Abstract

Previous theoretical models for linear and ring self-pumped phase-conjugate mirrors are reviewed and modified to include the effects of linear absorption. The nonlinear photorefractive response at high modulation depths, present when large electric fields are applied in semiconductor and sillenite materials, is included in the coupled wave equations for the ring mirror, and the equations are solved numerically. Results of the analysis show that phase-conjugate reflectivities can be severely limited because of both linear absorption and large-signal effects. The calculations are compared with actual measurements of ring mirrors by using InP and Bi12TiO2o.

© 1992 Optical Society of America

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  1. J. O. White, M. Cronin-Golomb, B. Fisher, A. Yariv, “Coherent oscillation by self-induced gratings in the photorefractive BaTiO3,” Appl. Phys. Lett. 40, 450 (1982).
    [CrossRef]
  2. J. Feinberg, “Self-pumped, continuous-wave phase conjugator using internal reflection,” Opt. Lett. 7, 486 (1982).
    [CrossRef] [PubMed]
  3. M. Cronin-Golomb, B. Fisher, J. O. White, A. Yariv, “Passive phase conjugate mirror based on self-induced oscillation in an optical ring cavity,” Appl. Phys. Lett. 42, 919 (1983).
    [CrossRef]
  4. T. Y. Chang, R. W. Hellwarth, “Optical phase conjugation by backscattering in barium titanate,” Opt. Lett. 10, 408 (1985).
    [CrossRef] [PubMed]
  5. M. Cronin-Golomb, B. Fisher, J. O. White, A. Yariv, “Theory and applications of four-wave mixing in photorefractive media,” IEEE J. Quantum Electron. QE-20, 12 (1984).
    [CrossRef]
  6. P. Günter, J.-P. Huignard, Photorefractive Materials and Their Applications II(Springer-Verlag, New York, 1989), Chap. 5.
  7. R. B. Bylsma, A. M. Glass, D. H. Olson, M. Cronin-Golomb, “Self-pumped phase conjugation in InP:Fe,” Appl. Phys. Lett. 54, 1968 (1989).
    [CrossRef]
  8. P. L. Chua, D. T. H. Liu, L. J. Cheng, “Self-pumped and double phase conjugation in GaAs with applied dc electric field,” Appl. Phys. Lett. 57, 858 (1990).
    [CrossRef]
  9. S. Sochava, S. Stepanov, M. Petrov “Ring oscillator using a photorefractive Bi12TiO20crystal,” Sov. Tech. Phys. Lett. 13, 274 (1988).
  10. J. E. Millerd, E. M. Garmire, M. B. Klein, “Self-pumped phase conjugation in InP:Fe using band-edge resonance and temperature stabilization: theory and experiments.” Opt. Lett. 17, 100 (1992).
    [CrossRef] [PubMed]
  11. N. Wolffer, P. Gravey, J. Y. Moisan, C. Laulan, J. C. Launay, “Analysis of double pumped phase conjugate mirror interaction in absorbing photorefractive crystals: applications to BGO:Cu,” Opt. Commun. 73, 351 (1989).
    [CrossRef]
  12. G. Picoli, P. Gravey, C. Ozkul, V. Vieux, “Theory of two wave mixing gain enhancement in photorefractive InP:Fe: a new mechanism of resonance,” J. Appl. Phys. 66, 3789 (1989).
    [CrossRef]
  13. C. Gu, P. Yeh, “Reciprocity in photorefractive wave mixing,” Opt. Lett. 16, 455 (1991).
    [CrossRef] [PubMed]
  14. J. E. Millerd, S. D. Koehler, E. M. Garmire, A. Partovi, A. M. Glass, M. B. Klein, “Photorefractive gain enhancement in InP: Fe using band edge resonance and temperature stabilization,” Appl. Phys. Lett. 57, 2776 (1990).
    [CrossRef]
  15. M. Cronin-Golomb, “Almost all transmission grating self-pumped phase conjugate mirrors are equivalent,” Opt. Lett. 15, 897 (1990).
    [CrossRef] [PubMed]
  16. Ph. Refregier, L. Solymar, H. Rajbenbach, J. P. Huignard, “Two beam coupling in photorefractive Bi12SiO20crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45 (1985).
    [CrossRef]
  17. B. Imbert, H. Rajbenbach, S. Mallick, J. P. Herriau, J. P. Huignard, “High photorefractive gain in two-beam coupling with moving fringes in GaAs:Cr crystals,” Opt. Lett. 13, 327 (1988).
    [CrossRef] [PubMed]
  18. J. Millerd, E. M. Garmire, M. B. Klein, B. A. Wechsler, F. P. Strohkendl, G. A. Brost, “Photorefractive response at high modulation depths in Bi12TiO20,” J. Opt. Soc. Am. B 9, 1449 (1992).
    [CrossRef]
  19. E. Ochoa, F. Vachss, L. Hesselink, “Higher-order analysis of the photorefractive effect for large modulation depths,” J. Opt. Soc. Am. A 3, 181, (1986).
    [CrossRef]
  20. F. Vachss, L. Hesselink, “Nonlinear photorefractive response at high-modulation depths,” J. Opt. Soc. Am. A 5, 690 (1988).
    [CrossRef]
  21. L. B. Au, L. Solymar, “Higher harmonic gratings in photorefractive materials at large modulation with moving fringes,” J. Opt. Soc. Am. A 7, 1554 (1990).
    [CrossRef]
  22. G. A. Swinburne, T. J. Hall, A. K. Powell, “Large modulation effects in photorefractive crystals,” in Proceedings of the International Conference on Holographic Systems, Components and Applications (Institution of Electrical Engineers, London, 1989), p. 175.
  23. A. Partovi, E. M. Garmire, “Band-edge photorefractivity in semiconductors: theory and experiment,” J. Appl. Phys. 69, 6885 (1991).
    [CrossRef]
  24. J. P. Wilde, L. Hesselink, S. W. McCahon, M. B. Klein, D. Rytz, B. A. Wechsler, “Measurement of electro-optic and electrogyratory effects in Bi12TiO20,” J. Appl. Phys. 67, 2245 (1990).
    [CrossRef]
  25. N. Wolffer, P. Gravey, G. Picoli, V. Vieux, “Double phase conjugate mirror and double color pumped oscillator band edge photorefractivity in InP:Fe,” Photorefractive Materials, Effects, and Devices, Vol. 14 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper WA3.

