (1998).

1998 (1)

A. M. Darwish, M. Dokhanian, P. R. K. Rao, M. Curley, and P. Venkateswarlu, “Oscillations in coherent beam pumped mutual phase conjugate emissions,” in Photorefractive Fiber and Crystal Devices: Materials, Optical Properties, and Applications, S. Yin and F. T. Yu, eds., Proc. SPIE 3470, 137–145 (1998).

1995 (5)

A. Zozulya and D. Anderson, “Spatial structure of light and a nonlinear refractive index generated by fanning in photorefractive media,” Phys. Rev. A 52, 878–881 (1995).

K. Kamra and K. Singh, “Characterization of beam fanning in BaTiO3 under biasing illumination and its application as log processor,” Opt. Eng. 34, 2266–2273 (1995).

G. Montemezzani, A. A. Zozulya, L. Czaia, D. Z. Anderson, M. Zgonik, and P. Gunter, “Origin of the lobe structure in photorefractive beam fanning,” Phys. Rev. A 52, 1791–1794 (1995).

A. Kamshilin, V. Prokoviev, and T. Jaaskelainen, “Beam fanning and double phase conjugation in a fiber-like photorefractive sample,” IEEE J. Quantum Electron. 31, 1642–1647 (1995).

A. Kamshilin, H. Tuovinen, V. Prokoviev, and T. Jaaskelainen, “Phase conjugate mirrors on the base of BiTiO20 photorefractive fibre,” Opt. Mater. 4, 399–403 (1995).

1994 (1)

P. Xie, J. Dai, P. Wang, and H. Zhang, “A two-dimensional theory and propagation of beam fanning in photorefractive crystals,” J. Appl. Phys. 75, 1891–1895 (1994).

1993 (4)

P. Banerjee and R. Misra, “Dependence of photorefractive beam fanning on beam parameters,” Opt. Commun. 100, 166–172 (1993).

P. Xie, Y. H. Hong, J. H. Dai, Y. Zhu, and H. J. Zhang, “Theoretical and experimental studies of fanning effects in photorefractive crystals,” J. Appl. Phys. 74, 813–818 (1993).

Y. H. Hong, P. Xie, J. H. Dai, Y. Zhu, H. G. Yang, and H. J. Zhang, “Fanning effect in photorefractive crystals,” Opt. Lett. 18, 772–774 (1993).

M. Segev, D. Engin, A. Yariv, and G. Valley, “Temporal evolution of fanning in photorefractive materials,” Opt. Lett. 18, 956–958 (1993).

1992 (4)

G. Li, T. Yang, Y. Y. Teng, F. C. Lin, and M. A. Fiddy, “Scattering and beam fanning in a BaTiO3 crystal,” Waves Random Media 2, 303–315 (1992).

N. Wolffer, P. Gravey, and V. Royer, “Thresholding of two facing double phase conjugate mirror and semilinear phase conjugate mirror with fanning in BTO,” Opt. Commun. 89, 380–384 (1992).

Q. He, P. Yeh, C. Gu, and R. Neurgaonkar, “Multigrating competition effects in photorefractive mutually pumped phase conjugation,” J. Opt. Soc. Am. B 9, 114–120 (1992).

M. Garrett, J. Chang, H. Jenssen, and C. Warde, “High beam-coupling gain and deep- and shallow-trap effects in cobalt-doped barium titanate, BaTiO3:Co,” J. Opt. Soc. Am. B 9, 1407–1415 (1992).

1990 (1)

M. Segev, Y. Ophir, and B. Fischer, “Nonlinear multi two-wave mixing, the fanning process and its bleaching in photorefractive media,” Opt. Commun. 77, 265–274 (1990).

1987 (2)

D. Gauthier, P. Narum, and R. Boyd, “Observation of deterministic chaos in a phase-conjugate mirror,” Phys. Rev. Lett. 58, 1640–1643 (1987).

S. Weiss, S. Sternklar, and B. Fischer, “Double phase-conjugate mirror: analysis, demonstration, and applications,” Opt. Lett. 12, 114–116 (1987).

1986 (1)

A. Smout, R. Eason, and M. Gower, “Regular oscillations and self-pulsating in self-pumped BaTiO3,” Opt. Commun. 59, 77–82 (1986).

1985 (1)

P. Gunter, E. Voit, and M. Zha, “Self-pulsation and optical chaos in self-pumped photorefractive BaTiO3,” Opt. Commun. 55, 210–214 (1985).

1984 (1)

M. Cronin-Golomb, B. Fisher, J. White, and A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12–30 (1984).

1982 (2)

Anderson, D.

