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Annual Meeting Optical Society of America

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

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

Published Jan 1, 1986• 0 citations
Publisher

Abstract

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

DOI
10.1364/oam.1986.tui4

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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
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.
The response of a phase-conjugate mirror (PCM) based on nondegenerate four-wave mixing to an incident photon wave packet has been calculated. In the monochromatic limit the phase-compensating property of the PCM, which makes the response independent of optical path length, is recovered. However, for a photon wave packet of nonzero bandwidth, the response of the PCM varies in a fairly complicated manner with the wave-packet length. In particular, the length of the pulse reflected from the PCM becomes independent of the length of the incident pulse for sufficiently short pulses.
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.
The fidelity of the image beam produced by a phase conjugate mirror (PCM) is less when pump beams are not plane waves. On the other hand, high fidelity is a desirable property for most proposed applications, while energy or power should also be economized. We show that PCM fidelity may be characterized in terms of eigenfunctions—and values—of the reflection operator, and optimization may be achieved through use of an appropriate phase filter.1,2 In the present view, the filter has the role of transforming the incident object field into a (near) eigenfunction of the reflectivity operator. An equivalence theorem is presented which demonstrates parallels between the PCM and a certain kind of optical cavity. Perturbation theory applied in the small distortion case leads to an alternative approach to characterization and calculation technique.