Abstract

We investigate the transverse and longitudinal modes of a resonator consisting of a spherical mirror, a Gaussian aperture, and a dispersive phase-conjugate mirror (PCM). The photorefractive PCM introduces spatial dispersion in the form of lateral and focal shifts along with temporal dispersion. For both degenerate and nondegenerate operation, the decentered Gaussian beam was found to be a mode whose peak intensity is displaced from the resonator axis. In the nondegenerate case, the components of a mode oscillating at a pair of frequencies that are up and down shifted from the pump frequency by the same amount have different spatial distributions, so that the intensity pattern moves periodically across the output mirror. The resonance frequencies of the longitudinal modes are calculated numerically.

© 1997 Optical Society of America

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  1. P. A. Belanger, A. Hardy, A. E. Siegman, “Resonant modes of optical cavities with phase-conjugate mirrors,” Appl. Opt. 19, 602–609 (1980).
    [CrossRef] [PubMed]
  2. P. A. Belanger, A. Hardy, A. E. Siegman, “Resonant modes of optical cavities with phase-conjugate mirrors: higher-order modes,” Appl. Opt. 19, 479–481 (1980).
    [CrossRef]
  3. J. F. Lam, W. P. Brown, “Optical resonators with phase-conjugate mirrors,” Opt. Lett. 5, 61–63 (1980).
    [CrossRef] [PubMed]
  4. J. Auyeung, D. Fekete, D. M. Pepper, A. Yariv, “A theoretical and experimental investigation of the modes of optical resonators with phase-conjugate mirrors,” IEEE J. Quantum Electron. QE-15, 1180–1188 (1979).
    [CrossRef]
  5. I. M. Bel’dyugin, E. M. Zemskov, “Theory of resonators with wavefront-reversing mirrors,” Sov. J. Quantum Electron. 9, 1198–1199 (1979).
    [CrossRef]
  6. I. M. Bel’dyugin, M. G. Galushkin, E. M. Zemskov, “Properties of resonators with wavefront-reversing mirrors,” Sov. J. Quantum Electron. 9, 20–23 (1979).
    [CrossRef]
  7. I. M. Bel’dyugin, E. M. Zemskov, “Calculation of the field in a laser resonator with a wavefront-reversing mirror,” Sov. J. Quantum Electron. 10, 764–765 (1980).
    [CrossRef]
  8. M. G. Reznikow, A. I. Khizhnyak, “Properties of a resonator with a wavefront-reversing mirror,” Sov. J. Quantum Electron. 10, 633–634 (1980).
    [CrossRef]
  9. I. M. Bel’dyugin, B. Ya. Zel’dovich, M. V. Zolotarev, V. V. Shkunov, “Lasers with wavefront-reversing mirrors (review),” Sov. J. Quantum Electron. 15, 1583–1597 (1985).
    [CrossRef]
  10. A. Hardy, S. Hochhauser, “Higher-order modes of phase-conjugate resonators,” Appl. Opt. 21, 2330–2338 (1982).
    [CrossRef] [PubMed]
  11. P. A. Belanger, C. Pare, M. Piche, “Modes of phase-conjugate resonators with bounded mirrors,” J. Opt. Soc. Am. 73, 567–571 (1983).
    [CrossRef]
  12. A. Hardy, S. Hochhauser, “Phase-conjugate resonators with intracavity amplitude perturbations,” Appl. Opt. 21, 1118–1121 (1982).
    [CrossRef] [PubMed]
  13. A. Hardy, “Sensitivity of phase-conjugate resonators to intracavity phase perturbations,” IEEE J. Quantum Electron. QE-17, 1581–1585 (1981).
    [CrossRef]
  14. G. C. Valley, D. Fink, “Three-dimensional phase-conjugate-resonator performance,” J. Opt. Soc. Am. 73, 572–575 (1983).
    [CrossRef]
  15. M. Cronin-Golomb, B. Fischer, J. Nilsen, J. O. White, A. Yariv, “Laser with dynamic holographic intracavity distortion correction capability,” Appl. Phys. Lett. 41, 219–220 (1982).
    [CrossRef]
  16. R. C. Lind, D. G. Steel, “Demonstration of the longitudinal modes and aberration-correction properties of a continuous-wave dye laser with a phase-conjugate mirror,” Opt. Lett. 6, 554–556 (1981).
    [CrossRef] [PubMed]
  17. J. Feinberg, R. W. Hellwarth, “Phase-conjugating mirror with continuous-wave gain,” Opt. Lett. 5, 519–521 (1980).
    [CrossRef] [PubMed]
  18. R. K. Jain, G. J. Dunning, “Spatial and temporal properties of a continuous-wave phase-conjugate resonator based on the photorefractive crystal BaTiO3,” Opt. Lett. 7, 420–422 (1982).
    [CrossRef] [PubMed]
  19. M. B. Klein, G. L. Dunning, G. C. Valley, R. C. Lind, T. R. O’Meara, “Imaging threshold detector using a phase-conjugate resonator in BaTiO3,” Opt. Lett. 11, 575–577 (1986).
    [CrossRef] [PubMed]
  20. K. P. Lo, G. Indebetouw, “Iterative image processing using a cavity with a phase-conjugate mirror,” Appl. Opt. 31, 1745–1753 (1992).
    [CrossRef] [PubMed]
  21. L. E. Adams, R. S. Bondurant, “Adaptive spatially injection-locked heterodyne receiver,” Opt. Lett. 18, 226–228 (1993).
    [CrossRef] [PubMed]
  22. A. Yariv, S.-K. Kwong, “Associative memories based on message-bearing optical modes in phase-conjugate resonators,” Opt. Lett. 11, 186–188 (1986).
    [CrossRef] [PubMed]
  23. D. Z. Anderson, M. C. Erie, “Resonator memories and optical novelty filters,” Opt. Eng. 26, 434–444 (1987).
    [CrossRef]
  24. B. H. Soffer, G. J. Dunning, Y. Owechko, E. Marom, “Associative holographic memory with feedback using phase-conjugate mirrors,” Opt. Lett. 11, 118–120 (1986).
