Abstract

A general formalism is developed to study intracavity phase conjugation through resonant degenerate four-wave mixing. The effects of spatial hole burning, arising from interference of the counterpropagating pump waves, are fully incorporated. The analysis is applied to discuss intracavity phase conjugation in nonlinear media that can be modeled using either a two-level system or a A-type three-level system. In both cases, the phase-conjugate reflectivity exhibits bistability for an appropriate choice of the input parameters. For a two-level system, the tuning characteristics of the Fabry–Perot cavity significantly affect the phase-conjugate spectrum that displays hysteresis when the cavity is detuned from the applied laser frequency.

© 1983 Optical Society of America

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  1. For a review see, for example, D. M. Pepper, "Nonlinear optical phase conjugation," Opt. Eng. 21, 155–183 (1982); see also R. A. Fisher, ed., Optical Phase Conjugation (Academic, New York, 1983).
  2. P. F. Liao, D. M. Bloom, and N. P. Economou, "Cw optical wave-front conjugation by saturated absorption in atomic sodium vapor," Appl. Phys. Lett. 32, 813–815 (1978).
  3. R. L. Abrams and R. C. Lind, "Degenerate four-wave mixing in absorbing media," Opt. Lett. 2, 94–96 (1978); errata, Opt. Lett. 3, 205 (1978).
  4. T. Fu and M. Sargent III, "Theory of two-photon phase conjugation," Opt. Lett. 5, 433–435 (1980).
  5. G. P. Agrawal, "Phase conjugation and degenerate four-wave mixing in three-level systems," IEEE J. Quantum Electron. QE-17, 2335–2340 (1981).
  6. In some of the early experiments on phase conjugation, the laser cavity of the pump wave itself was used. See E. F. Bergmann, I. J. Bigio, B. J. Feldman, and R. A. Fisher, "High-efficiency pulsed 10.6-µm phase-conjugate reflection via degenerate fourwave mixing," Opt. Lett. 3, 82–84 (1978).
  7. H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, "Differential gain and bistability using a sodium-filled Fabry–Perot interferometer," Phys. Rev. Lett. 36, 1135–1138 (1976).
  8. R. Bonifacio and L. A. Lugiato, "Optical bistability and cooperative effects in resonance fluorescence," Phys. Rev. A 18, 1129–1144 (1978).
  9. G. P. Agrawal and H. J. Carmichael, "Optical bistability through nonlinear dispersion and absorption," Phys. Rev. A 19, 2074–2086 (1979).
  10. G. P. Agrawal and C. Flytzanis, "Bistability and hysteresis in phase-conjugated reflectivity," IEEE J. Quantum Electron. QE-14, 374–380 (1981).
  11. G. P. Agrawal, C. Flytzanis, R. Frey, and F. Pradere, "Bistable reflectivity of phase-conjugated signal through intracavity degenerate four-wave mixing," Appl. Phys. Lett. 38, 492–494 (1981).
  12. L. Fu-Li, J. A. Hermann, and J. N. Elgin, "Effects of two-photon optical bistability upon phase conjugation," Opt. Commun. 40, 446–450 (1982).
  13. C. Flytzanis and C. L. Tang, "Light-induced critical behavior in four-wave interaction in nonlinear systems," Phys. Rev. Lett. 45, 441–444 (1980).
  14. H. G. Winful and J. H. Marburger, "Hysteresis and optical bistability in degenerate four-wave mixing," Appl. Phys. Lett. 36, 613–614 (1980).
  15. C. Flytzanis, G. P. Agrawal, and C. L. Tang, "Critical behavior in optical phase conjugation," in Lasers and Their Applications, W. O. N. Guimaraes, C.-T. Lin, and A. Mooradian, eds. (Springer-Verlag, Berlin, 1981).
  16. A. Borshch, M. Brodin, V. Volkov, and N. Kukhtarev, "Optical bistability and hysteresis in phase conjugation by degenerate six-photon mixing," Opt. Commun. 41, 213–215 (1982).
  17. G. P. Agrawal and H. J. Carmichael, "Inhomogeneous broadening and the mean-field approximation for optical bistability in a Fabry–Perot," Opt. Acta. 27, 651–660 (1980).
  18. R. K. Raj, D. Bloch, J. J. Snyder, G. Camy, and M. Ducloy, "High-frequency optically heterodyned saturation spectroscopy via resonant degenerate four-wave mixing," Phys. Rev. Lett. 44, 1251–1254 (1980).
  19. P. Aubourg, J. P. Bettini, G. P. Agrawal, P. Cottin, D. Guérin, O. Meunier, and J. L. Boulnois, "Doppler-free cw phase-conjugate spectrum of SF6 by resonant degenerate four-wave mixing at 10.6 µm," Opt. Lett. 6, 383–385 (1981).
  20. D. G. Steel and J. F. Lam, "Saturation effects and inhomogeneous broadening in Doppler-free degenerate four-wave mixing," Opt. Commun. 40, 77–80 (1981).
  21. For the case of pulsed radiation, the analysis can be applied if the medium-response time is shorter than the duration of the optical pulse.
  22. In the literature on optical bistability, this is often referred to as the mean-field approximation (see Refs. 8, 9, and 17).
  23. G. P. Agrawal, J. L. Boulnois, P. Aubourg, and A. van Lerberghe, "Saturation splitting in the spectrum of resonant degenerate four-wave mixing," Opt. Lett. 7, 540–542 (1982).
  24. D. F. Walls and P. Zoller, "A coherent nonlinear mechanism for optical bistability from three-level atoms," Opt. Commun. 34, 260–264 (1980).
  25. R. G. Brewer and E. L. Hahn, "Coherent two-photon processes: transient and steady-state cases," Phys. Rev. A 11, 1641–1649 (1975).
  26. H. R. Gray, R. M. Whitley, and C. R. Stroud, "Coherent trapping of atomic populations," Opt. Lett. 3, 218–220 (1978).
  27. It is not appropriate to use the term reflectivity spectrum because the laser frequency is kept fixed.
  28. J. Mlynek, F. Mitschke, R. Deserno, and W. Lange, "Optical bistability by transverse optical pumping," Appl. Phys. B 28, 135 (1982).

