Abstract

Reflection of a linearly polarized electromagnetic plane wave from an ordinary lossless stratified plane mirror is analyzed in the presence of a phase-conjugate mirror. It is shown that, if the conjugated waves are generated without losses or gains and also without a change in the state of polarization, the specularly reflected wave will be extinguished completely and a phase-conjugated replica of the incident wave will be formed. This result, which clearly illustrates a recently derived general theorem on phase conjugation, is independent of the reflectivity of the ordinary mirror and the separation between the two mirrors. New results for arbitrary reflectivities are also obtained.

© 1983 Optical Society of America

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  1. G. S. Agarwal, A. T. Friberg, and E. Wolf, "Scattering theory of distortion correction by phase conjugation," J. Opt. Soc. Am. 73, 529–538 (1983).
  2. The transformation [Eq. (1)] represents a complete reversal of the state of polarization of the wave on interaction with the PCM. It implies, for example, that a right-hand circularly polarized wave propagating in free space toward the PCM is turned into a right-hand circularly polarized wave propagating away from the PCM. A linearly polarized wave remains linearly polarized in the same plane.
  3. From now on we omit the harmonic factor exp (-iωt) of the various fields.
  4. The fact that the amplitude reflectivity µ is assumed to be constant represents, of course, an idealization. In general, µ will depend on both the direction of propagation and the state of polarization of the wave incident upon the PCM. However, experimental techniques for producing PCM's with the property expressed by Eq. (1), at least for sufficiently small angles of incidence, have been discussed, for example, by B. Ya. Zel'dovich and V. V. Shkunov, "Spatial-polarization wavefront reversal in four-photon interaction," Sov. J. Quantum Electron. 9, 379–381 (1979); B. Ya. Zel'dovich and T. V. Yakovleva, "Spatial-polarization wavefront reversal in stimulated scattering of the Rayleigh line wing," Sov. J. Quantum Electron. 10, 501–505 (1980); and J. F. Lam, D. G. Steel, R. A. McFarlane, and C. R. Lind, "Atomic coherence effects in resonant degenerate four-wave mixing," Appl. Phys. Lett. 38, 977–979 (1981).
  5. By making appropriate changes (see, for example, Sec. 1.6.1 of Ref. 6 below), results similar to those derived in this note for TE waves can also be obtained for TM waves.
  6. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), Sec. 1.6, Eqs. (49) and (50).
  7. In this connection, see Sec. 7 of Ref. 1 and also E. Wolf, "Phase conjugacy and symmetries in spatially bandlimited wavefields containing no evanescent components," J. Opt. Soc. Am. 70, 1311–1319 (1980), Theorem VI.
  8. R. Jacobsson, "Light reflection from films of continuously varying refractive index," in Progress in Optics V, E. Wolf, ed. (North-Holland, Amsterdam, 1966), Chap. 4, Theorem 1, pp. 247–286.
  9. See, for example, A. Vasicek, Optics of Thin Films (North-Holland, Amsterdam, 1960), Chap. 4.
  10. P. D. Drummond and A. T. Friberg, "Specular-reflection cancelation in an interferometer with a phase-conjugate mirror" J. Appl. Phys. (to be published).

1983

1980

Agarwal, G. S.

Born, M.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), Sec. 1.6, Eqs. (49) and (50).

Drummond, P. D.

P. D. Drummond and A. T. Friberg, "Specular-reflection cancelation in an interferometer with a phase-conjugate mirror" J. Appl. Phys. (to be published).

Friberg, A. T.

G. S. Agarwal, A. T. Friberg, and E. Wolf, "Scattering theory of distortion correction by phase conjugation," J. Opt. Soc. Am. 73, 529–538 (1983).

P. D. Drummond and A. T. Friberg, "Specular-reflection cancelation in an interferometer with a phase-conjugate mirror" J. Appl. Phys. (to be published).

Jacobsson, R.

R. Jacobsson, "Light reflection from films of continuously varying refractive index," in Progress in Optics V, E. Wolf, ed. (North-Holland, Amsterdam, 1966), Chap. 4, Theorem 1, pp. 247–286.

Shkunov, V. V.