1992 (2)

1991 (2)

C. Gu, P. Yeh, “Reciprocity in photorefractive wave mixing,” Opt. Lett. 16, 455 (1991).
[CrossRef] [PubMed]

A. Partovi, E. M. Garmire, “Band-edge photorefractivity in semiconductors: theory and experiment,” J. Appl. Phys. 69, 6885 (1991).
[CrossRef]

1990 (5)

J. P. Wilde, L. Hesselink, S. W. McCahon, M. B. Klein, D. Rytz, B. A. Wechsler, “Measurement of electro-optic and electrogyratory effects in Bi12TiO20,” J. Appl. Phys. 67, 2245 (1990).
[CrossRef]

L. B. Au, L. Solymar, “Higher harmonic gratings in photorefractive materials at large modulation with moving fringes,” J. Opt. Soc. Am. A 7, 1554 (1990).
[CrossRef]

J. E. Millerd, S. D. Koehler, E. M. Garmire, A. Partovi, A. M. Glass, M. B. Klein, “Photorefractive gain enhancement in InP: Fe using band edge resonance and temperature stabilization,” Appl. Phys. Lett. 57, 2776 (1990).
[CrossRef]

M. Cronin-Golomb, “Almost all transmission grating self-pumped phase conjugate mirrors are equivalent,” Opt. Lett. 15, 897 (1990).
[CrossRef] [PubMed]

P. L. Chua, D. T. H. Liu, L. J. Cheng, “Self-pumped and double phase conjugation in GaAs with applied dc electric field,” Appl. Phys. Lett. 57, 858 (1990).
[CrossRef]

1989 (3)

R. B. Bylsma, A. M. Glass, D. H. Olson, M. Cronin-Golomb, “Self-pumped phase conjugation in InP:Fe,” Appl. Phys. Lett. 54, 1968 (1989).
[CrossRef]

