Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Applied Physics

Specular reflection cancellation in an interferometer with a phase-conjugate mirror

P. D. Drummond, Ari T. Friberg

Published Oct 1, 1983• 31 citations
Publisher

Abstract

An ordinary mirror placed in front of a phase-conjugate mirror forms a type of Fabry–Perot interferometer with unusual reflection properties. The specularly reflected and phase-conjugate reflected intensities are analyzed for arbitrary reflection coefficients, given an incident monochromatic linearly polarized plane wave. It is shown that if the ordinary mirror is lossless and the phase-conjugate reflectivity is unity, the specularly reflected wave disappears completely. This leaves only the phase-conjugate reflected wave that propagates in the direction opposite to that of the incident wave. The above result is independent of the reflectivity of the ordinary mirror and the separation between the two interferometer mirrors. Some of the main effects due to absorption in the ordinary mirror are briefly discussed.

DOI
10.1063/1.331821

Related papers

Cancellation of specular reflection in the presence of a phase conjugate mirror

I. Lindsay, John Christopher Dainty

We present experimental results showing the partial cancellation of the specular reflection off a lossless partially transmitting ordinary plane mirror in the presence of a phase conjugate mirror. This effect was first theoretically predicted by Drummond and Friberg.1 In the experimental situation a single domain photorefractive crystal of barium titanate operating via degenerate four-wave mixing acted as the phase conjugate mirror. It was placed behind a lossless partially transmitting ordinary plane mirror so that an optical resonant activity was created. Collimated light was directed onto the ordinary mirror at non-normal incidence. The intensity of the specular reflection was monitored, the extent of its cancellation for the measured phase conjugate reflectivities agreed well with the proposed theory.2 The experimental results lay marginally above the theoretical curve. The reason for such a systematic error is considered to lie with the fidelity of the phase conjugate generated.

Annual Meeting Optical Society of America•Jan 1, 1986•0 citations

Fields generated by a Fabry–Perot interferometer with a phase-conjugate mirror

Manuel Nieto‐Vesperinas

We study theoretically a Fabry–Perot interferometer with one phase-conjugate mirror. Comparisons with results previously obtained by Kastler [ Appl. Opt.1, 17 ( 1962)] for an ordinary Fabry–Perot interferometer are made. Specifically, we discuss the field intensity of the light both outside and inside the interferometer. We also study the intensity of the exterior field that is due to atoms radiating incoherently inside the interferometer. The operating characteristics below the threshold of the interferometer when it is filled with a gain medium are also analyzed and are found to be different from those of the ordinary interferometer. Finally, conditions are obtained under which the cavity can act as a regenerative amplifier.

Journal of the Optical Society of America A•Mar 1, 1985•7 citations

Interference pattern produced on reflection at a phase-conjugate mirror II: Experiment

Arturo A. Jacobs, Wayne R. Tompkin, Robert W. Boyd +1 more

The nature of the fringe pattern produced by interference between a wave incident upon a phase-conjugate mirror and that leaving the mirror has been studied experimentally for a phase-conjugate mirror based on degenerate four-wave mixing. The fringe locations are found to depend on the phase of the wave incident upon the mirror, in agreement with recent theoretical predictions but in contrast to the results observed for the interference pattern produced on reflection at an ordinary metal mirror. The phases of the waves that pump the phase-conjugate mirror are shown to provide the reference with respect to which the phase of the incident wave is determined.

Journal of the Optical Society of America B•Aug 1, 1987•12 citations

Nature of the interference pattern produced on reflection at a phase-conjugate mirror

Arturo A. Jacobs, Wayne R. Tompkin, Robert W. Boyd

We have repeated the classic experiment of Wiener,1 which established the nature of the standing-wave pattern produced by reflection at the surface of a metallic mirror, with the metallic mirror used in his experiment replaced by a phase-conjugate mirror. We find that the positions of the fringes produced by interference between the wave incident on the phase-conjugate mirror and the wave leaving the mirror depends on the phase of the incident wave. This result is in contrast to that obtained through the use of a metallic mirror, in which case the interference pattern is found to be independent of the phase of the incident wave. The origin of the different behavior in these two cases lies in the fact that the phases of the waves that pump the PCM provide a reference through which phase information carried by the signal wave can be obtained. The experimental results are in excellent quantitative agreement with recent theoretical predictions.2

Annual Meeting Optical Society of America•Jan 1, 1986•0 citations

Fresnel coefficients for a phase conjugator

Henk F. Arnoldus, Thomas F. George

Optical phase conjugation by four-wave mixing is examined in detail. The Fresnel coefficients for reflection and transmission of a plane wave irradiating the surface of the phase conjugator are calculated. It appears that for normal incidence and a weak nonlinear interaction the device produces the phase-conjugated beam with respect to the incoming beam. For finite angles of incidence or stronger nonlinearities in the crystal, the generated wave deviates from the ideal conjugated wave, and also a second, specularly reflected, wave appears.

