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Multi-Wave Mixing

LASZLO SOLYMAR, David John Webb, A. Grunnet-Jepsen

Published Aug 15, 1996• 0 citations
Publisher

Abstract

Abstract In the preceding chapters we have seen that the interaction of two beams within a photorefractive medium involves a great deal of interesting physics and can result in optical amplification. As might be expected, the interaction of three or more waves in such a medium leads to additional surprising effects, perhaps the most remarkable of which is phase conjugation.

DOI
10.1093/oso/9780198565017.003.0009

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Abstract In the preceding chapters we have seen that the interaction of two beams within a photorefractive medium involves a great deal of interesting physics and can result in optical amplification. As might be expected, the interaction of three or more waves in such a medium leads to additional surprising effects, perhaps the most remarkable of which is phase conjugation.
While the interaction of optical beams in photorefractive crystals can often be accurately described in terms of 1-D plane-wave approximation, 2-D models are sometimes more suitable, as suggested by recent work.1 Here we discuss some aspects of photorefractive interaction of finite size optical beams. We have solved the system of partial differential equations governing two- and four-wave mixing numerically by using iterative procedures. Simulations of beam amplification in two-beam coupling show strong beam deformation even without any spatial information imposed on them. Spatially nonuniform energy transfer is responsible for this effect. The pump beam loses energy during propagation and at the end of its passage through the beam intersection region (which was completely inside the crystal) it is strongly depleted and cannot contribute significantly to beam amplification. As the pump beam crosses through the probe, it amplifies most strongly that side of the probe that it meets first. By the time the pump has reached the far side of the probe, it is strongly depleted and less effective at probe amplification. In the case of phase conjugation through four-wave mixing, we found that the conjugate beam is strongly deformed only when the coupling constant is negative (corresponding to deamplification of the probe input beam). For positive coupling constants the output conjugate beam is a good replica of the input probe beam.
There is presently a growing interest in nearly degenerate four-wave mixing, both for application in optical phase conjugation and the generation of squeezed states. In particular, the self-oscillation of a system interacting with one or two pump beams has been investigated in great detail in the case of photorefractive materials, but very few experiments have been done in vapors in the cw regime. The results that we obtained using sodium are presented here. They are strikingly different from the results obtained with photorefractive materials. For example, the oscillating beam and pump beam frequencies coincide with a precision better than 10−2 Hz. Another interesting aspect of this oscillating beam is that it exhibits a phase sensitive noise: just above threshold, the noise on one quadrature of the field can be 10−2 times smaller than the noise on the other quadrature.
Optical phase conjugation is concerned with the use of nonlinear optical effects to precisely reverse the direction of propagation of each plane wave in an arbitrary beam of light. This causes the return beam to exactly retrace the path of the incident beam, leading to many applications of automatic pointing and tracking (even in the presence of an inhomogeneous medium). The main goals of this course are familiarization with how each of the many nonlinear optical effects gives rise to a phase conjugate signal, and understanding and appreciation of the many potential applications for optical phase conjugation. Conjugation techniques involving Kerr-like degenerate four-wave mixing, resonant degenerate four-wave mixing, stimulated Brillouin scattering, photorefractive effects, surface phenomena, and others will be carefully reviewed. Applications of particular importance to this course will include distortion correction, pointing, tracking, laser-resonator design, optical information processing, etc. Throughout the course, key references will be identified for those wishing to pursue any topic more vigorously.