N. Wolffer, P. Gravey, J. Y. Moisan, C. Laulan, J. C. Launay, “Analysis of double pumped phase conjugate mirror interaction in absorbing photorefractive crystals: applications to BGO:Cu,” Opt. Commun. 73, 351 (1989).
[CrossRef]

G. Picoli, P. Gravey, C. Ozkul, V. Vieux, “Theory of two wave mixing gain enhancement in photorefractive InP:Fe: a new mechanism of resonance,” J. Appl. Phys. 66, 3789 (1989).
[CrossRef]

1988 (3)

1986 (1)

1985 (2)

Ph. Refregier, L. Solymar, H. Rajbenbach, J. P. Huignard, “Two beam coupling in photorefractive Bi12SiO20crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45 (1985).
[CrossRef]

T. Y. Chang, R. W. Hellwarth, “Optical phase conjugation by backscattering in barium titanate,” Opt. Lett. 10, 408 (1985).
[CrossRef] [PubMed]

1984 (1)

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

1983 (1)

M. Cronin-Golomb, B. Fisher, J. O. White, A. Yariv, “Passive phase conjugate mirror based on self-induced oscillation in an optical ring cavity,” Appl. Phys. Lett. 42, 919 (1983).
[CrossRef]

1982 (2)

J. O. White, M. Cronin-Golomb, B. Fisher, A. Yariv, “Coherent oscillation by self-induced gratings in the photorefractive BaTiO3,” Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

J. Feinberg, “Self-pumped, continuous-wave phase conjugator using internal reflection,” Opt. Lett. 7, 486 (1982).
[CrossRef] [PubMed]

Au, L. B.

Brost, G. A.

Bylsma, R. B.

R. B. Bylsma, A. M. Glass, D. H. Olson, M. Cronin-Golomb, “Self-pumped phase conjugation in InP:Fe,” Appl. Phys. Lett. 54, 1968 (1989).
[CrossRef]

Chang, T. Y.

Cheng, L. J.

P. L. Chua, D. T. H. Liu, L. J. Cheng, “Self-pumped and double phase conjugation in GaAs with applied dc electric field,” Appl. Phys. Lett. 57, 858 (1990).
[CrossRef]

Chua, P. L.

P. L. Chua, D. T. H. Liu, L. J. Cheng, “Self-pumped and double phase conjugation in GaAs with applied dc electric field,” Appl. Phys. Lett. 57, 858 (1990).
[CrossRef]

Cronin-Golomb, M.

M. Cronin-Golomb, “Almost all transmission grating self-pumped phase conjugate mirrors are equivalent,” Opt. Lett. 15, 897 (1990).
[CrossRef] [PubMed]

R. B. Bylsma, A. M. Glass, D. H. Olson, M. Cronin-Golomb, “Self-pumped phase conjugation in InP:Fe,” Appl. Phys. Lett. 54, 1968 (1989).
[CrossRef]

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

M. Cronin-Golomb, B. Fisher, J. O. White, A. Yariv, “Passive phase conjugate mirror based on self-induced oscillation in an optical ring cavity,” Appl. Phys. Lett. 42, 919 (1983).
[CrossRef]

J. O. White, M. Cronin-Golomb, B. Fisher, A. Yariv, “Coherent oscillation by self-induced gratings in the photorefractive BaTiO3,” Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

Feinberg, J.

Fisher, B.

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

M. Cronin-Golomb, B. Fisher, J. O. White, A. Yariv, “Passive phase conjugate mirror based on self-induced oscillation in an optical ring cavity,” Appl. Phys. Lett. 42, 919 (1983).
[CrossRef]

J. O. White, M. Cronin-Golomb, B. Fisher, A. Yariv, “Coherent oscillation by self-induced gratings in the photorefractive BaTiO3,” Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

Garmire, E. M.