1982 (4)

A. Borshch, M. Brodin, V. Volkov, and N. Kukhtarev, "Optical bistability and hysteresis in phase conjugation by degenerate six-photon mixing," Opt. Commun. 41, 213–215 (1982).

L. Fu-Li, J. A. Hermann, and J. N. Elgin, "Effects of two-photon optical bistability upon phase conjugation," Opt. Commun. 40, 446–450 (1982).

J. Mlynek, F. Mitschke, R. Deserno, and W. Lange, "Optical bistability by transverse optical pumping," Appl. Phys. B 28, 135 (1982).

G. P. Agrawal, J. L. Boulnois, P. Aubourg, and A. van Lerberghe, "Saturation splitting in the spectrum of resonant degenerate four-wave mixing," Opt. Lett. 7, 540–542 (1982).

1981 (5)

P. Aubourg, J. P. Bettini, G. P. Agrawal, P. Cottin, D. Guérin, O. Meunier, and J. L. Boulnois, "Doppler-free cw phase-conjugate spectrum of SF6 by resonant degenerate four-wave mixing at 10.6 µm," Opt. Lett. 6, 383–385 (1981).

G. P. Agrawal, "Phase conjugation and degenerate four-wave mixing in three-level systems," IEEE J. Quantum Electron. QE-17, 2335–2340 (1981).

D. G. Steel and J. F. Lam, "Saturation effects and inhomogeneous broadening in Doppler-free degenerate four-wave mixing," Opt. Commun. 40, 77–80 (1981).

