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Nonlinear Optics

Effects of Phase Distortions in Conjugating Media

Matthew C. Bashaw, Abraham Aharoni, Lambertus Hesselink

Published Jan 1, 1992• 0 citations
Publisher

Abstract

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.

DOI
10.1364/nlo.1992.fa4

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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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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jun 17, 2003•0 citations
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].
Recent experimental results have shown that the highly directional frequency-upconverted backward-stimulated emission from a two-photon-pumped lasing medium possesses the property of optical phase conjugation. To explain this property, a Gabor’s quasi-collinear holographic model is proposed for a two-photon-pumped gain medium. According to this model, the input IR pump beam (after passing through a phase-distorting medium or an aberration plate) can be assumed to consist of two parts: an undisturbed regular portion and a phase-distorted irregular portion. These two portions interfere with each other and create a volume holographic grating within the pumped region inside the gain medium. While an initial regular backward-stimulated emission (as a reading beam) is passing through this holographic grating, a diffracted wave is created and amplified together with the reading beam. A rigorous mathematical analysis shows that under certain conditions the combination of these two parts (the reading beam plus the diffracted wave) of the backward-stimulated emission can be an approximate phase-conjugate field of the total input-pump field.
When a Kerr medium is pumped by a strong laser beam, the nonlinear process of four-wave mixing (FWM) can mix the pump laser and a weak signal to generate a phase-conjugated version of the signal. Optical phase conjugation (OPC) may be employed to compensate the chromatic dispersion and nonlinearity of transmission fibers. It may even serve as a parametric amplifier when the pump is sufficiently intense. Furthermore, the FWM effect is capable of phase-conjugating or amplifying many wavelength-division multiplexed (WDM) signals simultaneously. However, the same FWM effect results in parasitic processes by generating inter-mixing terms among the WDM signals. The center frequency of such unwanted mixing terms may coincide with some of the original or conjugated WDM signals to cause significant interference. This paper studies such interference effect by means of theoretical calculation and computer simulation. It is shown that the coherent interference effect decreases as the pump-power to signal-power ratio (PSR) increases. Unfortunately, there could still be strong interference even with a PSR of 20dB. Some guard-band in the frequency domain is necessary to avoid such coherent interference: if the total bandwidth of the WDM signals is W, then the nearest signal should be more than W away from the pump frequency.