J. E. Millerd, E. M. Garmire, M. B. Klein, “Self-pumped phase conjugation in InP:Fe using band-edge resonance and temperature stabilization: theory and experiments.” Opt. Lett. 17, 100 (1992).
[CrossRef] [PubMed]

J. Millerd, E. M. Garmire, M. B. Klein, B. A. Wechsler, F. P. Strohkendl, G. A. Brost, “Photorefractive response at high modulation depths in Bi12TiO20,” J. Opt. Soc. Am. B 9, 1449 (1992).
[CrossRef]

A. Partovi, E. M. Garmire, “Band-edge photorefractivity in semiconductors: theory and experiment,” J. Appl. Phys. 69, 6885 (1991).
[CrossRef]

J. E. Millerd, S. D. Koehler, E. M. Garmire, A. Partovi, A. M. Glass, M. B. Klein, “Photorefractive gain enhancement in InP: Fe using band edge resonance and temperature stabilization,” Appl. Phys. Lett. 57, 2776 (1990).
[CrossRef]

Glass, A. M.

J. E. Millerd, S. D. Koehler, E. M. Garmire, A. Partovi, A. M. Glass, M. B. Klein, “Photorefractive gain enhancement in InP: Fe using band edge resonance and temperature stabilization,” Appl. Phys. Lett. 57, 2776 (1990).
[CrossRef]

R. B. Bylsma, A. M. Glass, D. H. Olson, M. Cronin-Golomb, “Self-pumped phase conjugation in InP:Fe,” Appl. Phys. Lett. 54, 1968 (1989).
[CrossRef]

Gravey, P.

N. Wolffer, P. Gravey, J. Y. Moisan, C. Laulan, J. C. Launay, “Analysis of double pumped phase conjugate mirror interaction in absorbing photorefractive crystals: applications to BGO:Cu,” Opt. Commun. 73, 351 (1989).
[CrossRef]

G. Picoli, P. Gravey, C. Ozkul, V. Vieux, “Theory of two wave mixing gain enhancement in photorefractive InP:Fe: a new mechanism of resonance,” J. Appl. Phys. 66, 3789 (1989).
[CrossRef]

N. Wolffer, P. Gravey, G. Picoli, V. Vieux, “Double phase conjugate mirror and double color pumped oscillator band edge photorefractivity in InP:Fe,” Photorefractive Materials, Effects, and Devices, Vol. 14 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper WA3.

Gu, C.

Günter, P.

P. Günter, J.-P. Huignard, Photorefractive Materials and Their Applications II(Springer-Verlag, New York, 1989), Chap. 5.

Hall, T. J.

G. A. Swinburne, T. J. Hall, A. K. Powell, “Large modulation effects in photorefractive crystals,” in Proceedings of the International Conference on Holographic Systems, Components and Applications (Institution of Electrical Engineers, London, 1989), p. 175.

Hellwarth, R. W.

Herriau, J. P.

Hesselink, L.

Huignard, J. P.

B. Imbert, H. Rajbenbach, S. Mallick, J. P. Herriau, J. P. Huignard, “High photorefractive gain in two-beam coupling with moving fringes in GaAs:Cr crystals,” Opt. Lett. 13, 327 (1988).
[CrossRef] [PubMed]

Ph. Refregier, L. Solymar, H. Rajbenbach, J. P. Huignard, “Two beam coupling in photorefractive Bi12SiO20crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45 (1985).
[CrossRef]

Huignard, J.-P.

P. Günter, J.-P. Huignard, Photorefractive Materials and Their Applications II(Springer-Verlag, New York, 1989), Chap. 5.

Imbert, B.

Klein, M. B.

J. Millerd, E. M. Garmire, M. B. Klein, B. A. Wechsler, F. P. Strohkendl, G. A. Brost, “Photorefractive response at high modulation depths in Bi12TiO20,” J. Opt. Soc. Am. B 9, 1449 (1992).
[CrossRef]

J. E. Millerd, E. M. Garmire, M. B. Klein, “Self-pumped phase conjugation in InP:Fe using band-edge resonance and temperature stabilization: theory and experiments.” Opt. Lett. 17, 100 (1992).
[CrossRef] [PubMed]

J. E. Millerd, S. D. Koehler, E. M. Garmire, A. Partovi, A. M. Glass, M. B. Klein, “Photorefractive gain enhancement in InP: Fe using band edge resonance and temperature stabilization,” Appl. Phys. Lett. 57, 2776 (1990).
[CrossRef]

J. P. Wilde, L. Hesselink, S. W. McCahon, M. B. Klein, D. Rytz, B. A. Wechsler, “Measurement of electro-optic and electrogyratory effects in Bi12TiO20,” J. Appl. Phys. 67, 2245 (1990).
[CrossRef]

Koehler, S. D.