The fact that the amplitude reflectivity µ is assumed to be constant represents, of course, an idealization. In general, µ will depend on both the direction of propagation and the state of polarization of the wave incident upon the PCM. However, experimental techniques for producing PCM's with the property expressed by Eq. (1), at least for sufficiently small angles of incidence, have been discussed, for example, by B. Ya. Zel'dovich and V. V. Shkunov, "Spatial-polarization wavefront reversal in four-photon interaction," Sov. J. Quantum Electron. 9, 379–381 (1979); B. Ya. Zel'dovich and T. V. Yakovleva, "Spatial-polarization wavefront reversal in stimulated scattering of the Rayleigh line wing," Sov. J. Quantum Electron. 10, 501–505 (1980); and J. F. Lam, D. G. Steel, R. A. McFarlane, and C. R. Lind, "Atomic coherence effects in resonant degenerate four-wave mixing," Appl. Phys. Lett. 38, 977–979 (1981).

Vasicek, A.

See, for example, A. Vasicek, Optics of Thin Films (North-Holland, Amsterdam, 1960), Chap. 4.

Wolf, E.

Zel’dovich, B. Ya.

The fact that the amplitude reflectivity µ is assumed to be constant represents, of course, an idealization. In general, µ will depend on both the direction of propagation and the state of polarization of the wave incident upon the PCM. However, experimental techniques for producing PCM's with the property expressed by Eq. (1), at least for sufficiently small angles of incidence, have been discussed, for example, by B. Ya. Zel'dovich and V. V. Shkunov, "Spatial-polarization wavefront reversal in four-photon interaction," Sov. J. Quantum Electron. 9, 379–381 (1979); B. Ya. Zel'dovich and T. V. Yakovleva, "Spatial-polarization wavefront reversal in stimulated scattering of the Rayleigh line wing," Sov. J. Quantum Electron. 10, 501–505 (1980); and J. F. Lam, D. G. Steel, R. A. McFarlane, and C. R. Lind, "Atomic coherence effects in resonant degenerate four-wave mixing," Appl. Phys. Lett. 38, 977–979 (1981).

J. Opt. Soc. Am.

Sov. J. Quantum Electron.

The fact that the amplitude reflectivity µ is assumed to be constant represents, of course, an idealization. In general, µ will depend on both the direction of propagation and the state of polarization of the wave incident upon the PCM. However, experimental techniques for producing PCM's with the property expressed by Eq. (1), at least for sufficiently small angles of incidence, have been discussed, for example, by B. Ya. Zel'dovich and V. V. Shkunov, "Spatial-polarization wavefront reversal in four-photon interaction," Sov. J. Quantum Electron. 9, 379–381 (1979); B. Ya. Zel'dovich and T. V. Yakovleva, "Spatial-polarization wavefront reversal in stimulated scattering of the Rayleigh line wing," Sov. J. Quantum Electron. 10, 501–505 (1980); and J. F. Lam, D. G. Steel, R. A. McFarlane, and C. R. Lind, "Atomic coherence effects in resonant degenerate four-wave mixing," Appl. Phys. Lett. 38, 977–979 (1981).

Other

By making appropriate changes (see, for example, Sec. 1.6.1 of Ref. 6 below), results similar to those derived in this note for TE waves can also be obtained for TM waves.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), Sec. 1.6, Eqs. (49) and (50).

R. Jacobsson, "Light reflection from films of continuously varying refractive index," in Progress in Optics V, E. Wolf, ed. (North-Holland, Amsterdam, 1966), Chap. 4, Theorem 1, pp. 247–286.

See, for example, A. Vasicek, Optics of Thin Films (North-Holland, Amsterdam, 1960), Chap. 4.

P. D. Drummond and A. T. Friberg, "Specular-reflection cancelation in an interferometer with a phase-conjugate mirror" J. Appl. Phys. (to be published).

The transformation [Eq. (1)] represents a complete reversal of the state of polarization of the wave on interaction with the PCM. It implies, for example, that a right-hand circularly polarized wave propagating in free space toward the PCM is turned into a right-hand circularly polarized wave propagating away from the PCM. A linearly polarized wave remains linearly polarized in the same plane.

From now on we omit the harmonic factor exp (-iωt) of the various fields.

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