    [CrossRef] [PubMed]
  25. A. Desfarges, V. Kermene, B. Colombeau, M. Vampuille, C. Froehly, “Wave-front reconstruction with a Fourier hologram in a phase-conjugating mirror oscillator,” Opt. Lett. 20, 1940–1942 (1995).
    [CrossRef] [PubMed]
  26. A. E. Siegman, Lasers (University Science Books, Mill Valley, Calif., 1986).
  27. H. Kogelnik, T. Li, “Laser beams and resonators,” Appl. Opt. 5, 1550–1567 (1966).
    [CrossRef] [PubMed]
  28. R. A. Fisher, ed., Optical Phase Conjugation (Academic, San Diego, Calif., 1983), Chap. 13.
  29. W. Shaomin, H. Weber, “A spherical resonator equivalent to arbitrary phase-conjugate resonators,” Opt. Commun. 41, 360–362 (1982).
    [CrossRef]
  30. W. Shaomin, H. Weber, “Fundamental modes of stimulated scattering phase-conjugate resonators,” Opt. Acta 31, 971–977 (1984).
    [CrossRef]
  31. S. Umegaki, A. Kurita, S. Tanaka, “Unstable phase-conjugate resonator,” Jpn. J. Appl. Phys. 23, 436–441 (1984).
    [CrossRef]
  32. L. Qiang, L. Xuanhui, W. Shaomin, “Fundamental modes of phase-conjugate resonators with asymmetric Gaussian reflectivities,” Chin. J. Lasers 15, 715–717 (1988).
  33. G. Reiner, P. Meystre, E. M. Wright, “Transverse dynamics of a phase-conjugate resonator. I. Sluggish nonlinear medium,” J. Opt. Soc. Am. B 4, 675–686 (1987).
    [CrossRef]
  34. G. Reiner, M. R. Belic, P. Meystre, “Optical turbulence in phase-conjugate resonators,” J. Opt. Soc. Am. B 5, 1193–1210 (1988).
    [CrossRef]
  35. S. R. Liu, G. Indebetouw, “Spatiotemporal patterns and vortices motions in phase-conjugate resonators,” Opt. Commun. 101, 442–455 (1993).
    [CrossRef]
  36. G. C. Papen, B. E. A. Saleh, J. A. Tataronis, “Analysis of transient phase conjugation in photorefractive media,” J. Opt. Soc. Am. B 5, 1763–1774 (1988).
    [CrossRef]
  37. G. C. Papen, “Transient nonlinear wave mixing in photorefractive materials and plasmas, Ph.D. dissertation (University of Wisconsin, Madison, Wis., 1989).
  38. G. C. Papen, B. E. A. Saleh, “Lateral and focal shift of phase-conjugated beams in photorefractive materials,” Opt. Lett. 14, 745–747 (1989).
    [CrossRef] [PubMed]
  39. L. V. Nosova, “Modes and losses of a misaligned conjugate resonator,” Opt. Spectrosc. 62, 516–518 (1987).
  40. A. A. Kalinina, L. V. Nosova, V. E. Semenov, “Aberration properties of a conjugate resonator,” Sov. J. Quantum Electron. 18, 1282–1283 (1988).
    [CrossRef]
  41. A.-A. R. Al-Rashed, B. E. A. Saleh, “Decentered Gaussian beams,” Appl. Opt. 34, 6819–6825 (1995).
    [CrossRef] [PubMed]
  42. S. R. Liu, G. Indebetouw, “Periodic and chaotic spatiotemporal states in a phase-conjugate resonator using a photorefractive BaTiO3 phase-conjugate mirror,” J. Opt. Soc. Am. B 9, 1507–1520 (1992).
    [CrossRef]
  43. G. Indebetouw, S. R. Liu, “Defect-mediated spatial complexity and chaos in a phase-conjugate resonator,” Opt. Commun. 91, 321–336 (1992).
    [CrossRef]
  44. G. Indebetouw, D. R. Korwan, “Model of vortices nucleation in a photorefractive phase-conjugate resonator,” J. Mod. Opt. 41, 941–950 (1994).
    [CrossRef]
  45. D. R. Korwan, G. Indebetouw, “Effects of phase mismatch on the transverse dynamics of a phase-conjugate resonator at low Fresnel number,” Opt. Commun. 119, 305–312 (1995).
    [CrossRef]
  46. G. C. Valley, G. J. Dunning, “Observation of optical chaos in a phase-conjugate resonator,” Opt. Lett. 9, 513–515 (1984).
    [CrossRef] [PubMed]
  47. M. D. Skeldon, R. W. Boyd, “Transverse-mode structure of a phase-conjugate oscillator based on Brillouin-enhanced four-wave mixing,” IEEE J. Quantum. Electron. QE-25, 588–594 (1989).
    [CrossRef]
  48. M. Gower, D. Proch, eds., Optical Phase Conjugation (Springer-Verlag, New York, 1994), Chap. 8, p. 232.
  49. See, for example, P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993), Chap. 3, p. 93.
  50. L. W. Casperson, “Gaussian light beams in inhomogenous media,” Appl. Opt. 12, 2434–2441 (1973).
    [CrossRef] [PubMed]
  51. Y. Sun, A. E. Siegman, “Optical mode properties of laterally offset gain and index guiding structures,” IEEE J. Quantum Electron. 32, 1–6 (1996).
  52. A. Tovar, L. W. Casperson, “Off-axis complex-argument polynomial-Gaussian beams in optical systems,” J. Opt. Soc. Am. A 8, 60–68 (1991).
    [CrossRef]
  53. See, for example, B. E. A. Saleh, M. Teich, Fundamentals of Photonics (Wiley, New York, 1991), Chap. 3.
  54. R. Trebino, A. E. Siegman, “Phase-conjugate reflection at arbitrary angles using TEM00 pump beams,” Opt. Commun. 32, 1–3 (1980).
    [CrossRef]
  55. P. Gunter, J.-P. Huignard, eds., Photorefractive Materials and Their Applications, I, Vol. 61: Topics in Applied Physics (Springer Verlag, New York, 1988), Chap. 8, p. 238.
  56. M. B. Klein, “Beam coupling in undoped GaAs at 1.06 µm using the photorefractive effect,” Opt. Lett. 9, 350–352 (1984).
    [CrossRef] [PubMed]

1996

Y. Sun, A. E. Siegman, “Optical mode properties of laterally offset gain and index guiding structures,” IEEE J. Quantum Electron. 32, 1–6 (1996).