A. Zozulya and D. Anderson, “Spatial structure of light and a nonlinear refractive index generated by fanning in photorefractive media,” Phys. Rev. A 52, 878–881 (1995).

Anderson, D. Z.

G. Montemezzani, A. A. Zozulya, L. Czaia, D. Z. Anderson, M. Zgonik, and P. Gunter, “Origin of the lobe structure in photorefractive beam fanning,” Phys. Rev. A 52, 1791–1794 (1995).

Banerjee, P.

P. Banerjee and R. Misra, “Dependence of photorefractive beam fanning on beam parameters,” Opt. Commun. 100, 166–172 (1993).

Boyd, R.

D. Gauthier, P. Narum, and R. Boyd, “Observation of deterministic chaos in a phase-conjugate mirror,” Phys. Rev. Lett. 58, 1640–1643 (1987).

Chang, J.

Cronin-Golomb, M.

M. Cronin-Golomb, B. Fisher, J. White, and A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12–30 (1984).

Curley, M.

A. M. Darwish, M. Dokhanian, P. R. K. Rao, M. Curley, and P. Venkateswarlu, “Oscillations in coherent beam pumped mutual phase conjugate emissions,” in Photorefractive Fiber and Crystal Devices: Materials, Optical Properties, and Applications, S. Yin and F. T. Yu, eds., Proc. SPIE 3470, 137–145 (1998).

Czaia, L.

G. Montemezzani, A. A. Zozulya, L. Czaia, D. Z. Anderson, M. Zgonik, and P. Gunter, “Origin of the lobe structure in photorefractive beam fanning,” Phys. Rev. A 52, 1791–1794 (1995).

Dai, J.

P. Xie, J. Dai, P. Wang, and H. Zhang, “A two-dimensional theory and propagation of beam fanning in photorefractive crystals,” J. Appl. Phys. 75, 1891–1895 (1994).

Dai, J. H.

P. Xie, Y. H. Hong, J. H. Dai, Y. Zhu, and H. J. Zhang, “Theoretical and experimental studies of fanning effects in photorefractive crystals,” J. Appl. Phys. 74, 813–818 (1993).

Y. H. Hong, P. Xie, J. H. Dai, Y. Zhu, H. G. Yang, and H. J. Zhang, “Fanning effect in photorefractive crystals,” Opt. Lett. 18, 772–774 (1993).

Darwish, A. M.

A. M. Darwish, M. Dokhanian, P. R. K. Rao, M. Curley, and P. Venkateswarlu, “Oscillations in coherent beam pumped mutual phase conjugate emissions,” in Photorefractive Fiber and Crystal Devices: Materials, Optical Properties, and Applications, S. Yin and F. T. Yu, eds., Proc. SPIE 3470, 137–145 (1998).

Dokhanian, M.

A. M. Darwish, M. Dokhanian, P. R. K. Rao, M. Curley, and P. Venkateswarlu, “Oscillations in coherent beam pumped mutual phase conjugate emissions,” in Photorefractive Fiber and Crystal Devices: Materials, Optical Properties, and Applications, S. Yin and F. T. Yu, eds., Proc. SPIE 3470, 137–145 (1998).

Eason, R.

A. Smout, R. Eason, and M. Gower, “Regular oscillations and self-pulsating in self-pumped BaTiO3,” Opt. Commun. 59, 77–82 (1986).

Engin, D.

Feinberg, J.

Fiddy, M. A.

G. Li, T. Yang, Y. Y. Teng, F. C. Lin, and M. A. Fiddy, “Scattering and beam fanning in a BaTiO3 crystal,” Waves Random Media 2, 303–315 (1992).

Fischer, B.

M. Segev, Y. Ophir, and B. Fischer, “Nonlinear multi two-wave mixing, the fanning process and its bleaching in photorefractive media,” Opt. Commun. 77, 265–274 (1990).

S. Weiss, S. Sternklar, and B. Fischer, “Double phase-conjugate mirror: analysis, demonstration, and applications,” Opt. Lett. 12, 114–116 (1987).

Fisher, B.

M. Cronin-Golomb, B. Fisher, J. White, and A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12–30 (1984).

Garrett, M.

Gauthier, D.

D. Gauthier, P. Narum, and R. Boyd, “Observation of deterministic chaos in a phase-conjugate mirror,” Phys. Rev. Lett. 58, 1640–1643 (1987).

Gower, M.

A. Smout, R. Eason, and M. Gower, “Regular oscillations and self-pulsating in self-pumped BaTiO3,” Opt. Commun. 59, 77–82 (1986).

Gravey, P.

