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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Reciprocity and conjugation fidelity in double phase conjugate mirrors

Philippe Delaye, Andrei A. Fotiadi, Gérald Roosen

Published Sep 20, 1999• 0 citations

Abstract

It is well known that the conservation of energy in an optical system can be described by an invariant (intensity of the optical wave) during propagation. We identically show that reciprocity can be described by an invariant. This invariant is the overlap integral of two counterpropagating waves, that stays constant in every place of a reciprocal optical system. Applied to the double phase conjugate mirror (DPCM) this invariant can be rewritten as an equality between the ratio of the conjugation fidelity of the two ports of the DPCM and the ratio of the transmission in intensity of the two beams. If restricted to a plane wave case this relation becomes the well known equality of the diffraction efficiencies in both directions. We have implemented an experimental set-up that allows to show that the double phase conjugate mirror is reciprocal what confirms all the above discussion. We use the same set-up to measure the conjugation fidelity of the DPCM.

DOI: 10.1117/12.363924

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It is well known that the conservation of energy in an optical system can be described by an invariant (intensity of the optical wave) during propagation. We identically show that reciprocity can be described by an invariant. This invariant is the overlap integral of two counterpropagating waves, that stays constant in every place of a reciprocal optical system. Applied to the double phase conjugate mirror (DPCM) this invariant can be rewritten as an equality between the ratio of the conjugation fidelity of the two ports of the DPCM and the ratio of the transmission in intensity of the two beams. If restricted to a plane wave case this relation becomes the well known equality of the diffraction efficiencies in both directions. We have implemented an experimental set-up that allows to show that the double phase conjugate mirror is reciprocal what confirms all the above discussion. We use the same set-up to measure the conjugation fidelity of the DPCM.

The double phase-conjugate mirror (DPCM) is a stimulated four-wave mixing effect, mediated by either a chi(3) mechanism or a photorefractive effect. The type of grating that operates in the DPCM can be a transmission or reflection grating, depending on the wave-mixing configuration. Any combination of nonlinearity and grating geometry is possible, so that four general DPCM classes emerge. An analytic solution of the last unsolved class, the photorefractive reflection DPCM, is presented. With these results, general observations concerning the four categories of double phase conjugation are made. An important conclusion is that the type of grating geometry and its associated boundary conditions dictate many of the basic features of the DPCM, regardless of the nonlinearity involved.

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.

The fidelity of phase conjugation by degenerate four-wave mixing in ruby and semiconductor-doped glasses has been measured by means of our own modified Twyman–Green interferometer [Opt. Lett. 14, 183 (1989)] implementing two phase conjugate mirrors. It is shown that the fidelity of phase conjugators with an OG530 color filter as the nonlinear medium reaches a value of 99%. The fidelity of ruby is also reported. Additionally the effect of the recording system on the value of the fidelity is discussed.