Abstract

The Fox–Li iterative method [Bell Syst. Tech. J. <b>40</b>, 253 (1961)] is used to find solutions for a three-dimensional phase-conjugate resonator with a saturated gain, a random aberrator, and a pinhole spatial filter. The performance of such a resonator is excellent for resonator Fresnel numbers as small as 5 and for phase-error standard deviations as large as 2π. The use of a spatial filter to control the transverse mode shape is demonstrated.

© 1983 Optical Society of America

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  1. J. AuYeung, D. Fekete, D. M. Pepper, and 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).
  2. J. F. Lam and W. P. Brown, "Optical resonators with phaseconjugate mirrors," Opt. Lett. 5, 61–63 (1980).
  3. I. M. Bel'dyugin, M. G. Galushkin, and E. M. Zemskov, "Properties of resonators with wavefront-reversing mirrors," Sov. J. Quantum Electron. 9, 20–23 (1979).
  4. I. M. Bel'dyugin and E. M. Zemskov, "Theory of resonators with wavefront-reversing mirrors," Sov. J. Quantum Electron. 9, 1198–1199 (1980).
  5. I. M. Bel'dyugin and A: P. Pogibel'skii, "Influence of random inhomgeneities of the refractive index of a medium on the nature of fields in a laser resonator with wavefront-reversing mirrors," Sov. J. Quantum Electron. 10, 1271–1272 (1980).
  6. I. M. Bel'dyugin and E. M. Zemskov, "Calculation of the field in a laser resonator with a wavefront-reversing mirror," Sov. J. Quantum Electron. 10, 764–765 (1980).
  7. P. A. Belanger, A. Hardy, and A. E. Siegman, "Resonant modes of optical cavities with phase-conjugate mirrors, "Appl. Opt. 19, 602–609, 479–480 (1980).
  8. A. Hardy, "Sensitivity of phase-conjugate resonators to intracavity phase perturbations," IEEE J. Quantum Electron. QE-17, 1581–1585 (1981).
  9. A. Hardy and S. Mochhauser, "Phase-conjugate resonators with intracavity amplitude perturbations," Appl. Opt.21, 1118–1121 (1982).
  10. A. E. Siegman, P. A. Belanger, and A. Hardy, "Optical resonators using phase-conjugate mirrors," in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), Chap. 13.
  11. M. G. Reznikov and A. I. Khizhnyak, "Properties of a resonator with a wavefront-reversing mirror," Sov. J. Quantum Electron. 10, 633–634 (1980).
  12. A. Hardy, P. A. Belanger, and A. E. Siegman, "Orthogonality properties of phase conjugate optical resonators," Appl. Opt. 21, 1122–1124 (1982).
  13. P. A. Belanger, "Phase conjugation and optical resonators," Opt. Eng. 21, 266–270 (1982).
  14. T. J. Karr and H. J. Hoffman, "Intraresonator phase conjugation," Proc. Soc. Photo-Opt. Instrum. Eng. 293, 162–182 (1981).
  15. A. G. Fox and T. Li, "Resonant modes in a maser interferometer," Bell Syst. Tech. J. 40, 253–488 (1961).
  16. E. A. Sziklas and A. E. Siegman, "Mode calculations in unstable resonators with flowing saturable gain. II: Fast Fourier transform method," Appl. Opt. 14, 1874–1889 (1975).
  17. A. E. Siegman and E. A. Sziklas, "Mode calculations in unstable resonators with flowing saturable gain. I: Hermite–Gaussian expansion," Appl. Opt. 13, 2775–2792 (1974).
  18. G. C. Valley, Long- and short-term Strehl ratios for turbulence with finite inner and outer scales," Appl. Opt. 18, 984–987 (1979).
  19. T. R. O'Meara, "Jinc trap resonators," in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1982), pp. 10–11.
  20. E. M. Phillip-Rutz, "Spatially coherent radiation from an array of GaAs lasers," Appl. Phys. Lett. 26, 475–477 (1975).

1982 (3)

1981 (2)

T. J. Karr and H. J. Hoffman, "Intraresonator phase conjugation," Proc. Soc. Photo-Opt. Instrum. Eng. 293, 162–182 (1981).

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

1980 (6)

I. M. Bel'dyugin and E. M. Zemskov, "Theory of resonators with wavefront-reversing mirrors," Sov. J. Quantum Electron. 9, 1198–1199 (1980).

I. M. Bel'dyugin and A: P. Pogibel'skii, "Influence of random inhomgeneities of the refractive index of a medium on the nature of fields in a laser resonator with wavefront-reversing mirrors," Sov. J. Quantum Electron. 10, 1271–1272 (1980).