N. Wolffer, P. Gravey, and V. Royer, “Thresholding of two facing double phase conjugate mirror and semilinear phase conjugate mirror with fanning in BTO,” Opt. Commun. 89, 380–384 (1992).

Gu, C.

Gunter, P.

G. Montemezzani, A. A. Zozulya, L. Czaia, D. Z. Anderson, M. Zgonik, and P. Gunter, “Origin of the lobe structure in photorefractive beam fanning,” Phys. Rev. A 52, 1791–1794 (1995).

P. Gunter, E. Voit, and M. Zha, “Self-pulsation and optical chaos in self-pumped photorefractive BaTiO3,” Opt. Commun. 55, 210–214 (1985).

He, Q.

Hong, Y. H.

Y. H. Hong, P. Xie, J. H. Dai, Y. Zhu, H. G. Yang, and H. J. Zhang, “Fanning effect in photorefractive crystals,” Opt. Lett. 18, 772–774 (1993).

P. Xie, Y. H. Hong, J. H. Dai, Y. Zhu, and H. J. Zhang, “Theoretical and experimental studies of fanning effects in photorefractive crystals,” J. Appl. Phys. 74, 813–818 (1993).

Jaaskelainen, T.

A. Kamshilin, V. Prokoviev, and T. Jaaskelainen, “Beam fanning and double phase conjugation in a fiber-like photorefractive sample,” IEEE J. Quantum Electron. 31, 1642–1647 (1995).

A. Kamshilin, H. Tuovinen, V. Prokoviev, and T. Jaaskelainen, “Phase conjugate mirrors on the base of BiTiO20 photorefractive fibre,” Opt. Mater. 4, 399–403 (1995).

Jenssen, H.

Kamra, K.

K. Kamra and K. Singh, “Characterization of beam fanning in BaTiO3 under biasing illumination and its application as log processor,” Opt. Eng. 34, 2266–2273 (1995).

Kamshilin, A.

A. Kamshilin, V. Prokoviev, and T. Jaaskelainen, “Beam fanning and double phase conjugation in a fiber-like photorefractive sample,” IEEE J. Quantum Electron. 31, 1642–1647 (1995).

A. Kamshilin, H. Tuovinen, V. Prokoviev, and T. Jaaskelainen, “Phase conjugate mirrors on the base of BiTiO20 photorefractive fibre,” Opt. Mater. 4, 399–403 (1995).

Li, G.

G. Li, T. Yang, Y. Y. Teng, F. C. Lin, and M. A. Fiddy, “Scattering and beam fanning in a BaTiO3 crystal,” Waves Random Media 2, 303–315 (1992).

Lin, F. C.

G. Li, T. Yang, Y. Y. Teng, F. C. Lin, and M. A. Fiddy, “Scattering and beam fanning in a BaTiO3 crystal,” Waves Random Media 2, 303–315 (1992).

Misra, R.

P. Banerjee and R. Misra, “Dependence of photorefractive beam fanning on beam parameters,” Opt. Commun. 100, 166–172 (1993).

Montemezzani, G.

G. Montemezzani, A. A. Zozulya, L. Czaia, D. Z. Anderson, M. Zgonik, and P. Gunter, “Origin of the lobe structure in photorefractive beam fanning,” Phys. Rev. A 52, 1791–1794 (1995).

Narum, P.

D. Gauthier, P. Narum, and R. Boyd, “Observation of deterministic chaos in a phase-conjugate mirror,” Phys. Rev. Lett. 58, 1640–1643 (1987).

Neurgaonkar, R.

Ophir, Y.

M. Segev, Y. Ophir, and B. Fischer, “Nonlinear multi two-wave mixing, the fanning process and its bleaching in photorefractive media,” Opt. Commun. 77, 265–274 (1990).

Prokoviev, V.

A. Kamshilin, H. Tuovinen, V. Prokoviev, and T. Jaaskelainen, “Phase conjugate mirrors on the base of BiTiO20 photorefractive fibre,” Opt. Mater. 4, 399–403 (1995).

A. Kamshilin, V. Prokoviev, and T. Jaaskelainen, “Beam fanning and double phase conjugation in a fiber-like photorefractive sample,” IEEE J. Quantum Electron. 31, 1642–1647 (1995).

Rao, P. R. K.

A. M. Darwish, M. Dokhanian, P. R. K. Rao, M. Curley, and P. Venkateswarlu, “Oscillations in coherent beam pumped mutual phase conjugate emissions,” in Photorefractive Fiber and Crystal Devices: Materials, Optical Properties, and Applications, S. Yin and F. T. Yu, eds., Proc. SPIE 3470, 137–145 (1998).