G. P. Agrawal and C. Flytzanis, "Bistability and hysteresis in phase-conjugated reflectivity," IEEE J. Quantum Electron. QE-14, 374–380 (1981).

G. P. Agrawal, C. Flytzanis, R. Frey, and F. Pradere, "Bistable reflectivity of phase-conjugated signal through intracavity degenerate four-wave mixing," Appl. Phys. Lett. 38, 492–494 (1981).

1980 (6)

G. P. Agrawal and H. J. Carmichael, "Inhomogeneous broadening and the mean-field approximation for optical bistability in a Fabry–Perot," Opt. Acta. 27, 651–660 (1980).

R. K. Raj, D. Bloch, J. J. Snyder, G. Camy, and M. Ducloy, "High-frequency optically heterodyned saturation spectroscopy via resonant degenerate four-wave mixing," Phys. Rev. Lett. 44, 1251–1254 (1980).

D. F. Walls and P. Zoller, "A coherent nonlinear mechanism for optical bistability from three-level atoms," Opt. Commun. 34, 260–264 (1980).

C. Flytzanis and C. L. Tang, "Light-induced critical behavior in four-wave interaction in nonlinear systems," Phys. Rev. Lett. 45, 441–444 (1980).

H. G. Winful and J. H. Marburger, "Hysteresis and optical bistability in degenerate four-wave mixing," Appl. Phys. Lett. 36, 613–614 (1980).

T. Fu and M. Sargent III, "Theory of two-photon phase conjugation," Opt. Lett. 5, 433–435 (1980).

1979 (1)

G. P. Agrawal and H. J. Carmichael, "Optical bistability through nonlinear dispersion and absorption," Phys. Rev. A 19, 2074–2086 (1979).

1978 (4)

In some of the early experiments on phase conjugation, the laser cavity of the pump wave itself was used. See E. F. Bergmann, I. J. Bigio, B. J. Feldman, and R. A. Fisher, "High-efficiency pulsed 10.6-µm phase-conjugate reflection via degenerate fourwave mixing," Opt. Lett. 3, 82–84 (1978).

H. R. Gray, R. M. Whitley, and C. R. Stroud, "Coherent trapping of atomic populations," Opt. Lett. 3, 218–220 (1978).

P. F. Liao, D. M. Bloom, and N. P. Economou, "Cw optical wave-front conjugation by saturated absorption in atomic sodium vapor," Appl. Phys. Lett. 32, 813–815 (1978).

R. Bonifacio and L. A. Lugiato, "Optical bistability and cooperative effects in resonance fluorescence," Phys. Rev. A 18, 1129–1144 (1978).

1976 (1)

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, "Differential gain and bistability using a sodium-filled Fabry–Perot interferometer," Phys. Rev. Lett. 36, 1135–1138 (1976).

1975 (1)

R. G. Brewer and E. L. Hahn, "Coherent two-photon processes: transient and steady-state cases," Phys. Rev. A 11, 1641–1649 (1975).

Abrams, R. L.

R. L. Abrams and R. C. Lind, "Degenerate four-wave mixing in absorbing media," Opt. Lett. 2, 94–96 (1978); errata, Opt. Lett. 3, 205 (1978).

Agrawal, G. P.

G. P. Agrawal, J. L. Boulnois, P. Aubourg, and A. van Lerberghe, "Saturation splitting in the spectrum of resonant degenerate four-wave mixing," Opt. Lett. 7, 540–542 (1982).

G. P. Agrawal, "Phase conjugation and degenerate four-wave mixing in three-level systems," IEEE J. Quantum Electron. QE-17, 2335–2340 (1981).

P. Aubourg, J. P. Bettini, G. P. Agrawal, P. Cottin, D. Guérin, O. Meunier, and J. L. Boulnois, "Doppler-free cw phase-conjugate spectrum of SF6 by resonant degenerate four-wave mixing at 10.6 µm," Opt. Lett. 6, 383–385 (1981).