Journal of the Optical Society of America B•Jan 1, 1989•1 citation

Dynamics of Fabry–Perot resonators with a phase-conjugate mirror

Ari T. Friberg, Martti Olavi Kauranen, Rainer Salomaa

We study the dynamics of a stable Fabry–Perot resonator in which one mirror is a phase-conjugate mirror (PCM) with instantaneous response. The temporal variations in the model are caused by round-trip effects. An exact solution is given in a form of an infinite series. The step-function response is summed exactly. Numerical studies with Gaussian input pulses and PCM reflectivity variations are presented, and their behavior is explained. Approximate formulas for responses to slowly varying pulses are derived. Noise effects are simulated with a model in which the phases of the probe and the amplitude reflection coefficient of the PCM make uncorrelated jumps with Poissonian statistics. The theoretical model is aimed for optimizing experiments on phase-conjugate resonators involving transients and fluctuating fields.

Journal of the Optical Society of America B•Dec 1, 1986•9 citations
An ordinary mirror placed in front of a phase-conjugate mirror forms a type of Fabry–Perot interferometer with unusual reflection properties. The specularly reflected and phase-conjugate reflected intensities are analyzed for arbitrary reflection coefficients, given an incident monochromatic linearly polarized plane wave. It is shown that if the ordinary mirror is lossless and the phase-conjugate reflectivity is unity, the specularly reflected wave disappears completely. This leaves only the phase-conjugate reflected wave that propagates in the direction opposite to that of the incident wave. The above result is independent of the reflectivity of the ordinary mirror and the separation between the two interferometer mirrors. Some of the main effects due to absorption in the ordinary mirror are briefly discussed.
We present experimental results showing the partial cancellation of the specular reflection off a lossless partially transmitting ordinary plane mirror in the presence of a phase conjugate mirror. This effect was first theoretically predicted by Drummond and Friberg.1 In the experimental situation a single domain photorefractive crystal of barium titanate operating via degenerate four-wave mixing acted as the phase conjugate mirror. It was placed behind a lossless partially transmitting ordinary plane mirror so that an optical resonant activity was created. Collimated light was directed onto the ordinary mirror at non-normal incidence. The intensity of the specular reflection was monitored, the extent of its cancellation for the measured phase conjugate reflectivities agreed well with the proposed theory.2 The experimental results lay marginally above the theoretical curve. The reason for such a systematic error is considered to lie with the fidelity of the phase conjugate generated.
We study theoretically a Fabry–Perot interferometer with one phase-conjugate mirror. Comparisons with results previously obtained by Kastler [ Appl. Opt.1, 17 ( 1962)] for an ordinary Fabry–Perot interferometer are made. Specifically, we discuss the field intensity of the light both outside and inside the interferometer. We also study the intensity of the exterior field that is due to atoms radiating incoherently inside the interferometer. The operating characteristics below the threshold of the interferometer when it is filled with a gain medium are also analyzed and are found to be different from those of the ordinary interferometer. Finally, conditions are obtained under which the cavity can act as a regenerative amplifier.
The nature of the fringe pattern produced by interference between a wave incident upon a phase-conjugate mirror and that leaving the mirror has been studied experimentally for a phase-conjugate mirror based on degenerate four-wave mixing. The fringe locations are found to depend on the phase of the wave incident upon the mirror, in agreement with recent theoretical predictions but in contrast to the results observed for the interference pattern produced on reflection at an ordinary metal mirror. The phases of the waves that pump the phase-conjugate mirror are shown to provide the reference with respect to which the phase of the incident wave is determined.
We have repeated the classic experiment of Wiener,1 which established the nature of the standing-wave pattern produced by reflection at the surface of a metallic mirror, with the metallic mirror used in his experiment replaced by a phase-conjugate mirror. We find that the positions of the fringes produced by interference between the wave incident on the phase-conjugate mirror and the wave leaving the mirror depends on the phase of the incident wave. This result is in contrast to that obtained through the use of a metallic mirror, in which case the interference pattern is found to be independent of the phase of the incident wave. The origin of the different behavior in these two cases lies in the fact that the phases of the waves that pump the PCM provide a reference through which phase information carried by the signal wave can be obtained. The experimental results are in excellent quantitative agreement with recent theoretical predictions.2
Optical phase conjugation by four-wave mixing is examined in detail. The Fresnel coefficients for reflection and transmission of a plane wave irradiating the surface of the phase conjugator are calculated. It appears that for normal incidence and a weak nonlinear interaction the device produces the phase-conjugated beam with respect to the incoming beam. For finite angles of incidence or stronger nonlinearities in the crystal, the generated wave deviates from the ideal conjugated wave, and also a second, specularly reflected, wave appears.
We study the dynamics of a stable Fabry–Perot resonator in which one mirror is a phase-conjugate mirror (PCM) with instantaneous response. The temporal variations in the model are caused by round-trip effects. An exact solution is given in a form of an infinite series. The step-function response is summed exactly. Numerical studies with Gaussian input pulses and PCM reflectivity variations are presented, and their behavior is explained. Approximate formulas for responses to slowly varying pulses are derived. Noise effects are simulated with a model in which the phases of the probe and the amplitude reflection coefficient of the PCM make uncorrelated jumps with Poissonian statistics. The theoretical model is aimed for optimizing experiments on phase-conjugate resonators involving transients and fluctuating fields.