1995

1994

G. Indebetouw, D. R. Korwan, “Model of vortices nucleation in a photorefractive phase-conjugate resonator,” J. Mod. Opt. 41, 941–950 (1994).
[CrossRef]

1993

L. E. Adams, R. S. Bondurant, “Adaptive spatially injection-locked heterodyne receiver,” Opt. Lett. 18, 226–228 (1993).
[CrossRef] [PubMed]

S. R. Liu, G. Indebetouw, “Spatiotemporal patterns and vortices motions in phase-conjugate resonators,” Opt. Commun. 101, 442–455 (1993).
[CrossRef]

1992

1991

1989

M. D. Skeldon, R. W. Boyd, “Transverse-mode structure of a phase-conjugate oscillator based on Brillouin-enhanced four-wave mixing,” IEEE J. Quantum. Electron. QE-25, 588–594 (1989).
[CrossRef]

G. C. Papen, B. E. A. Saleh, “Lateral and focal shift of phase-conjugated beams in photorefractive materials,” Opt. Lett. 14, 745–747 (1989).
[CrossRef] [PubMed]

1988

G. C. Papen, B. E. A. Saleh, J. A. Tataronis, “Analysis of transient phase conjugation in photorefractive media,” J. Opt. Soc. Am. B 5, 1763–1774 (1988).
[CrossRef]

L. Qiang, L. Xuanhui, W. Shaomin, “Fundamental modes of phase-conjugate resonators with asymmetric Gaussian reflectivities,” Chin. J. Lasers 15, 715–717 (1988).

G. Reiner, M. R. Belic, P. Meystre, “Optical turbulence in phase-conjugate resonators,” J. Opt. Soc. Am. B 5, 1193–1210 (1988).
[CrossRef]

A. A. Kalinina, L. V. Nosova, V. E. Semenov, “Aberration properties of a conjugate resonator,” Sov. J. Quantum Electron. 18, 1282–1283 (1988).
[CrossRef]

1987

G. Reiner, P. Meystre, E. M. Wright, “Transverse dynamics of a phase-conjugate resonator. I. Sluggish nonlinear medium,” J. Opt. Soc. Am. B 4, 675–686 (1987).
[CrossRef]

L. V. Nosova, “Modes and losses of a misaligned conjugate resonator,” Opt. Spectrosc. 62, 516–518 (1987).

D. Z. Anderson, M. C. Erie, “Resonator memories and optical novelty filters,” Opt. Eng. 26, 434–444 (1987).
[CrossRef]

1986

1985

I. M. Bel’dyugin, B. Ya. Zel’dovich, M. V. Zolotarev, V. V. Shkunov, “Lasers with wavefront-reversing mirrors (review),” Sov. J. Quantum Electron. 15, 1583–1597 (1985).
[CrossRef]

1984

W. Shaomin, H. Weber, “Fundamental modes of stimulated scattering phase-conjugate resonators,” Opt. Acta 31, 971–977 (1984).
[CrossRef]

S. Umegaki, A. Kurita, S. Tanaka, “Unstable phase-conjugate resonator,” Jpn. J. Appl. Phys. 23, 436–441 (1984).
[CrossRef]

G. C. Valley, G. J. Dunning, “Observation of optical chaos in a phase-conjugate resonator,” Opt. Lett. 9, 513–515 (1984).
[CrossRef] [PubMed]

M. B. Klein, “Beam coupling in undoped GaAs at 1.06 µm using the photorefractive effect,” Opt. Lett. 9, 350–352 (1984).
[CrossRef] [PubMed]

1983

1982

1981

1980

J. Feinberg, R. W. Hellwarth, “Phase-conjugating mirror with continuous-wave gain,” Opt. Lett. 5, 519–521 (1980).
[CrossRef] [PubMed]

I. M. Bel’dyugin, E. M. Zemskov, “Calculation of the field in a laser resonator with a wavefront-reversing mirror,” Sov. J. Quantum Electron. 10, 764–765 (1980).
[CrossRef]

M. G. Reznikow, A. I. Khizhnyak, “Properties of a resonator with a wavefront-reversing mirror,” Sov. J. Quantum Electron. 10, 633–634 (1980).
[CrossRef]

P. A. Belanger, A. Hardy, A. E. Siegman, “Resonant modes of optical cavities with phase-conjugate mirrors,” Appl. Opt. 19, 602–609 (1980).
[CrossRef] [PubMed]

P. A. Belanger, A. Hardy, A. E. Siegman, “Resonant modes of optical cavities with phase-conjugate mirrors: higher-order modes,” Appl. Opt. 19, 479–481 (1980).
[CrossRef]

J. F. Lam, W. P. Brown, “Optical resonators with phase-conjugate mirrors,” Opt. Lett. 5, 61–63 (1980).
[CrossRef] [PubMed]

R. Trebino, A. E. Siegman, “Phase-conjugate reflection at arbitrary angles using TEM00 pump beams,” Opt. Commun. 32, 1–3 (1980).
[CrossRef]

1979

J. Auyeung, D. Fekete, D. M. Pepper, A. Yariv, “A theoretical and experimental investigation of the modes of optical resonators with phase-conjugate mirrors,” IEEE J. Quantum Electron. QE-15, 1180–1188 (1979).
[CrossRef]

I. M. Bel’dyugin, E. M. Zemskov, “Theory of resonators with wavefront-reversing mirrors,” Sov. J. Quantum Electron. 9, 1198–1199 (1979).
[CrossRef]

I. M. Bel’dyugin, M. G. Galushkin, E. M. Zemskov, “Properties of resonators with wavefront-reversing mirrors,” Sov. J. Quantum Electron. 9, 20–23 (1979).
[CrossRef]

1973

1966

Adams, L. E.

Al-Rashed, A.-A. R.

Anderson, D. Z.

D. Z. Anderson, M. C. Erie, “Resonator memories and optical novelty filters,” Opt. Eng. 26, 434–444 (1987).
[CrossRef]

Auyeung, J.