J. E. Millerd, S. D. Koehler, E. M. Garmire, A. Partovi, A. M. Glass, M. B. Klein, “Photorefractive gain enhancement in InP: Fe using band edge resonance and temperature stabilization,” Appl. Phys. Lett. 57, 2776 (1990).
[CrossRef]

Laulan, C.

N. Wolffer, P. Gravey, J. Y. Moisan, C. Laulan, J. C. Launay, “Analysis of double pumped phase conjugate mirror interaction in absorbing photorefractive crystals: applications to BGO:Cu,” Opt. Commun. 73, 351 (1989).
[CrossRef]

Launay, J. C.

N. Wolffer, P. Gravey, J. Y. Moisan, C. Laulan, J. C. Launay, “Analysis of double pumped phase conjugate mirror interaction in absorbing photorefractive crystals: applications to BGO:Cu,” Opt. Commun. 73, 351 (1989).
[CrossRef]

Liu, D. T. H.

P. L. Chua, D. T. H. Liu, L. J. Cheng, “Self-pumped and double phase conjugation in GaAs with applied dc electric field,” Appl. Phys. Lett. 57, 858 (1990).
[CrossRef]

Mallick, S.

McCahon, S. W.

J. P. Wilde, L. Hesselink, S. W. McCahon, M. B. Klein, D. Rytz, B. A. Wechsler, “Measurement of electro-optic and electrogyratory effects in Bi12TiO20,” J. Appl. Phys. 67, 2245 (1990).
[CrossRef]

Millerd, J.

Millerd, J. E.

J. E. Millerd, E. M. Garmire, M. B. Klein, “Self-pumped phase conjugation in InP:Fe using band-edge resonance and temperature stabilization: theory and experiments.” Opt. Lett. 17, 100 (1992).
[CrossRef] [PubMed]

J. E. Millerd, S. D. Koehler, E. M. Garmire, A. Partovi, A. M. Glass, M. B. Klein, “Photorefractive gain enhancement in InP: Fe using band edge resonance and temperature stabilization,” Appl. Phys. Lett. 57, 2776 (1990).
[CrossRef]

Moisan, J. Y.

N. Wolffer, P. Gravey, J. Y. Moisan, C. Laulan, J. C. Launay, “Analysis of double pumped phase conjugate mirror interaction in absorbing photorefractive crystals: applications to BGO:Cu,” Opt. Commun. 73, 351 (1989).
[CrossRef]

Ochoa, E.

Olson, D. H.

R. B. Bylsma, A. M. Glass, D. H. Olson, M. Cronin-Golomb, “Self-pumped phase conjugation in InP:Fe,” Appl. Phys. Lett. 54, 1968 (1989).
[CrossRef]

Ozkul, C.

G. Picoli, P. Gravey, C. Ozkul, V. Vieux, “Theory of two wave mixing gain enhancement in photorefractive InP:Fe: a new mechanism of resonance,” J. Appl. Phys. 66, 3789 (1989).
[CrossRef]

Partovi, A.

A. Partovi, E. M. Garmire, “Band-edge photorefractivity in semiconductors: theory and experiment,” J. Appl. Phys. 69, 6885 (1991).
[CrossRef]

J. E. Millerd, S. D. Koehler, E. M. Garmire, A. Partovi, A. M. Glass, M. B. Klein, “Photorefractive gain enhancement in InP: Fe using band edge resonance and temperature stabilization,” Appl. Phys. Lett. 57, 2776 (1990).
[CrossRef]

Petrov, M.

S. Sochava, S. Stepanov, M. Petrov “Ring oscillator using a photorefractive Bi12TiO20crystal,” Sov. Tech. Phys. Lett. 13, 274 (1988).

Picoli, G.

G. Picoli, P. Gravey, C. Ozkul, V. Vieux, “Theory of two wave mixing gain enhancement in photorefractive InP:Fe: a new mechanism of resonance,” J. Appl. Phys. 66, 3789 (1989).
[CrossRef]

N. Wolffer, P. Gravey, G. Picoli, V. Vieux, “Double phase conjugate mirror and double color pumped oscillator band edge photorefractivity in InP:Fe,” Photorefractive Materials, Effects, and Devices, Vol. 14 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper WA3.