G. P. Agrawal and C. Flytzanis, "Bistability and hysteresis in phase-conjugated reflectivity," IEEE J. Quantum Electron. QE-14, 374–380 (1981).

G. P. Agrawal, C. Flytzanis, R. Frey, and F. Pradere, "Bistable reflectivity of phase-conjugated signal through intracavity degenerate four-wave mixing," Appl. Phys. Lett. 38, 492–494 (1981).

G. P. Agrawal and H. J. Carmichael, "Inhomogeneous broadening and the mean-field approximation for optical bistability in a Fabry–Perot," Opt. Acta. 27, 651–660 (1980).

G. P. Agrawal and H. J. Carmichael, "Optical bistability through nonlinear dispersion and absorption," Phys. Rev. A 19, 2074–2086 (1979).

C. Flytzanis, G. P. Agrawal, and C. L. Tang, "Critical behavior in optical phase conjugation," in Lasers and Their Applications, W. O. N. Guimaraes, C.-T. Lin, and A. Mooradian, eds. (Springer-Verlag, Berlin, 1981).

Aubourg, P.

Bergmann, E. F.

Bettini, J. P.

Bigio, I. J.

Bloch, D.

R. K. Raj, D. Bloch, J. J. Snyder, G. Camy, and M. Ducloy, "High-frequency optically heterodyned saturation spectroscopy via resonant degenerate four-wave mixing," Phys. Rev. Lett. 44, 1251–1254 (1980).

Bloom, D. M.

P. F. Liao, D. M. Bloom, and N. P. Economou, "Cw optical wave-front conjugation by saturated absorption in atomic sodium vapor," Appl. Phys. Lett. 32, 813–815 (1978).

Bonifacio, R.

R. Bonifacio and L. A. Lugiato, "Optical bistability and cooperative effects in resonance fluorescence," Phys. Rev. A 18, 1129–1144 (1978).

Borshch, A.

A. Borshch, M. Brodin, V. Volkov, and N. Kukhtarev, "Optical bistability and hysteresis in phase conjugation by degenerate six-photon mixing," Opt. Commun. 41, 213–215 (1982).

Boulnois, J. L.

Brewer, R. G.

R. G. Brewer and E. L. Hahn, "Coherent two-photon processes: transient and steady-state cases," Phys. Rev. A 11, 1641–1649 (1975).

Brodin, M.

A. Borshch, M. Brodin, V. Volkov, and N. Kukhtarev, "Optical bistability and hysteresis in phase conjugation by degenerate six-photon mixing," Opt. Commun. 41, 213–215 (1982).

Camy, G.

R. K. Raj, D. Bloch, J. J. Snyder, G. Camy, and M. Ducloy, "High-frequency optically heterodyned saturation spectroscopy via resonant degenerate four-wave mixing," Phys. Rev. Lett. 44, 1251–1254 (1980).

Carmichael, H. J.

G. P. Agrawal and H. J. Carmichael, "Inhomogeneous broadening and the mean-field approximation for optical bistability in a Fabry–Perot," Opt. Acta. 27, 651–660 (1980).

G. P. Agrawal and H. J. Carmichael, "Optical bistability through nonlinear dispersion and absorption," Phys. Rev. A 19, 2074–2086 (1979).

Cottin, P.

Deserno, R.

J. Mlynek, F. Mitschke, R. Deserno, and W. Lange, "Optical bistability by transverse optical pumping," Appl. Phys. B 28, 135 (1982).

Ducloy, M.

R. K. Raj, D. Bloch, J. J. Snyder, G. Camy, and M. Ducloy, "High-frequency optically heterodyned saturation spectroscopy via resonant degenerate four-wave mixing," Phys. Rev. Lett. 44, 1251–1254 (1980).

Economou, N. P.

P. F. Liao, D. M. Bloom, and N. P. Economou, "Cw optical wave-front conjugation by saturated absorption in atomic sodium vapor," Appl. Phys. Lett. 32, 813–815 (1978).