J. Auyeung, D. Fekete, D. M. Pepper, A. Yariv, “A theoretical and experimental investigation of the modes of optical resonators with phase-conjugate mirrors,” IEEE J. Quantum Electron. QE-15, 1180–1188 (1979).
[CrossRef]

Bel’dyugin, I. M.

I. M. Bel’dyugin, B. Ya. Zel’dovich, M. V. Zolotarev, V. V. Shkunov, “Lasers with wavefront-reversing mirrors (review),” Sov. J. Quantum Electron. 15, 1583–1597 (1985).
[CrossRef]

I. M. Bel’dyugin, E. M. Zemskov, “Calculation of the field in a laser resonator with a wavefront-reversing mirror,” Sov. J. Quantum Electron. 10, 764–765 (1980).
[CrossRef]

I. M. Bel’dyugin, M. G. Galushkin, E. M. Zemskov, “Properties of resonators with wavefront-reversing mirrors,” Sov. J. Quantum Electron. 9, 20–23 (1979).
[CrossRef]

I. M. Bel’dyugin, E. M. Zemskov, “Theory of resonators with wavefront-reversing mirrors,” Sov. J. Quantum Electron. 9, 1198–1199 (1979).
[CrossRef]

Belanger, P. A.

Belic, M. R.

Bondurant, R. S.

Boyd, R. W.

M. D. Skeldon, R. W. Boyd, “Transverse-mode structure of a phase-conjugate oscillator based on Brillouin-enhanced four-wave mixing,” IEEE J. Quantum. Electron. QE-25, 588–594 (1989).
[CrossRef]

Brown, W. P.

Casperson, L. W.

Colombeau, B.

Cronin-Golomb, M.

M. Cronin-Golomb, B. Fischer, J. Nilsen, J. O. White, A. Yariv, “Laser with dynamic holographic intracavity distortion correction capability,” Appl. Phys. Lett. 41, 219–220 (1982).
[CrossRef]

Desfarges, A.

Dunning, G. J.

Dunning, G. L.

Erie, M. C.

D. Z. Anderson, M. C. Erie, “Resonator memories and optical novelty filters,” Opt. Eng. 26, 434–444 (1987).
[CrossRef]

Feinberg, J.

Fekete, D.

J. Auyeung, D. Fekete, D. M. Pepper, A. Yariv, “A theoretical and experimental investigation of the modes of optical resonators with phase-conjugate mirrors,” IEEE J. Quantum Electron. QE-15, 1180–1188 (1979).
[CrossRef]

Fink, D.

Fischer, B.

M. Cronin-Golomb, B. Fischer, J. Nilsen, J. O. White, A. Yariv, “Laser with dynamic holographic intracavity distortion correction capability,” Appl. Phys. Lett. 41, 219–220 (1982).
[CrossRef]

Froehly, C.

Galushkin, M. G.

I. M. Bel’dyugin, M. G. Galushkin, E. M. Zemskov, “Properties of resonators with wavefront-reversing mirrors,” Sov. J. Quantum Electron. 9, 20–23 (1979).
[CrossRef]

Hardy, A.

Hellwarth, R. W.

Hochhauser, S.

Indebetouw, G.

D. R. Korwan, G. Indebetouw, “Effects of phase mismatch on the transverse dynamics of a phase-conjugate resonator at low Fresnel number,” Opt. Commun. 119, 305–312 (1995).
[CrossRef]

G. Indebetouw, D. R. Korwan, “Model of vortices nucleation in a photorefractive phase-conjugate resonator,” J. Mod. Opt. 41, 941–950 (1994).
[CrossRef]

S. R. Liu, G. Indebetouw, “Spatiotemporal patterns and vortices motions in phase-conjugate resonators,” Opt. Commun. 101, 442–455 (1993).
[CrossRef]

S. R. Liu, G. Indebetouw, “Periodic and chaotic spatiotemporal states in a phase-conjugate resonator using a photorefractive BaTiO3 phase-conjugate mirror,” J. Opt. Soc. Am. B 9, 1507–1520 (1992).
[CrossRef]

G. Indebetouw, S. R. Liu, “Defect-mediated spatial complexity and chaos in a phase-conjugate resonator,” Opt. Commun. 91, 321–336 (1992).
[CrossRef]

K. P. Lo, G. Indebetouw, “Iterative image processing using a cavity with a phase-conjugate mirror,” Appl. Opt. 31, 1745–1753 (1992).
[CrossRef] [PubMed]

Jain, R. K.

Kalinina, A. A.

A. A. Kalinina, L. V. Nosova, V. E. Semenov, “Aberration properties of a conjugate resonator,” Sov. J. Quantum Electron. 18, 1282–1283 (1988).
[CrossRef]

Kermene, V.

Khizhnyak, A. I.

M. G. Reznikow, A. I. Khizhnyak, “Properties of a resonator with a wavefront-reversing mirror,” Sov. J. Quantum Electron. 10, 633–634 (1980).
[CrossRef]

Klein, M. B.

Kogelnik, H.

Korwan, D. R.

D. R. Korwan, G. Indebetouw, “Effects of phase mismatch on the transverse dynamics of a phase-conjugate resonator at low Fresnel number,” Opt. Commun. 119, 305–312 (1995).
[CrossRef]

G. Indebetouw, D. R. Korwan, “Model of vortices nucleation in a photorefractive phase-conjugate resonator,” J. Mod. Opt. 41, 941–950 (1994).
[CrossRef]

Kurita, A.

S. Umegaki, A. Kurita, S. Tanaka, “Unstable phase-conjugate resonator,” Jpn. J. Appl. Phys. 23, 436–441 (1984).
[CrossRef]

Kwong, S.-K.

Lam, J. F.

Li, T.

Lind, R. C.

Liu, S. R.

S. R. Liu, G. Indebetouw, “Spatiotemporal patterns and vortices motions in phase-conjugate resonators,” Opt. Commun. 101, 442–455 (1993).
[CrossRef]

G. Indebetouw, S. R. Liu, “Defect-mediated spatial complexity and chaos in a phase-conjugate resonator,” Opt. Commun. 91, 321–336 (1992).
[CrossRef]

S. R. Liu, G. Indebetouw, “Periodic and chaotic spatiotemporal states in a phase-conjugate resonator using a photorefractive BaTiO3 phase-conjugate mirror,” J. Opt. Soc. Am. B 9, 1507–1520 (1992).
[CrossRef]

Lo, K. P.