Royer, V.

N. Wolffer, P. Gravey, and V. Royer, “Thresholding of two facing double phase conjugate mirror and semilinear phase conjugate mirror with fanning in BTO,” Opt. Commun. 89, 380–384 (1992).

Segev, M.

M. Segev, D. Engin, A. Yariv, and G. Valley, “Temporal evolution of fanning in photorefractive materials,” Opt. Lett. 18, 956–958 (1993).

M. Segev, Y. Ophir, and B. Fischer, “Nonlinear multi two-wave mixing, the fanning process and its bleaching in photorefractive media,” Opt. Commun. 77, 265–274 (1990).

Singh, K.

K. Kamra and K. Singh, “Characterization of beam fanning in BaTiO3 under biasing illumination and its application as log processor,” Opt. Eng. 34, 2266–2273 (1995).

Smout, A.

A. Smout, R. Eason, and M. Gower, “Regular oscillations and self-pulsating in self-pumped BaTiO3,” Opt. Commun. 59, 77–82 (1986).

Sternklar, S.

Teng, Y. Y.

G. Li, T. Yang, Y. Y. Teng, F. C. Lin, and M. A. Fiddy, “Scattering and beam fanning in a BaTiO3 crystal,” Waves Random Media 2, 303–315 (1992).

Tuovinen, H.

A. Kamshilin, H. Tuovinen, V. Prokoviev, and T. Jaaskelainen, “Phase conjugate mirrors on the base of BiTiO20 photorefractive fibre,” Opt. Mater. 4, 399–403 (1995).

Valley, G.

Venkateswarlu, P.

A. M. Darwish, M. Dokhanian, P. R. K. Rao, M. Curley, and P. Venkateswarlu, “Oscillations in coherent beam pumped mutual phase conjugate emissions,” in Photorefractive Fiber and Crystal Devices: Materials, Optical Properties, and Applications, S. Yin and F. T. Yu, eds., Proc. SPIE 3470, 137–145 (1998).

Voit, E.

P. Gunter, E. Voit, and M. Zha, “Self-pulsation and optical chaos in self-pumped photorefractive BaTiO3,” Opt. Commun. 55, 210–214 (1985).

Wang, P.

P. Xie, J. Dai, P. Wang, and H. Zhang, “A two-dimensional theory and propagation of beam fanning in photorefractive crystals,” J. Appl. Phys. 75, 1891–1895 (1994).

Warde, C.

Weiss, S.

White, J.

M. Cronin-Golomb, B. Fisher, J. White, and A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12–30 (1984).

Wolffer, N.

N. Wolffer, P. Gravey, and V. Royer, “Thresholding of two facing double phase conjugate mirror and semilinear phase conjugate mirror with fanning in BTO,” Opt. Commun. 89, 380–384 (1992).

Xie, P.

P. Xie, J. Dai, P. Wang, and H. Zhang, “A two-dimensional theory and propagation of beam fanning in photorefractive crystals,” J. Appl. Phys. 75, 1891–1895 (1994).

P. Xie, Y. H. Hong, J. H. Dai, Y. Zhu, and H. J. Zhang, “Theoretical and experimental studies of fanning effects in photorefractive crystals,” J. Appl. Phys. 74, 813–818 (1993).

Y. H. Hong, P. Xie, J. H. Dai, Y. Zhu, H. G. Yang, and H. J. Zhang, “Fanning effect in photorefractive crystals,” Opt. Lett. 18, 772–774 (1993).

Yang, H. G.

Yang, T.

G. Li, T. Yang, Y. Y. Teng, F. C. Lin, and M. A. Fiddy, “Scattering and beam fanning in a BaTiO3 crystal,” Waves Random Media 2, 303–315 (1992).

Yariv, A.

M. Segev, D. Engin, A. Yariv, and G. Valley, “Temporal evolution of fanning in photorefractive materials,” Opt. Lett. 18, 956–958 (1993).

M. Cronin-Golomb, B. Fisher, J. White, and A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12–30 (1984).

Yeh, P.

Zgonik, M.

G. Montemezzani, A. A. Zozulya, L. Czaia, D. Z. Anderson, M. Zgonik, and P. Gunter, “Origin of the lobe structure in photorefractive beam fanning,” Phys. Rev. A 52, 1791–1794 (1995).

Zha, M.

P. Gunter, E. Voit, and M. Zha, “Self-pulsation and optical chaos in self-pumped photorefractive BaTiO3,” Opt. Commun. 55, 210–214 (1985).

Zhang, H.