Elgin, J. N.

L. Fu-Li, J. A. Hermann, and J. N. Elgin, "Effects of two-photon optical bistability upon phase conjugation," Opt. Commun. 40, 446–450 (1982).

Feldman, B. J.

Fisher, R. A.

Flytzanis, C.

G. P. Agrawal and C. Flytzanis, "Bistability and hysteresis in phase-conjugated reflectivity," IEEE J. Quantum Electron. QE-14, 374–380 (1981).

G. P. Agrawal, C. Flytzanis, R. Frey, and F. Pradere, "Bistable reflectivity of phase-conjugated signal through intracavity degenerate four-wave mixing," Appl. Phys. Lett. 38, 492–494 (1981).

C. Flytzanis and C. L. Tang, "Light-induced critical behavior in four-wave interaction in nonlinear systems," Phys. Rev. Lett. 45, 441–444 (1980).

C. Flytzanis, G. P. Agrawal, and C. L. Tang, "Critical behavior in optical phase conjugation," in Lasers and Their Applications, W. O. N. Guimaraes, C.-T. Lin, and A. Mooradian, eds. (Springer-Verlag, Berlin, 1981).

Frey, R.

G. P. Agrawal, C. Flytzanis, R. Frey, and F. Pradere, "Bistable reflectivity of phase-conjugated signal through intracavity degenerate four-wave mixing," Appl. Phys. Lett. 38, 492–494 (1981).

Fu, T.

Fu-Li, L.

L. Fu-Li, J. A. Hermann, and J. N. Elgin, "Effects of two-photon optical bistability upon phase conjugation," Opt. Commun. 40, 446–450 (1982).

Gibbs, H. M.

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, "Differential gain and bistability using a sodium-filled Fabry–Perot interferometer," Phys. Rev. Lett. 36, 1135–1138 (1976).

Gray, H. R.

Guérin, D.

Hahn, E. L.

R. G. Brewer and E. L. Hahn, "Coherent two-photon processes: transient and steady-state cases," Phys. Rev. A 11, 1641–1649 (1975).

Hermann, J. A.

L. Fu-Li, J. A. Hermann, and J. N. Elgin, "Effects of two-photon optical bistability upon phase conjugation," Opt. Commun. 40, 446–450 (1982).

Kukhtarev, N.

A. Borshch, M. Brodin, V. Volkov, and N. Kukhtarev, "Optical bistability and hysteresis in phase conjugation by degenerate six-photon mixing," Opt. Commun. 41, 213–215 (1982).

Lam, J. F.

D. G. Steel and J. F. Lam, "Saturation effects and inhomogeneous broadening in Doppler-free degenerate four-wave mixing," Opt. Commun. 40, 77–80 (1981).

Lange, W.

J. Mlynek, F. Mitschke, R. Deserno, and W. Lange, "Optical bistability by transverse optical pumping," Appl. Phys. B 28, 135 (1982).

Liao, P. F.

P. F. Liao, D. M. Bloom, and N. P. Economou, "Cw optical wave-front conjugation by saturated absorption in atomic sodium vapor," Appl. Phys. Lett. 32, 813–815 (1978).

Lind, R. C.

R. L. Abrams and R. C. Lind, "Degenerate four-wave mixing in absorbing media," Opt. Lett. 2, 94–96 (1978); errata, Opt. Lett. 3, 205 (1978).

Lugiato, L. A.

R. Bonifacio and L. A. Lugiato, "Optical bistability and cooperative effects in resonance fluorescence," Phys. Rev. A 18, 1129–1144 (1978).

Marburger, J. H.

H. G. Winful and J. H. Marburger, "Hysteresis and optical bistability in degenerate four-wave mixing," Appl. Phys. Lett. 36, 613–614 (1980).

McCall, S. L.

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, "Differential gain and bistability using a sodium-filled Fabry–Perot interferometer," Phys. Rev. Lett. 36, 1135–1138 (1976).