Marom, E.

Meystre, P.

Nilsen, J.

M. Cronin-Golomb, B. Fischer, J. Nilsen, J. O. White, A. Yariv, “Laser with dynamic holographic intracavity distortion correction capability,” Appl. Phys. Lett. 41, 219–220 (1982).
[CrossRef]

Nosova, L. V.

A. A. Kalinina, L. V. Nosova, V. E. Semenov, “Aberration properties of a conjugate resonator,” Sov. J. Quantum Electron. 18, 1282–1283 (1988).
[CrossRef]

L. V. Nosova, “Modes and losses of a misaligned conjugate resonator,” Opt. Spectrosc. 62, 516–518 (1987).

O’Meara, T. R.

Owechko, Y.

Papen, G. C.

Pare, C.

Pepper, D. M.

J. Auyeung, D. Fekete, D. M. Pepper, A. Yariv, “A theoretical and experimental investigation of the modes of optical resonators with phase-conjugate mirrors,” IEEE J. Quantum Electron. QE-15, 1180–1188 (1979).
[CrossRef]

Piche, M.

Qiang, L.

L. Qiang, L. Xuanhui, W. Shaomin, “Fundamental modes of phase-conjugate resonators with asymmetric Gaussian reflectivities,” Chin. J. Lasers 15, 715–717 (1988).

Reiner, G.

Reznikow, M. G.

M. G. Reznikow, A. I. Khizhnyak, “Properties of a resonator with a wavefront-reversing mirror,” Sov. J. Quantum Electron. 10, 633–634 (1980).
[CrossRef]

Saleh, B. E. A.

Semenov, V. E.

A. A. Kalinina, L. V. Nosova, V. E. Semenov, “Aberration properties of a conjugate resonator,” Sov. J. Quantum Electron. 18, 1282–1283 (1988).
[CrossRef]

Shaomin, W.

L. Qiang, L. Xuanhui, W. Shaomin, “Fundamental modes of phase-conjugate resonators with asymmetric Gaussian reflectivities,” Chin. J. Lasers 15, 715–717 (1988).

W. Shaomin, H. Weber, “Fundamental modes of stimulated scattering phase-conjugate resonators,” Opt. Acta 31, 971–977 (1984).
[CrossRef]

W. Shaomin, H. Weber, “A spherical resonator equivalent to arbitrary phase-conjugate resonators,” Opt. Commun. 41, 360–362 (1982).
[CrossRef]

Shkunov, V. V.

I. M. Bel’dyugin, B. Ya. Zel’dovich, M. V. Zolotarev, V. V. Shkunov, “Lasers with wavefront-reversing mirrors (review),” Sov. J. Quantum Electron. 15, 1583–1597 (1985).
[CrossRef]

Siegman, A. E.

Y. Sun, A. E. Siegman, “Optical mode properties of laterally offset gain and index guiding structures,” IEEE J. Quantum Electron. 32, 1–6 (1996).

R. Trebino, A. E. Siegman, “Phase-conjugate reflection at arbitrary angles using TEM00 pump beams,” Opt. Commun. 32, 1–3 (1980).
[CrossRef]

P. A. Belanger, A. Hardy, A. E. Siegman, “Resonant modes of optical cavities with phase-conjugate mirrors,” Appl. Opt. 19, 602–609 (1980).
[CrossRef] [PubMed]

P. A. Belanger, A. Hardy, A. E. Siegman, “Resonant modes of optical cavities with phase-conjugate mirrors: higher-order modes,” Appl. Opt. 19, 479–481 (1980).
[CrossRef]

A. E. Siegman, Lasers (University Science Books, Mill Valley, Calif., 1986).

Skeldon, M. D.

M. D. Skeldon, R. W. Boyd, “Transverse-mode structure of a phase-conjugate oscillator based on Brillouin-enhanced four-wave mixing,” IEEE J. Quantum. Electron. QE-25, 588–594 (1989).
[CrossRef]

Soffer, B. H.

Steel, D. G.

Sun, Y.

Y. Sun, A. E. Siegman, “Optical mode properties of laterally offset gain and index guiding structures,” IEEE J. Quantum Electron. 32, 1–6 (1996).

Tanaka, S.

S. Umegaki, A. Kurita, S. Tanaka, “Unstable phase-conjugate resonator,” Jpn. J. Appl. Phys. 23, 436–441 (1984).
[CrossRef]

Tataronis, J. A.

Tovar, A.

Trebino, R.

R. Trebino, A. E. Siegman, “Phase-conjugate reflection at arbitrary angles using TEM00 pump beams,” Opt. Commun. 32, 1–3 (1980).
[CrossRef]

Umegaki, S.

S. Umegaki, A. Kurita, S. Tanaka, “Unstable phase-conjugate resonator,” Jpn. J. Appl. Phys. 23, 436–441 (1984).
[CrossRef]

Valley, G. C.

Vampuille, M.

Weber, H.

W. Shaomin, H. Weber, “Fundamental modes of stimulated scattering phase-conjugate resonators,” Opt. Acta 31, 971–977 (1984).
[CrossRef]

W. Shaomin, H. Weber, “A spherical resonator equivalent to arbitrary phase-conjugate resonators,” Opt. Commun. 41, 360–362 (1982).
[CrossRef]

White, J. O.

M. Cronin-Golomb, B. Fischer, J. Nilsen, J. O. White, A. Yariv, “Laser with dynamic holographic intracavity distortion correction capability,” Appl. Phys. Lett. 41, 219–220 (1982).
[CrossRef]

Wright, E. M.

Xuanhui, L.

L. Qiang, L. Xuanhui, W. Shaomin, “Fundamental modes of phase-conjugate resonators with asymmetric Gaussian reflectivities,” Chin. J. Lasers 15, 715–717 (1988).

Yariv, A.