Powell, A. K.

G. A. Swinburne, T. J. Hall, A. K. Powell, “Large modulation effects in photorefractive crystals,” in Proceedings of the International Conference on Holographic Systems, Components and Applications (Institution of Electrical Engineers, London, 1989), p. 175.

Rajbenbach, H.

B. Imbert, H. Rajbenbach, S. Mallick, J. P. Herriau, J. P. Huignard, “High photorefractive gain in two-beam coupling with moving fringes in GaAs:Cr crystals,” Opt. Lett. 13, 327 (1988).
[CrossRef] [PubMed]

Ph. Refregier, L. Solymar, H. Rajbenbach, J. P. Huignard, “Two beam coupling in photorefractive Bi12SiO20crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45 (1985).
[CrossRef]

Refregier, Ph.

Ph. Refregier, L. Solymar, H. Rajbenbach, J. P. Huignard, “Two beam coupling in photorefractive Bi12SiO20crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45 (1985).
[CrossRef]

Rytz, D.

J. P. Wilde, L. Hesselink, S. W. McCahon, M. B. Klein, D. Rytz, B. A. Wechsler, “Measurement of electro-optic and electrogyratory effects in Bi12TiO20,” J. Appl. Phys. 67, 2245 (1990).
[CrossRef]

Sochava, S.

S. Sochava, S. Stepanov, M. Petrov “Ring oscillator using a photorefractive Bi12TiO20crystal,” Sov. Tech. Phys. Lett. 13, 274 (1988).

Solymar, L.

L. B. Au, L. Solymar, “Higher harmonic gratings in photorefractive materials at large modulation with moving fringes,” J. Opt. Soc. Am. A 7, 1554 (1990).
[CrossRef]

Ph. Refregier, L. Solymar, H. Rajbenbach, J. P. Huignard, “Two beam coupling in photorefractive Bi12SiO20crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45 (1985).
[CrossRef]

Stepanov, S.

S. Sochava, S. Stepanov, M. Petrov “Ring oscillator using a photorefractive Bi12TiO20crystal,” Sov. Tech. Phys. Lett. 13, 274 (1988).

Strohkendl, F. P.

Swinburne, G. A.

G. A. Swinburne, T. J. Hall, A. K. Powell, “Large modulation effects in photorefractive crystals,” in Proceedings of the International Conference on Holographic Systems, Components and Applications (Institution of Electrical Engineers, London, 1989), p. 175.

Vachss, F.

Vieux, V.

G. Picoli, P. Gravey, C. Ozkul, V. Vieux, “Theory of two wave mixing gain enhancement in photorefractive InP:Fe: a new mechanism of resonance,” J. Appl. Phys. 66, 3789 (1989).
[CrossRef]

N. Wolffer, P. Gravey, G. Picoli, V. Vieux, “Double phase conjugate mirror and double color pumped oscillator band edge photorefractivity in InP:Fe,” Photorefractive Materials, Effects, and Devices, Vol. 14 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper WA3.

Wechsler, B. A.

J. Millerd, E. M. Garmire, M. B. Klein, B. A. Wechsler, F. P. Strohkendl, G. A. Brost, “Photorefractive response at high modulation depths in Bi12TiO20,” J. Opt. Soc. Am. B 9, 1449 (1992).
[CrossRef]

J. P. Wilde, L. Hesselink, S. W. McCahon, M. B. Klein, D. Rytz, B. A. Wechsler, “Measurement of electro-optic and electrogyratory effects in Bi12TiO20,” J. Appl. Phys. 67, 2245 (1990).
[CrossRef]

White, J. O.

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

M. Cronin-Golomb, B. Fisher, J. O. White, A. Yariv, “Passive phase conjugate mirror based on self-induced oscillation in an optical ring cavity,” Appl. Phys. Lett. 42, 919 (1983).
[CrossRef]

J. O. White, M. Cronin-Golomb, B. Fisher, A. Yariv, “Coherent oscillation by self-induced gratings in the photorefractive BaTiO3,” Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

Wilde, J. P.