Meunier, O.

Mitschke, F.

J. Mlynek, F. Mitschke, R. Deserno, and W. Lange, "Optical bistability by transverse optical pumping," Appl. Phys. B 28, 135 (1982).

Mlynek, J.

J. Mlynek, F. Mitschke, R. Deserno, and W. Lange, "Optical bistability by transverse optical pumping," Appl. Phys. B 28, 135 (1982).

Pepper, D. M.

For a review see, for example, D. M. Pepper, "Nonlinear optical phase conjugation," Opt. Eng. 21, 155–183 (1982); see also R. A. Fisher, ed., Optical Phase Conjugation (Academic, New York, 1983).

Pradere, F.

G. P. Agrawal, C. Flytzanis, R. Frey, and F. Pradere, "Bistable reflectivity of phase-conjugated signal through intracavity degenerate four-wave mixing," Appl. Phys. Lett. 38, 492–494 (1981).

Raj, R. K.

R. K. Raj, D. Bloch, J. J. Snyder, G. Camy, and M. Ducloy, "High-frequency optically heterodyned saturation spectroscopy via resonant degenerate four-wave mixing," Phys. Rev. Lett. 44, 1251–1254 (1980).

Sargent III, M.

Snyder, J. J.

R. K. Raj, D. Bloch, J. J. Snyder, G. Camy, and M. Ducloy, "High-frequency optically heterodyned saturation spectroscopy via resonant degenerate four-wave mixing," Phys. Rev. Lett. 44, 1251–1254 (1980).

Steel, D. G.

D. G. Steel and J. F. Lam, "Saturation effects and inhomogeneous broadening in Doppler-free degenerate four-wave mixing," Opt. Commun. 40, 77–80 (1981).

Stroud, C. R.

Tang, C. L.

C. Flytzanis and C. L. Tang, "Light-induced critical behavior in four-wave interaction in nonlinear systems," Phys. Rev. Lett. 45, 441–444 (1980).

C. Flytzanis, G. P. Agrawal, and C. L. Tang, "Critical behavior in optical phase conjugation," in Lasers and Their Applications, W. O. N. Guimaraes, C.-T. Lin, and A. Mooradian, eds. (Springer-Verlag, Berlin, 1981).

van Lerberghe, A.

Venkatesan, T. N. C.

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, "Differential gain and bistability using a sodium-filled Fabry–Perot interferometer," Phys. Rev. Lett. 36, 1135–1138 (1976).

Volkov, V.

A. Borshch, M. Brodin, V. Volkov, and N. Kukhtarev, "Optical bistability and hysteresis in phase conjugation by degenerate six-photon mixing," Opt. Commun. 41, 213–215 (1982).

Walls, D. F.

D. F. Walls and P. Zoller, "A coherent nonlinear mechanism for optical bistability from three-level atoms," Opt. Commun. 34, 260–264 (1980).

Whitley, R. M.

Winful, H. G.

H. G. Winful and J. H. Marburger, "Hysteresis and optical bistability in degenerate four-wave mixing," Appl. Phys. Lett. 36, 613–614 (1980).

Zoller, P.

D. F. Walls and P. Zoller, "A coherent nonlinear mechanism for optical bistability from three-level atoms," Opt. Commun. 34, 260–264 (1980).

Appl. Phys. (1)

J. Mlynek, F. Mitschke, R. Deserno, and W. Lange, "Optical bistability by transverse optical pumping," Appl. Phys. B 28, 135 (1982).

Appl. Phys. Lett. (3)

G. P. Agrawal, C. Flytzanis, R. Frey, and F. Pradere, "Bistable reflectivity of phase-conjugated signal through intracavity degenerate four-wave mixing," Appl. Phys. Lett. 38, 492–494 (1981).

H. G. Winful and J. H. Marburger, "Hysteresis and optical bistability in degenerate four-wave mixing," Appl. Phys. Lett. 36, 613–614 (1980).