A. Yariv, S.-K. Kwong, “Associative memories based on message-bearing optical modes in phase-conjugate resonators,” Opt. Lett. 11, 186–188 (1986).
[CrossRef] [PubMed]

M. Cronin-Golomb, B. Fischer, J. Nilsen, J. O. White, A. Yariv, “Laser with dynamic holographic intracavity distortion correction capability,” Appl. Phys. Lett. 41, 219–220 (1982).
[CrossRef]

J. Auyeung, D. Fekete, D. M. Pepper, A. Yariv, “A theoretical and experimental investigation of the modes of optical resonators with phase-conjugate mirrors,” IEEE J. Quantum Electron. QE-15, 1180–1188 (1979).
[CrossRef]

Zel’dovich, B. Ya.

I. M. Bel’dyugin, B. Ya. Zel’dovich, M. V. Zolotarev, V. V. Shkunov, “Lasers with wavefront-reversing mirrors (review),” Sov. J. Quantum Electron. 15, 1583–1597 (1985).
[CrossRef]

Zemskov, E. M.

I. M. Bel’dyugin, E. M. Zemskov, “Calculation of the field in a laser resonator with a wavefront-reversing mirror,” Sov. J. Quantum Electron. 10, 764–765 (1980).
[CrossRef]

I. M. Bel’dyugin, M. G. Galushkin, E. M. Zemskov, “Properties of resonators with wavefront-reversing mirrors,” Sov. J. Quantum Electron. 9, 20–23 (1979).
[CrossRef]

I. M. Bel’dyugin, E. M. Zemskov, “Theory of resonators with wavefront-reversing mirrors,” Sov. J. Quantum Electron. 9, 1198–1199 (1979).
[CrossRef]

Zolotarev, M. V.

I. M. Bel’dyugin, B. Ya. Zel’dovich, M. V. Zolotarev, V. V. Shkunov, “Lasers with wavefront-reversing mirrors (review),” Sov. J. Quantum Electron. 15, 1583–1597 (1985).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

M. Cronin-Golomb, B. Fischer, J. Nilsen, J. O. White, A. Yariv, “Laser with dynamic holographic intracavity distortion correction capability,” Appl. Phys. Lett. 41, 219–220 (1982).
[CrossRef]

Chin. J. Lasers

L. Qiang, L. Xuanhui, W. Shaomin, “Fundamental modes of phase-conjugate resonators with asymmetric Gaussian reflectivities,” Chin. J. Lasers 15, 715–717 (1988).

IEEE J. Quantum Electron.

A. Hardy, “Sensitivity of phase-conjugate resonators to intracavity phase perturbations,” IEEE J. Quantum Electron. QE-17, 1581–1585 (1981).
[CrossRef]

J. Auyeung, D. Fekete, D. M. Pepper, A. Yariv, “A theoretical and experimental investigation of the modes of optical resonators with phase-conjugate mirrors,” IEEE J. Quantum Electron. QE-15, 1180–1188 (1979).
[CrossRef]

Y. Sun, A. E. Siegman, “Optical mode properties of laterally offset gain and index guiding structures,” IEEE J. Quantum Electron. 32, 1–6 (1996).

IEEE J. Quantum. Electron.

M. D. Skeldon, R. W. Boyd, “Transverse-mode structure of a phase-conjugate oscillator based on Brillouin-enhanced four-wave mixing,” IEEE J. Quantum. Electron. QE-25, 588–594 (1989).
[CrossRef]

J. Mod. Opt.

G. Indebetouw, D. R. Korwan, “Model of vortices nucleation in a photorefractive phase-conjugate resonator,” J. Mod. Opt. 41, 941–950 (1994).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Jpn. J. Appl. Phys.

S. Umegaki, A. Kurita, S. Tanaka, “Unstable phase-conjugate resonator,” Jpn. J. Appl. Phys. 23, 436–441 (1984).
[CrossRef]

Opt. Acta

W. Shaomin, H. Weber, “Fundamental modes of stimulated scattering phase-conjugate resonators,” Opt. Acta 31, 971–977 (1984).
[CrossRef]

Opt. Commun.

W. Shaomin, H. Weber, “A spherical resonator equivalent to arbitrary phase-conjugate resonators,” Opt. Commun. 41, 360–362 (1982).
[CrossRef]

S. R. Liu, G. Indebetouw, “Spatiotemporal patterns and vortices motions in phase-conjugate resonators,” Opt. Commun. 101, 442–455 (1993).
[CrossRef]

R. Trebino, A. E. Siegman, “Phase-conjugate reflection at arbitrary angles using TEM00 pump beams,” Opt. Commun. 32, 1–3 (1980).
[CrossRef]

G. Indebetouw, S. R. Liu, “Defect-mediated spatial complexity and chaos in a phase-conjugate resonator,” Opt. Commun. 91, 321–336 (1992).
[CrossRef]

D. R. Korwan, G. Indebetouw, “Effects of phase mismatch on the transverse dynamics of a phase-conjugate resonator at low Fresnel number,” Opt. Commun. 119, 305–312 (1995).
[CrossRef]

Opt. Eng.

D. Z. Anderson, M. C. Erie, “Resonator memories and optical novelty filters,” Opt. Eng. 26, 434–444 (1987).
[CrossRef]

Opt. Lett.

B. H. Soffer, G. J. Dunning, Y. Owechko, E. Marom, “Associative holographic memory with feedback using phase-conjugate mirrors,” Opt. Lett. 11, 118–120 (1986).
[CrossRef] [PubMed]

A. Desfarges, V. Kermene, B. Colombeau, M. Vampuille, C. Froehly, “Wave-front reconstruction with a Fourier hologram in a phase-conjugating mirror oscillator,” Opt. Lett. 20, 1940–1942 (1995).
[CrossRef] [PubMed]

G. C. Papen, B. E. A. Saleh, “Lateral and focal shift of phase-conjugated beams in photorefractive materials,” Opt. Lett. 14, 745–747 (1989).
[CrossRef] [PubMed]

L. E. Adams, R. S. Bondurant, “Adaptive spatially injection-locked heterodyne receiver,” Opt. Lett. 18, 226–228 (1993).
[CrossRef] [PubMed]

A. Yariv, S.-K. Kwong, “Associative memories based on message-bearing optical modes in phase-conjugate resonators,” Opt. Lett. 11, 186–188 (1986).
[CrossRef] [PubMed]

