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Optics Letters

Perturbative analysis of self-oscillation in degenerate four-wave mixing

Kikuo Ujihara

Published Dec 1, 1982• 4 citations
Publisher

Abstract

Self-oscillation of two counterpropagating waves in four-wave mixing under orthogonal pump configuration is analyzed perturbatively, taking into account the pump depletion and the refractive-index variation. A number of threshold pump intensities corresponding to different oscillating field distributions are obtained. Certain values of pump intensity permit multiple solutions for the oscillating field distribution and the corresponding output power of the oscillating waves, indicating a possibility of multistability.

DOI
10.1364/ol.7.000614

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Self-oscillation of two counterpropagating waves in four-wave mixing under orthogonal pump configuration is analyzed perturbatively, taking into account the pump depletion and the refractive-index variation. A number of threshold pump intensities corresponding to different oscillating field distributions are obtained. Certain values of pump intensity permit multiple solutions for the oscillating field distribution and the corresponding output power of the oscillating waves, indicating a possibility of multistability.
A theoretical investigation is made of parametric generation of light by four-wave mixing in an optical cavity with two pump fields of different frequencies. Mixing configurations resulting in the excitation of one and three cavity modes are considered taking into account the effects of phase modulation and of depletion of the pump fields. An analysis is made of stable steady-state oscillation regimes. Calculations are reported of the intensities of the generated radiation modes at the exit from the cavity above the threshold. An analysis is made of the conditions for the appearance of optical bistability at nonzero values of the cavity detuning.
A theoretical investigation is made of parametric generation of light by four-wave mixing in an optical cavity with two pump fields of different frequencies. Mixing configurations resulting in the excitation of one and three cavity modes are are considered taking into account the effects of phase modulation and ef depletion of the pump fields. An analysis is made of stable steady-state oscillation regimes. Calculations are reported or the intensities of the generated radiation modes at the exit from the cavity above the threshold. An analysis is made of the conditions for the appearance of optical bistability at nonzero values of the cavity detuning.
The exact theory of degenerate four-wave mixing in a Kerr-like medium in the Bragg scattering regime is used to study the reflectivity of phase-conjugate mirrors pumped by intense laser beams. The analysis takes into account pump depletion, nonlinear phase modulation and the relaxation time of the nonlinearity. The steady-state response exhibits multivalued reflectivity, hysteresis and potential bistability; however, the transient response shows that at most one value of the phase-conjugate reflectivity is stable. Periodic or chaotic pulsations are predicted beyond threshold values of pump intensity. The onset of a natural oscillation in the Kerr-like medium is also predicted in the absence of a continuous probe beam; the resulting field amplitude is stable and weakly sensitive upon the presence of external noise.
The effects of linear absorption on the degenerate and nondegenerate self-oscillation of a photorefractive phase-conjugate mirror under condition of anisotropic four-wave mixing are considered. The phase conjugation results from nonlinear mixing of two strong undepleted orthogonally polarized counterpropagating pump waves with a probe wave. We consider two types of situation for orthogonally polarized pump beams corresponding to two crystal families: one such as the Bi12SiO20 crystal family (sillenite family) and the other such as the BaTiO3 and strontium barium niobate crystal family. In both of these crystal families the degenerate and nondegenerate self-oscillations are shown to occur in the presence of linear absorption, which tends to increase the value of the coupling coefficient required for self-oscillation. Numerical results are presented that exhibit various features of degenerate and nondegenerate self-oscillation in both crystal families for different values of the phase ϕb of the backward grating.
The phase-conjugate reflectivity attainable by degenerate four-wave mixing in an idealized saturable absorbing medium is calculated for arbitrary values of the laser intensity, laser frequency, and absorption path-length of the nonlinear medium. The influence of pump-wave absorption, including saturation and standing-wave effects, is included in the theory. The treatment is based on an analytic expression for the intensity distribution of the counterpropagating waves. The theoretical predictions differ substantially from those based on theories that ignore pump absorption effects. The results of the present calculation are used to predict the minimum laser intensity, absorption path-length, and detuning required to obtain unit reflectivity and self-oscillation.
A theoretical study of the stationary regime of a four-wave mixing oscillator inside a cavity is presented. The theory is developed in a situation where the phase-conjugate reflection R/sub c/ is much smaller than 1. To find the intensity emitted by this oscillator, two types of saturation mechanism, pump-beam depletion and atomic saturation, are considered. The principal characteristics of the degenerate oscillation are the following: very-low-threshold, bistable behavior, and phase locking of the oscillating beam on the pump beams. In the nondegenerate case, it is shown that the position of the phase-conjugate medium inside the cavity is an essential parameter to determine the threshold condition.>