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Applied Physics Letters

Observation of amplified phase-conjugate reflection and optical parametric oscillation by degenerate four-wave mixing in a transparent medium

David M. Pepper, Dan Fekete, Amnon Yariv

Published Jul 1, 1978• 101 citations
Publisher

Abstract

We report on the observation of amplified reflection and optical parametric oscillation via degenerate four-wave mixing in a nonresonant medium. The process is mediated through the third-order nonlinear susceptibility in a transparent liquid medium, CS2. A collinear mixing geometry is utilized to obtain long interaction lengths and polarization discrimination is used to separate the pump and signal fields.

DOI
10.1063/1.90185

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Journal of the Optical Society of America B•Feb 1, 1988•8 citations
We report on the observation of amplified reflection and optical parametric oscillation via degenerate four-wave mixing in a nonresonant medium. The process is mediated through the third-order nonlinear susceptibility in a transparent liquid medium, CS2. A collinear mixing geometry is utilized to obtain long interaction lengths and polarization discrimination is used to separate the pump and signal fields.
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.
The functional relations have been presented between the complex amplitude (including polarization) of reflected wave on the one hand and amplitudes, polarizations of pump and probe waves, the third-order nonlinear susceptibility on the other hand, for degenerate four-wave mixing (DFWM) in isotropic medium, in which the polarizations are linear and/or circular, and the geometry is collinear or non-collinear. In the non-collinear geometry, when the polarizations of pump waves are parallel to each other, one can determine the ratio x1111/x1221 from the angles between polarization directions of probe and reflected waves; when the polarizations of pump are circular polarizations of the same handedness, one can get the ideal complex conjugate wave in this geometry. In the collinear geometry, there are always some non-conjugate component in the reflected wave, and the functional relation between reflection coefficient of amplitude and the thickness of sample can have the form of tangent function, hyperbolic tangent function and linear function; when the polarizations of pump waves are parallel to each other and |x1221|> |x1122|, this geometry is capable of generating self-oscillation; when polarizations of pump are circular ones of different handedness, DFWM acts as an ideal plane-mirror for probe wave with circular polarization, etc. The results can be used to explain some well-known experimental results and provide some theoretical guidance for designing new experiments.
Part I of this thesis describes the theoretical and experimental aspects of a new area in coherent optics known as phase conjugate optics. By using nonlinear optical mixing techniques, the complex conjugate of an arbitrary incident monochromatic wave can be generated. In particular, the theory of the degenerate four-wave mixing technique is presented. Experimental observation of phase conjugate wave front generation in a liquid crystal material (MBBA) is described. The ability of the conjugate wave front to correct for phase aberration is demonstrated. The quantum mechanical origin of the nonlinear third order susceptibility responsible for the four-wave mixing process is illustrated in an atomic system. Because of a finite memory time of such an atomic system, the electromagnetic waves taking part in the mixing process need not occur simultaneously. The applications of the phase conjugation process to real-time information processing and the characteristics of a phase conjugate resonator are discussed in detail. The ability of an optical fiber to confine the propagation of electromagnetic waves over a long distance and within a small cross sectional area implies that large optical intensities can be maintained over a long " interaction length even at moderate incident optical power. Part II of this thesis describes some third order nonlinear optical phenomena that have been observed under this condition. Especially, phase conjugation by degenerate four-wave mixing in a fiber has been shown to require significantly less pumping power. The theoretical and experimental studies of four-wave mixing in a liquid-filled fiber are presented. Extensive experimental efforts have been devoted over the last few years to the study of stimulated Raman scattering and the oscillation of the Stokes radiation inside fibers. A detailed theoretical treatment will be given here to describe these effects. The analysis shows that pump depletion due to the nonlinear process is very important in describing the stimulated Raman scattering in low loss fibers and is the dominant saturation effect in a fiber Raman oscillator. Finally, the implications of nonlinear optical phenomena to fiber optic communication will be mentioned.
We derive an exact solution for both amplitude and phase of a signal that is back-reflected by collinear nonlinear degenerate mixing of four circularly polarized waves of arbitrary intensity in a Kerr-like medium. Our analysis suggests that taking pump depletion into account may spoil the ideal phase-conjugation condition, even in the limit of weak nonlinear coupling, and indicates that substantial deterioration of the probe phase-reversal property may occur for strongly interacting waves in a manner that is highly sensitive to the anisotropy of the nonlinear susceptibility.