R. C. Lind, D. G. Steel, “Demonstration of the longitudinal modes and aberration-correction properties of a continuous-wave dye laser with a phase-conjugate mirror,” Opt. Lett. 6, 554–556 (1981).
[CrossRef] [PubMed]

J. Feinberg, R. W. Hellwarth, “Phase-conjugating mirror with continuous-wave gain,” Opt. Lett. 5, 519–521 (1980).
[CrossRef] [PubMed]

R. K. Jain, G. J. Dunning, “Spatial and temporal properties of a continuous-wave phase-conjugate resonator based on the photorefractive crystal BaTiO3,” Opt. Lett. 7, 420–422 (1982).
[CrossRef] [PubMed]

M. B. Klein, G. L. Dunning, G. C. Valley, R. C. Lind, T. R. O’Meara, “Imaging threshold detector using a phase-conjugate resonator in BaTiO3,” Opt. Lett. 11, 575–577 (1986).
[CrossRef] [PubMed]

J. F. Lam, W. P. Brown, “Optical resonators with phase-conjugate mirrors,” Opt. Lett. 5, 61–63 (1980).
[CrossRef] [PubMed]

G. C. Valley, G. J. Dunning, “Observation of optical chaos in a phase-conjugate resonator,” Opt. Lett. 9, 513–515 (1984).
[CrossRef] [PubMed]

M. B. Klein, “Beam coupling in undoped GaAs at 1.06 µm using the photorefractive effect,” Opt. Lett. 9, 350–352 (1984).
[CrossRef] [PubMed]

Opt. Spectrosc.

L. V. Nosova, “Modes and losses of a misaligned conjugate resonator,” Opt. Spectrosc. 62, 516–518 (1987).

Sov. J. Quantum Electron.

A. A. Kalinina, L. V. Nosova, V. E. Semenov, “Aberration properties of a conjugate resonator,” Sov. J. Quantum Electron. 18, 1282–1283 (1988).
[CrossRef]

I. M. Bel’dyugin, E. M. Zemskov, “Theory of resonators with wavefront-reversing mirrors,” Sov. J. Quantum Electron. 9, 1198–1199 (1979).
[CrossRef]

I. M. Bel’dyugin, M. G. Galushkin, E. M. Zemskov, “Properties of resonators with wavefront-reversing mirrors,” Sov. J. Quantum Electron. 9, 20–23 (1979).
[CrossRef]

I. M. Bel’dyugin, E. M. Zemskov, “Calculation of the field in a laser resonator with a wavefront-reversing mirror,” Sov. J. Quantum Electron. 10, 764–765 (1980).
[CrossRef]

M. G. Reznikow, A. I. Khizhnyak, “Properties of a resonator with a wavefront-reversing mirror,” Sov. J. Quantum Electron. 10, 633–634 (1980).
[CrossRef]

I. M. Bel’dyugin, B. Ya. Zel’dovich, M. V. Zolotarev, V. V. Shkunov, “Lasers with wavefront-reversing mirrors (review),” Sov. J. Quantum Electron. 15, 1583–1597 (1985).
[CrossRef]

Other

G. C. Papen, “Transient nonlinear wave mixing in photorefractive materials and plasmas, Ph.D. dissertation (University of Wisconsin, Madison, Wis., 1989).

A. E. Siegman, Lasers (University Science Books, Mill Valley, Calif., 1986).

R. A. Fisher, ed., Optical Phase Conjugation (Academic, San Diego, Calif., 1983), Chap. 13.

P. Gunter, J.-P. Huignard, eds., Photorefractive Materials and Their Applications, I, Vol. 61: Topics in Applied Physics (Springer Verlag, New York, 1988), Chap. 8, p. 238.

M. Gower, D. Proch, eds., Optical Phase Conjugation (Springer-Verlag, New York, 1994), Chap. 8, p. 232.

See, for example, P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993), Chap. 3, p. 93.

See, for example, B. E. A. Saleh, M. Teich, Fundamentals of Photonics (Wiley, New York, 1991), Chap. 3.

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Figures (12)

Fig. 1
Fig. 1

Four-wave mixing in a uniaxial crystal. The probe beam consists of plane-wave components at angles Δθ = θ - θ c with respect to the central component, which forms an angle θ c with the c axis. The forward pump is at an angle θ p.

Fig. 2
Fig. 2

Normalized lateral and focal shifts in BaTiO3 (at λ o = 514.5 nm) when the angle between the forward pump and the central component of the probe is θ pc = 2.55° and when θ pc = 15° for two values of the external electric field E o = 0 (dashed curve), 100 V/cm (solid curve). The total intensity is 1 W/cm2, r = exp(-π), and the angle between the central grating wave vector and the c axis is 20°. The interaction length (at θ c) is l = 0.5 cm, corresponding to |γ|l ≈ 3 (when θ pc = 2.55°), and |γ|l ≈ 10 (when θ pc = 15°) for E o = 0. The other parameters, obtained from Ref. 37, are ordinary refractive index = 2.505; extraordinary refractive index = 2.434; electro-optic coefficients r 13 = 24 pm/V, r 33 = 80 pm/V, r 42 = 1640 pm/V; dielectric constants ε11 = 3700, ε33 = 150; total trap density = 4 × 1018 cm-3; acceptor trap density = 6 × 1016 cm-3, absorption coefficient = 2 cm-1; mobility anisotropy μ3311 = 0.1; and mobility lifetime product μ33 τ R = 10-10 cm2/V.

Fig. 3
Fig. 3

Normalized lateral and focal shifts in undoped GaAs (at λ o = 1.06 µm) for three values of the external field E o = 0 (dashed curve) and 10 and 100 V/cm (solid curves). The total intensity is 1 kW/cm2, r = exp(-π). The angle between the central probe ray and the pump is θ pc = 2.55°, with a corresponding interaction length l = 1 cm. The intrinsic parameters (from Refs. 55 and56) are refractive index = 3.48, electro-optic coefficient r 41 = 1.43 pm/V, dielectric constant ε r = 12.9, total trap density = 1.3 × 1016 cm-3, acceptor trap density = 1.4 × 1015 cm-3, absorption coefficient = 1.2 cm-1, electron mobility lifetime product = 1 × 10-7 cm2/V.