I. M. Bel'dyugin and E. M. Zemskov, "Calculation of the field in a laser resonator with a wavefront-reversing mirror," Sov. J. Quantum Electron. 10, 764–765 (1980).

P. A. Belanger, A. Hardy, and A. E. Siegman, "Resonant modes of optical cavities with phase-conjugate mirrors, "Appl. Opt. 19, 602–609, 479–480 (1980).

M. G. Reznikov and A. I. Khizhnyak, "Properties of a resonator with a wavefront-reversing mirror," Sov. J. Quantum Electron. 10, 633–634 (1980).

J. F. Lam and W. P. Brown, "Optical resonators with phaseconjugate mirrors," Opt. Lett. 5, 61–63 (1980).

1979 (3)

G. C. Valley, Long- and short-term Strehl ratios for turbulence with finite inner and outer scales," Appl. Opt. 18, 984–987 (1979).

J. AuYeung, D. Fekete, D. M. Pepper, and 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).

I. M. Bel'dyugin, M. G. Galushkin, and E. M. Zemskov, "Properties of resonators with wavefront-reversing mirrors," Sov. J. Quantum Electron. 9, 20–23 (1979).

1975 (2)

E. A. Sziklas and A. E. Siegman, "Mode calculations in unstable resonators with flowing saturable gain. II: Fast Fourier transform method," Appl. Opt. 14, 1874–1889 (1975).

E. M. Phillip-Rutz, "Spatially coherent radiation from an array of GaAs lasers," Appl. Phys. Lett. 26, 475–477 (1975).

1974 (1)

1961 (1)

A. G. Fox and T. Li, "Resonant modes in a maser interferometer," Bell Syst. Tech. J. 40, 253–488 (1961).

AuYeung, J.

J. AuYeung, D. Fekete, D. M. Pepper, and 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).

Bel’dyugin, I. M.

I. M. Bel'dyugin and A: P. Pogibel'skii, "Influence of random inhomgeneities of the refractive index of a medium on the nature of fields in a laser resonator with wavefront-reversing mirrors," Sov. J. Quantum Electron. 10, 1271–1272 (1980).

I. M. Bel'dyugin and E. M. Zemskov, "Calculation of the field in a laser resonator with a wavefront-reversing mirror," Sov. J. Quantum Electron. 10, 764–765 (1980).

I. M. Bel'dyugin and E. M. Zemskov, "Theory of resonators with wavefront-reversing mirrors," Sov. J. Quantum Electron. 9, 1198–1199 (1980).

I. M. Bel'dyugin, M. G. Galushkin, and E. M. Zemskov, "Properties of resonators with wavefront-reversing mirrors," Sov. J. Quantum Electron. 9, 20–23 (1979).

Belanger, P. A.

A. Hardy, P. A. Belanger, and A. E. Siegman, "Orthogonality properties of phase conjugate optical resonators," Appl. Opt. 21, 1122–1124 (1982).

P. A. Belanger, "Phase conjugation and optical resonators," Opt. Eng. 21, 266–270 (1982).

P. A. Belanger, A. Hardy, and A. E. Siegman, "Resonant modes of optical cavities with phase-conjugate mirrors, "Appl. Opt. 19, 602–609, 479–480 (1980).

A. E. Siegman, P. A. Belanger, and A. Hardy, "Optical resonators using phase-conjugate mirrors," in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), Chap. 13.

Brown, W. P.

Fekete, D.

J. AuYeung, D. Fekete, D. M. Pepper, and 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).

Fox, A. G.

A. G. Fox and T. Li, "Resonant modes in a maser interferometer," Bell Syst. Tech. J. 40, 253–488 (1961).

Galushkin, M. G.

I. M. Bel'dyugin, M. G. Galushkin, and E. M. Zemskov, "Properties of resonators with wavefront-reversing mirrors," Sov. J. Quantum Electron. 9, 20–23 (1979).

Hardy, A.

A. Hardy, P. A. Belanger, and A. E. Siegman, "Orthogonality properties of phase conjugate optical resonators," Appl. Opt. 21, 1122–1124 (1982).

A. Hardy and S. Mochhauser, "Phase-conjugate resonators with intracavity amplitude perturbations," Appl. Opt.21, 1118–1121 (1982).

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

P. A. Belanger, A. Hardy, and A. E. Siegman, "Resonant modes of optical cavities with phase-conjugate mirrors, "Appl. Opt. 19, 602–609, 479–480 (1980).

A. E. Siegman, P. A. Belanger, and A. Hardy, "Optical resonators using phase-conjugate mirrors," in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), Chap. 13.

Hoffman, H. J.