P. Xie, J. Dai, P. Wang, and H. Zhang, “A two-dimensional theory and propagation of beam fanning in photorefractive crystals,” J. Appl. Phys. 75, 1891–1895 (1994).

Zhang, H. J.

P. Xie, Y. H. Hong, J. H. Dai, Y. Zhu, and H. J. Zhang, “Theoretical and experimental studies of fanning effects in photorefractive crystals,” J. Appl. Phys. 74, 813–818 (1993).

Y. H. Hong, P. Xie, J. H. Dai, Y. Zhu, H. G. Yang, and H. J. Zhang, “Fanning effect in photorefractive crystals,” Opt. Lett. 18, 772–774 (1993).

Zhu, Y.

Y. H. Hong, P. Xie, J. H. Dai, Y. Zhu, H. G. Yang, and H. J. Zhang, “Fanning effect in photorefractive crystals,” Opt. Lett. 18, 772–774 (1993).

P. Xie, Y. H. Hong, J. H. Dai, Y. Zhu, and H. J. Zhang, “Theoretical and experimental studies of fanning effects in photorefractive crystals,” J. Appl. Phys. 74, 813–818 (1993).

Zozulya, A.

A. Zozulya and D. Anderson, “Spatial structure of light and a nonlinear refractive index generated by fanning in photorefractive media,” Phys. Rev. A 52, 878–881 (1995).

Zozulya, A. A.

G. Montemezzani, A. A. Zozulya, L. Czaia, D. Z. Anderson, M. Zgonik, and P. Gunter, “Origin of the lobe structure in photorefractive beam fanning,” Phys. Rev. A 52, 1791–1794 (1995).

IEEE J. Quantum Electron. (2)

M. Cronin-Golomb, B. Fisher, J. White, and A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12–30 (1984).

A. Kamshilin, V. Prokoviev, and T. Jaaskelainen, “Beam fanning and double phase conjugation in a fiber-like photorefractive sample,” IEEE J. Quantum Electron. 31, 1642–1647 (1995).

J. Appl. Phys. (2)

P. Xie, J. Dai, P. Wang, and H. Zhang, “A two-dimensional theory and propagation of beam fanning in photorefractive crystals,” J. Appl. Phys. 75, 1891–1895 (1994).

P. Xie, Y. H. Hong, J. H. Dai, Y. Zhu, and H. J. Zhang, “Theoretical and experimental studies of fanning effects in photorefractive crystals,” J. Appl. Phys. 74, 813–818 (1993).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (2)

Opt. Commun. (5)

N. Wolffer, P. Gravey, and V. Royer, “Thresholding of two facing double phase conjugate mirror and semilinear phase conjugate mirror with fanning in BTO,” Opt. Commun. 89, 380–384 (1992).

P. Gunter, E. Voit, and M. Zha, “Self-pulsation and optical chaos in self-pumped photorefractive BaTiO3,” Opt. Commun. 55, 210–214 (1985).

A. Smout, R. Eason, and M. Gower, “Regular oscillations and self-pulsating in self-pumped BaTiO3,” Opt. Commun. 59, 77–82 (1986).

P. Banerjee and R. Misra, “Dependence of photorefractive beam fanning on beam parameters,” Opt. Commun. 100, 166–172 (1993).

M. Segev, Y. Ophir, and B. Fischer, “Nonlinear multi two-wave mixing, the fanning process and its bleaching in photorefractive media,” Opt. Commun. 77, 265–274 (1990).

Opt. Eng. (1)

K. Kamra and K. Singh, “Characterization of beam fanning in BaTiO3 under biasing illumination and its application as log processor,” Opt. Eng. 34, 2266–2273 (1995).

Opt. Lett. (4)

Opt. Mater. (1)

A. Kamshilin, H. Tuovinen, V. Prokoviev, and T. Jaaskelainen, “Phase conjugate mirrors on the base of BiTiO20 photorefractive fibre,” Opt. Mater. 4, 399–403 (1995).

Phys. Rev. A (2)

G. Montemezzani, A. A. Zozulya, L. Czaia, D. Z. Anderson, M. Zgonik, and P. Gunter, “Origin of the lobe structure in photorefractive beam fanning,” Phys. Rev. A 52, 1791–1794 (1995).

A. Zozulya and D. Anderson, “Spatial structure of light and a nonlinear refractive index generated by fanning in photorefractive media,” Phys. Rev. A 52, 878–881 (1995).

Phys. Rev. Lett. (1)

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Proc. SPIE (1)

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Other (3)

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Ref. 20, “Wave mixing in photorefractive media,” pp. 118–182.

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