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Conference on Lasers and Electro-Optics

Quality of phase-conjugation in nondegenerate four-wave mixing

M. H. Garrett, Hanna J. Hoffman, Thomas J. Karr

Published Jan 1, 1982• 0 citations
Publisher

Abstract

One more promising application of the four-wave mixing process is the correction of arbitrary phase aberrations in an optical beam. In such applications, the fidelity as well as the efficiency of the phase-conjugation process needs to be considered in practice. The process which has received the most extensive attention to date is degenerate four-wave mixing (DFWM). The nonlinear interaction in this case is known to result in a perfect phase-conjugate provided high-quality pump beams are available and competing effects such as local self-focusing (or defocusing) can be neglected.

DOI
10.1364/cleo.1982.fo5

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One more promising application of the four-wave mixing process is the correction of arbitrary phase aberrations in an optical beam. In such applications, the fidelity as well as the efficiency of the phase-conjugation process needs to be considered in practice. The process which has received the most extensive attention to date is degenerate four-wave mixing (DFWM). The nonlinear interaction in this case is known to result in a perfect phase-conjugate provided high-quality pump beams are available and competing effects such as local self-focusing (or defocusing) can be neglected.
Degenerate Four Wave Mixing (DFWM) and Nearly Degenerate Four Wave Mixing (NDFWM) have attracted a considerable attention in non-linear optics. DFWM has found several applications in phase conjugation, used in real time holography and adaptive optics. To realize a higher amplification of the conjugate wave, semiconductor amplifiers have been used. A theoretical analysis of the NDFWM process has been presented by Agrawal [1]. Here, an experimental and theoretical analysis of NDFWM in Distributed Feedback (DFB) lasers is proposed, where the FWM efficiency is enhanced by the cavity feedback mechanism.
Four wave mixing, a third-order optical parametric process, is the nonlinear optical process in which four waves interact with each other through the third-order optical nonlinearity. In this process, three waves form a nonlinear polarization at the frequency of the fourth wave. An important application of degenerate four wave mixing is the generation of phase conjugate wave or simply the phase conjugation. The phase conjugate wave has the same wavefront as the incident wave; however, it propagates backward. The phase conjugation is equivalent to the time reversal. Straightforward application of the time reversal is the correction of phase aberration. Suppose that, the incident wave propagates in the nonuniform medium, such as a laser amplifier, where the temperature is fluctuated by intense pumping. Then, the incident wave suffers severe phase aberration during the propagation and the transmitted wave is then reflected by the phase conjugate mirror and goes back into the same nonuniform medium.
Phase distortion correction of an optical wave propagating in laser media is a crucial problem to be taken into account in most of laser systems. For this purpose, phase conjugation through stimulated Brillouin scattering using the master oscillator-power amplification configuration has shown a very good potential to obtain high beam quality in solid-state lasers that operate at variable repetition rates. Another attractive alternative to generate the phase-conjugate wavefronts is to use a four-wave mixing (DFWM) process in the laser amplifier. In this medium, the interference between the interacting beams leads to a spatial modulation of the complex susceptibility of the medium by gain saturation (amplitude gain grating). This all-solid-state solution presents the advantage of suppressing the external nonlinear medium and would realize the required functions in the laser medium itself. Moreover, due to the amplification experienced by all the interacting beams, associated to the resonant nonlinearity of the gain saturation, high reflectivities already have been achieved in Nd:YAG amplifiers using a multipass geometry.1,2
Phase-conjugate beam fidelity is studied in degenerate four-wave mixing with spatially varying pump beams. The theory includes long-cell-length (or high-gain) effects, diffraction, and nonlinear phase variation, focusing of the probe beam, and, finally, losses. Relatively simple algebraic expressions for the reflectivity are given that cover the cases of collinear or near-collinear beam geometries. An easily calculated parameter is defined that characterizes phase-conjugate fidelity and is applied to study focusing effects. It is shown that focusing effects may be useful in greatly reducing the principal distortion of the phase-conjugate beam over a considerable range of variation of beam parameters.
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.