T. J. Karr and H. J. Hoffman, "Intraresonator phase conjugation," Proc. Soc. Photo-Opt. Instrum. Eng. 293, 162–182 (1981).

Karr, T. J.

T. J. Karr and H. J. Hoffman, "Intraresonator phase conjugation," Proc. Soc. Photo-Opt. Instrum. Eng. 293, 162–182 (1981).

Khizhnyak, A. I.

M. G. Reznikov and A. I. Khizhnyak, "Properties of a resonator with a wavefront-reversing mirror," Sov. J. Quantum Electron. 10, 633–634 (1980).

Lam, J. F.

Li, T.

A. G. Fox and T. Li, "Resonant modes in a maser interferometer," Bell Syst. Tech. J. 40, 253–488 (1961).

Mochhauser, S.

O’Meara, T. R.

T. R. O'Meara, "Jinc trap resonators," in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1982), pp. 10–11.

Pepper, D. M.

J. AuYeung, D. Fekete, D. M. Pepper, and 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).

Phillip-Rutz, E. M.

E. M. Phillip-Rutz, "Spatially coherent radiation from an array of GaAs lasers," Appl. Phys. Lett. 26, 475–477 (1975).

Pogibel’skii, A: P.

I. M. Bel'dyugin and A: P. Pogibel'skii, "Influence of random inhomgeneities of the refractive index of a medium on the nature of fields in a laser resonator with wavefront-reversing mirrors," Sov. J. Quantum Electron. 10, 1271–1272 (1980).

Reznikov, M. G.

M. G. Reznikov and A. I. Khizhnyak, "Properties of a resonator with a wavefront-reversing mirror," Sov. J. Quantum Electron. 10, 633–634 (1980).

Siegman, A. E.

Sziklas, E. A.

Valley, G. C.

Yariv, A.

J. AuYeung, D. Fekete, D. M. Pepper, and 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).

Zemskov, E. M.

I. M. Bel'dyugin and E. M. Zemskov, "Calculation of the field in a laser resonator with a wavefront-reversing mirror," Sov. J. Quantum Electron. 10, 764–765 (1980).

I. M. Bel'dyugin and E. M. Zemskov, "Theory of resonators with wavefront-reversing mirrors," Sov. J. Quantum Electron. 9, 1198–1199 (1980).

I. M. Bel'dyugin, M. G. Galushkin, and E. M. Zemskov, "Properties of resonators with wavefront-reversing mirrors," Sov. J. Quantum Electron. 9, 20–23 (1979).

Appl. Opt. (6)

Appl. Phys. Lett. (1)

E. M. Phillip-Rutz, "Spatially coherent radiation from an array of GaAs lasers," Appl. Phys. Lett. 26, 475–477 (1975).

Bell Syst. Tech. J. (1)

A. G. Fox and T. Li, "Resonant modes in a maser interferometer," Bell Syst. Tech. J. 40, 253–488 (1961).

IEEE J. Quantum Electron. (2)

J. AuYeung, D. Fekete, D. M. Pepper, and 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).

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

Opt. Eng. (1)

P. A. Belanger, "Phase conjugation and optical resonators," Opt. Eng. 21, 266–270 (1982).

Opt. Lett. (1)

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

T. J. Karr and H. J. Hoffman, "Intraresonator phase conjugation," Proc. Soc. Photo-Opt. Instrum. Eng. 293, 162–182 (1981).

Sov. J. Quantum Electron. (5)

I. M. Bel'dyugin, M. G. Galushkin, and E. M. Zemskov, "Properties of resonators with wavefront-reversing mirrors," Sov. J. Quantum Electron. 9, 20–23 (1979).

I. M. Bel'dyugin and E. M. Zemskov, "Theory of resonators with wavefront-reversing mirrors," Sov. J. Quantum Electron. 9, 1198–1199 (1980).

I. M. Bel'dyugin and A: P. Pogibel'skii, "Influence of random inhomgeneities of the refractive index of a medium on the nature of fields in a laser resonator with wavefront-reversing mirrors," Sov. J. Quantum Electron. 10, 1271–1272 (1980).

I. M. Bel'dyugin and E. M. Zemskov, "Calculation of the field in a laser resonator with a wavefront-reversing mirror," Sov. J. Quantum Electron. 10, 764–765 (1980).

M. G. Reznikov and A. I. Khizhnyak, "Properties of a resonator with a wavefront-reversing mirror," Sov. J. Quantum Electron. 10, 633–634 (1980).

Other (2)

T. R. O'Meara, "Jinc trap resonators," in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1982), pp. 10–11.

A. E. Siegman, P. A. Belanger, and A. Hardy, "Optical resonators using phase-conjugate mirrors," in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), Chap. 13.

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