P. F. Liao, D. M. Bloom, and N. P. Economou, "Cw optical wave-front conjugation by saturated absorption in atomic sodium vapor," Appl. Phys. Lett. 32, 813–815 (1978).

IEEE J. Quantum Electron. (2)

G. P. Agrawal, "Phase conjugation and degenerate four-wave mixing in three-level systems," IEEE J. Quantum Electron. QE-17, 2335–2340 (1981).

G. P. Agrawal and C. Flytzanis, "Bistability and hysteresis in phase-conjugated reflectivity," IEEE J. Quantum Electron. QE-14, 374–380 (1981).

Opt. Acta. (1)

G. P. Agrawal and H. J. Carmichael, "Inhomogeneous broadening and the mean-field approximation for optical bistability in a Fabry–Perot," Opt. Acta. 27, 651–660 (1980).

Opt. Commun. (4)

D. F. Walls and P. Zoller, "A coherent nonlinear mechanism for optical bistability from three-level atoms," Opt. Commun. 34, 260–264 (1980).

L. Fu-Li, J. A. Hermann, and J. N. Elgin, "Effects of two-photon optical bistability upon phase conjugation," Opt. Commun. 40, 446–450 (1982).

D. G. Steel and J. F. Lam, "Saturation effects and inhomogeneous broadening in Doppler-free degenerate four-wave mixing," Opt. Commun. 40, 77–80 (1981).

A. Borshch, M. Brodin, V. Volkov, and N. Kukhtarev, "Optical bistability and hysteresis in phase conjugation by degenerate six-photon mixing," Opt. Commun. 41, 213–215 (1982).

Opt. Lett. (5)

Phys. Rev. (3)

R. Bonifacio and L. A. Lugiato, "Optical bistability and cooperative effects in resonance fluorescence," Phys. Rev. A 18, 1129–1144 (1978).

G. P. Agrawal and H. J. Carmichael, "Optical bistability through nonlinear dispersion and absorption," Phys. Rev. A 19, 2074–2086 (1979).

R. G. Brewer and E. L. Hahn, "Coherent two-photon processes: transient and steady-state cases," Phys. Rev. A 11, 1641–1649 (1975).

Phys. Rev. Lett. (3)

R. K. Raj, D. Bloch, J. J. Snyder, G. Camy, and M. Ducloy, "High-frequency optically heterodyned saturation spectroscopy via resonant degenerate four-wave mixing," Phys. Rev. Lett. 44, 1251–1254 (1980).

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, "Differential gain and bistability using a sodium-filled Fabry–Perot interferometer," Phys. Rev. Lett. 36, 1135–1138 (1976).

C. Flytzanis and C. L. Tang, "Light-induced critical behavior in four-wave interaction in nonlinear systems," Phys. Rev. Lett. 45, 441–444 (1980).

Other (6)

C. Flytzanis, G. P. Agrawal, and C. L. Tang, "Critical behavior in optical phase conjugation," in Lasers and Their Applications, W. O. N. Guimaraes, C.-T. Lin, and A. Mooradian, eds. (Springer-Verlag, Berlin, 1981).

For a review see, for example, D. M. Pepper, "Nonlinear optical phase conjugation," Opt. Eng. 21, 155–183 (1982); see also R. A. Fisher, ed., Optical Phase Conjugation (Academic, New York, 1983).

R. L. Abrams and R. C. Lind, "Degenerate four-wave mixing in absorbing media," Opt. Lett. 2, 94–96 (1978); errata, Opt. Lett. 3, 205 (1978).

It is not appropriate to use the term reflectivity spectrum because the laser frequency is kept fixed.

For the case of pulsed radiation, the analysis can be applied if the medium-response time is shorter than the duration of the optical pulse.

In the literature on optical bistability, this is often referred to as the mean-field approximation (see Refs. 8, 9, and 17).

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