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Optics Letters

Compensation for phase distortions in nonlinear media by phase conjugation

David M. Pepper, Amnon Yariv

Published Feb 1, 1980• 130 citations
Publisher

Abstract

We demonstrate theoretically that the distortion-correction property of phase-conjugate beams propagating in reverse through aberrating media is also operative when the indices of refraction of the media depend on the intensity. A necessary condition is that the phase-conjugate mirror that generates the reflected beam possess a unity (magnitude) “reflection” coefficient.

DOI
10.1364/ol.5.000059

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Phase conjugated light waves reverse phase distortions in media with negligible absorption or for paraxial beam propagation [1]. We examine here a different case in which a volume conjugating medium is itself imperfect, possessing phase distortions and a conjugating efficiency dependent on grating spatial frequency. We show theoretically that for multiplexed signals, cross-talk-free phase-conjugation is obtained only for negligible spatial-frequency dispersion and a phase-conjugated reference or pump wave, and we present supporting experimental results.

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Compensation of phase distortions in conjugating media

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Phase-conjugated light waves are known to reverse phase distortions in media with negligible absorption or for paraxial beam propagation.1 We examine here a different case in which a volume conjugating medium is itself imperfect, possessing phase distortions and a conjugating efficiency dependent on grating spatial frequency. We show theoretically that for multiplexed signals, cross-talk-free phase conjugation is obtained only for negligible spatial-frequency dispersion and a phase-conjugated reference wave. We further present experimental results in a severely striated sample of photorefractive strontium barium niobate; using a phase-conjugated reference wave, we demonstrate the alleviation of distortion2 and the elimination of cross talk between closely spaced angularly multiplexed signals.

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Optical phase conjugation is a process that leads to the correction of wavefront distortions under conditions such that a beam of light passes twice in opposite directions through an aberrating optical medium. Analogously, the state of polarization of an optical beam can become aberrated, (for example, by passing through a stressed optical component), and these polarization aberrations can be removed by the process of polarization conjugation. In polarization conjugation, the polarization unit vector of the incident wave is replaced by its complex conjugate in the generated wave.

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Fundamental media considerations for the propagation of phase-conjugate waves

Amnon Yariv

Rigorous and approximate conditions that need to be satisfied by a propagation medium to enable phase conjugation to occur are derived. It is shown that, in spite of the fact that in general, losses spoil phase conjugation, in the important case of paraxial beam propagation (along z), a z-dependent loss can be tolerated. In addition, nonlinear losses (gain) and nonlinear dielectrics are also permitted under some fairly general circumstances.

Optics Letters•Sep 15, 1991•12 citations
We demonstrate theoretically that the distortion-correction property of phase-conjugate beams propagating in reverse through aberrating media is also operative when the indices of refraction of the media depend on the intensity. A necessary condition is that the phase-conjugate mirror that generates the reflected beam possess a unity (magnitude) “reflection” coefficient.
Phase conjugated light waves reverse phase distortions in media with negligible absorption or for paraxial beam propagation [1]. We examine here a different case in which a volume conjugating medium is itself imperfect, possessing phase distortions and a conjugating efficiency dependent on grating spatial frequency. We show theoretically that for multiplexed signals, cross-talk-free phase-conjugation is obtained only for negligible spatial-frequency dispersion and a phase-conjugated reference or pump wave, and we present supporting experimental results.
Phase-conjugated light waves are known to reverse phase distortions in media with negligible absorption or for paraxial beam propagation.1 We examine here a different case in which a volume conjugating medium is itself imperfect, possessing phase distortions and a conjugating efficiency dependent on grating spatial frequency. We show theoretically that for multiplexed signals, cross-talk-free phase conjugation is obtained only for negligible spatial-frequency dispersion and a phase-conjugated reference wave. We further present experimental results in a severely striated sample of photorefractive strontium barium niobate; using a phase-conjugated reference wave, we demonstrate the alleviation of distortion2 and the elimination of cross talk between closely spaced angularly multiplexed signals.
Nonlinear optics normally involves the change in the susceptibility of a material due to the presence of optical radiation. In many cases, the light-matter interaction produces a change in the refractive index of the medium, as occurs in photorefractive media, as well as in Kerr-like media, Brillouin-active media and absorbing media with thermallyinduced refractive index changes. Such nonlinear refractive index variation corresponds to a change in the real part of the optical susceptibility %. In resonant materials, the optical radiation induces stimulated emission (or absorption) causing transfer of population between different energy states of the medium. This can lead to saturation of the amplification (or absorption) corresponding to changes in the imaginary part of the susceptibility x= i2odk where the amplitude gain coefficient a(I) is a saturable function of the intensity /, and k is the magnitude of the wavevector of the optical radiation. The interference of two (or more) coherent beams I(x) in the laser amplifier can cause a modulation of the population inversion N(x). This modulation of the inversion is commonly known as spatial hole burning in lasers and leads to formation of a gain-grating a(x) = 1/2GN(X) where G is the stimulated emission cross-section. The gain grating can act as a very efficient diffractive optical element exhibiting high diffraction efficiency that may be even greater than unity [16] and also very high phase conjugate reflectivity using four-wave mixing (FWM) geometries [5-7].
Optical phase conjugation is a process that leads to the correction of wavefront distortions under conditions such that a beam of light passes twice in opposite directions through an aberrating optical medium. Analogously, the state of polarization of an optical beam can become aberrated, (for example, by passing through a stressed optical component), and these polarization aberrations can be removed by the process of polarization conjugation. In polarization conjugation, the polarization unit vector of the incident wave is replaced by its complex conjugate in the generated wave.