J. P. Wilde, L. Hesselink, S. W. McCahon, M. B. Klein, D. Rytz, B. A. Wechsler, “Measurement of electro-optic and electrogyratory effects in Bi12TiO20,” J. Appl. Phys. 67, 2245 (1990).
[CrossRef]

Wolffer, N.

N. Wolffer, P. Gravey, J. Y. Moisan, C. Laulan, J. C. Launay, “Analysis of double pumped phase conjugate mirror interaction in absorbing photorefractive crystals: applications to BGO:Cu,” Opt. Commun. 73, 351 (1989).
[CrossRef]

N. Wolffer, P. Gravey, G. Picoli, V. Vieux, “Double phase conjugate mirror and double color pumped oscillator band edge photorefractivity in InP:Fe,” Photorefractive Materials, Effects, and Devices, Vol. 14 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper WA3.

Yariv, A.

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

M. Cronin-Golomb, B. Fisher, J. O. White, A. Yariv, “Passive phase conjugate mirror based on self-induced oscillation in an optical ring cavity,” Appl. Phys. Lett. 42, 919 (1983).
[CrossRef]

J. O. White, M. Cronin-Golomb, B. Fisher, A. Yariv, “Coherent oscillation by self-induced gratings in the photorefractive BaTiO3,” Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

Yeh, P.

Appl. Phys. Lett. (5)

J. O. White, M. Cronin-Golomb, B. Fisher, A. Yariv, “Coherent oscillation by self-induced gratings in the photorefractive BaTiO3,” Appl. Phys. Lett. 40, 450 (1982).
[CrossRef]

M. Cronin-Golomb, B. Fisher, J. O. White, A. Yariv, “Passive phase conjugate mirror based on self-induced oscillation in an optical ring cavity,” Appl. Phys. Lett. 42, 919 (1983).
[CrossRef]

R. B. Bylsma, A. M. Glass, D. H. Olson, M. Cronin-Golomb, “Self-pumped phase conjugation in InP:Fe,” Appl. Phys. Lett. 54, 1968 (1989).
[CrossRef]

P. L. Chua, D. T. H. Liu, L. J. Cheng, “Self-pumped and double phase conjugation in GaAs with applied dc electric field,” Appl. Phys. Lett. 57, 858 (1990).
[CrossRef]

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[CrossRef]

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Ph. Refregier, L. Solymar, H. Rajbenbach, J. P. Huignard, “Two beam coupling in photorefractive Bi12SiO20crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45 (1985).
[CrossRef]

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[CrossRef]

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Other (3)

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N. Wolffer, P. Gravey, G. Picoli, V. Vieux, “Double phase conjugate mirror and double color pumped oscillator band edge photorefractivity in InP:Fe,” Photorefractive Materials, Effects, and Devices, Vol. 14 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper WA3.

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Figures (14)

Fig. 1
Fig. 1

Geometry and beam designations for ring and linear self-pumped phase-conjugate mirrors.

Fig. 2
Fig. 2

Theoretical reflectivity of the lossless ring mirror as a function of coupling strength for several values of external mirror reflectivity M.

Fig. 3
Fig. 3

Effects of absorption on the ring mirror reflectivity. The parameter η = α/Γ, the relative amount of absorption; M = 1. The points are illustrative examples plotted using the approximation of Eq. (11) for two cases.

Fig. 4
Fig. 4

Effects of absorption on the linear self-pumped phase-conjugate mirror reflectivity; M = 1.

Fig. 5
Fig. 5

Reflectivity of the ring mirror for various degrees of large-signal effects. The empirical fitting parameter, af, indicates the magnitude of large-signal effects; M = 1.

Fig. 6
Fig. 6

Combination of large-signal effects and linear absorption on the reflectivity of the ring mirror for the case of af = 4 and M = 1.

Fig. 7
Fig. 7

Combination of large-signal effects and linear absorption on the reflectivity of the ring mirror for the case of af = 6 and M = 1.

Fig. 8
Fig. 8

Gain coefficient versus incident intensity for two-wave mixing in two InP samples maintained at constant temperature. T = 20°C; applied field E0 = 10 kV/cm; ratio of pump to signal intensity β = 106; grating period Λ = 7.7 μm; Λ = 8 μm; λ= 970 nm; α = 5 cm−1.