Fig. 4
Fig. 4

Dependence of the lateral and focal shifts in GaAs on the applied electric field under the same conditions as in Fig. 3.

Fig. 5
Fig. 5

Phase-conjugate resonator.

Fig. 6
Fig. 6

Typical trajectory of the peak intensity axis of a degenerate mode for a complete round trip inside the resonator, for the cases when the mirror is (a) concave and (b) convex. The arrows on the surface of the PCM indicate the direction of the lateral shift.

Fig. 7
Fig. 7

Intensity distribution of the degenerate DG standing wave at three locations inside the resonator: (A) at the Gaussian aperture, (B) at the midpoint between the PCM and the spherical mirror, and (C) at the spherical mirror. The spherical mirror has unity reflectivity. The PCM has a = 10λ o and b = -200λ o. Other parameters are w a = 2 and R m/d = -0.5.

Fig. 8
Fig. 8

Normalized displacement of the peak of the output intensity measured from the resonator axis as a function of the lateral shift of the PCM assuming that the focal shift b = -100λ o. The normalized radius of the Gaussian aperture is changed from w a = 1 to 8.

Fig. 9
Fig. 9

Typical trajectory of the peak intensity axis of a nondegenerate mode for two full round trips inside the resonator. The arrows on the surface of the PCM indicate the direction of the lateral shift.

Fig. 10
Fig. 10

Dependence of the resonance frequencies of the PCR on the pump ratio for a fast (τ c g = 1, solid curves) and a slow (τ c g ≅ 0, dashed lines) photorefractive PCM with |γ|l = 3. The frequencies are normalized to Ω o = (2πc/4d), where d is the mirror spacing.

Fig. 11
Fig. 11

Dependence of the resonance frequencies on the response time for τ c = 0.1 ns. The frequencies are normalized to Ω o = 2π(c/4d) and |γ|l = 3.

Fig. 12
Fig. 12

Transverse distribution of the output beam intensity measured from the resonator axis at different instances of time. The PCM has lateral shift a = 10λ o and focal shift b = -100λ o. The normalized radius of curvature of the output mirror is R m/d = -0.5, and the normalized radius of the Gaussian aperture is w a = 2.

Equations (55)

Equations on this page are rendered with MathJax. Learn more.

Ac=RΩ, θAp*,
RΩ, θRexpjφRΩ, θ=-jηMβ cotβ+jτcτgωN+ρM
βΩ, θ=τcτgωN+ρM2+ηM21/2,  ρθ=r-1r+1 γl2,  ηθ=2r1/2r+1 γl2,  MΩ, θ=1+jδg1+jωN+δg,
Acx=RΩ, θAp*x.
φRφRθc+kaθ-θc+12kbθ-θc2,
AcxAp*x+aexp-jkx22b,
Ux, y, z=1z+jzo×exp-jkx+jxo2+y22z+jzoexp-jkz,
Ix, y, z=WoWz2 exp2xo2Wo2×exp-2x-xIz2+y2W2z
φx, y, z=kx-xpz2+y22Rz+kz-kxo2Rz-tan-1zzo-zozxo2W2z,
xIz=xoπW2zλRz=xozzo,
xpz=-xoλRzπW2z=-xozoz,
θI=tan-1xozo
Ux, 0, z=1qz exp-jkx-p22qzexp-jkz,
Uinx=exp-jkx-pin22qin,
Uoutx=Uo exp-jkx-pout22qout,
qout=Aqin+BCqin+D,
pout=pinCqin+D,
Uo=exp-jkLoA+B/qin exp-jkpin22qin1-DCqin+D
1qout=1qin+2Rm,
pout=pin2Rmqin+1.
pxd-jxo=1+Wo2Wa2+jλzaπWa21+Wo2Wa22+λzaπWa22xd-jxo,
1zc+jzo=1q=1q-jλπWa2,
xI=xd+xozazo,
xI=xd+xozczo,
Apx=exp-jk+x-pin22qin,
Acx=Aco exp-jk-x-pout22qout,
qout=-1-Ω/ωo1+Ω/ωoqin*-1-Ω/ωobΩnb,
pout=pin*+aΩ,
Aco=-1+1+Ω/ωobΩ/nbqin*-1/2,
A=-1-Ω/ωo/1+Ω/ωo,  B=-1-Ω/ωobΩ/nb,
qout=Aqin*+BCqin*+D.
q2=ATq0+BTCTq0+DT,
AT=AA*+BC*,
BT=AB*+BD*,
CT=CA*+DC*,
DT=CB*+DD*,
A=-1-jλodπWa2+jλodπWa21-bnbd1-jλodπWa2,
B=-d1-jλodπWa2+d1+jλodπWa2×1-bnbd1-jλodπWa2,
C=jλoπWa21+2dRm-2Rm+jλoπWa2×1+2dRm-bnb2Rm-jλoπWa21+2dRm,
D=-2dRm-jλodπWa21+2dRm+1+jλodπWa21+2dRm-bnb2Rm-jλoπWa21+2dRm.
p2=Ψ1q0p0+Ψ2q0,
1q=2CTAT-DT±DT-AT2+4CTBT1/2.
p=Ψ2q1-Ψ1q.
Δ1/qΔ1/q=1AT+BT1/q2<1,
ΔpΔp=Ψ1q<1.
φ2x-φ0x=φ20-φ00=Δφ0,
Δφo=ΔφoRm, wa, Ω=n2π,  n=1, 2, 3 .
n=Ω2πc/4d+12πφR-Ω, θc-φRΩ, θc+φcΩ+φaΩ+φmΩ+k=14Δξk,
Ux, t=A+ exp-jk+x-p+22q+exp-jΩt+A- exp-jk-x-p-22q-exp+jΩt,
p2=Ψ1q0p0+Ψ2q0,
Ψ1q0q2q1q4q3*q6q5*q8q7*q10q9q2q11,  Ψ2q0a1+q4q3*q6q5*q8q7*q10q9q2q11.
Md=1d01.
Mm=102/Rm1,  Ma=10-jλ/Wa21,
MPCM±=-1Ω/ωo1±Ω/ωo-1Ω/ωob±Ωnb01.
M=ATBTCTDT=H3H2*H1,

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