Fig. 9
Fig. 9

Two-wave mixing gain as a function of input-beam ratio: total intensity is 32 mW/cm2; T = 20°C; E0 = 10 kV/cm; λ = 970 nm; L = 4 mm. The circles are experimental results; the bold curve is a theoretical fit with Γsat = 18.5 cm−1 and a = 3.7; the thin curve is the falloff expected from pump depletion alone.

Fig. 10
Fig. 10

Grating spacing dependence of the saturated gain coefficient, Γsat, and the magnitude of the large-signal effects, af. T = 20°C; E0 = 10 kV/cm; λ = 970 nm; L = 4 mm. Curves are guides for the eye.

Fig. 11
Fig. 11

Theoretical and measured reflectivity in a ring mirror using InP near the band edge. T = 20°C; λ = 970 nm; L = 4 mm; Λ = 7.7 μm. The coupling strength was changed by reducing the applied voltage incrementally from 10 to 8.25 kV/cm.

Fig. 12
Fig. 12

Measured reflectivity from the ring mirror as a function of input intensity. Same parameters as in Fig. 11; E0 = 10 kV/cm.

Fig. 13
Fig. 13

Calculated reflectivity for the ring mirror as a function of grating spacing for data from Fig. 10. The square is the maximum measured reflectivity, shown also in Fig. 11. The curve is drawn as a guide to the eye; deviations come from data.

Fig. 14
Fig. 14

Theoretical and measured reflectivity in a ring mirror using BTO with 60-Hz ac fields. E0 = 10 kV/cm; λ = 633 nm; L = 1.37 mm; Λ = 5.5 μm. Coupling strength was changed by reducing the applied voltage from 10 to 7.2 kV/cm.

Equations (17)

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d A 1 d r = γ m 2 A 4 α 2 A 1 ,
d A 2 * d r = γ m 2 A 3 * + α 2 A 2 * ,
d A 3 d r = + γ m 2 A 2 + α 2 A 3 ,
d A 4 * d r = + γ m 2 A 1 * α 2 A 4 * ,
γ = i π n 0 3 r eff E sc m λ cos θ exp ( i Φ sc ) ,
m = 2 ( A 1 A 4 * + A 2 * A 3 ) / I 0 .
I 2 + I 3 I 1 I 4 = Δ , A 1 A 2 + A 3 A 4 = C / 2 , A 1 A 3 * + A 2 A 4 * = D / 2 ,
exp [ Γ L 2 I 0 ( Δ 2 + C 2 ) 1 / 2 ] = [ C * A 34 ( 0 ) + Δ + ( Δ 2 + C 2 ) 1 / 2 C * A 34 ( 0 ) + Δ ( Δ 2 + C 2 ) 1 / 2 ] × [ C * A 34 ( L ) + Δ ( Δ 2 + C 2 ) 1 / 2 C * A 34 ( L ) + Δ + ( Δ 2 + C 2 ) 1 / 2 ] ,
exp [ Γ L 2 I 0 ( Δ 2 + C 2 ) 1 / 2 ] = [ C * A 12 ( 0 ) Δ + ( Δ 2 + C 2 ) 1 / 2 C * A 12 ( 0 ) Δ ( Δ 2 + C 2 ) 1 / 2 ] × [ C * A 12 ( L ) Δ ( Δ 2 + C 2 ) 1 / 2 C * A 12 ( L ) Δ + ( Δ 2 + C 2 ) 1 / 2 ] .
I 4 ( 0 ) / I 2 ( 0 ) = M , I 1 ( 0 ) / I 3 ( 0 ) = M ,
Δ = M 1 M + 1 , A 12 ( L ) = C 2 I 2 ( L ) .
Γ L = 2 ( M + 1 ) M 1 ln ( M + 1 2 M ) .
A 12 2 ( 0 ) = M 1 , A 12 2 ( L ) = 1 / M 2 .
Γ L = ln M ,
η = α / Γ ,
M = M 1 M 2 exp ( 2 η Γ L ) .
I m ( E sc ) f ( m ) = 1 a f [ 1 exp ( a f m ) ] ,

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