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Optics Letters

Transverse-mode instability and chaos in an optical cavity with phase-conjugate mirror

Erik J. Bochove

Published Nov 1, 1986• 7 citations
Publisher

Abstract

We calculate the effect of pump-intensity variation on the mode structure of an optical cavity with a phaseconjugate mirror operated in the linear regime. Instabilities and chaos are predicted under conditions similar to those observed by Valley and Dunning [Opt. Lett. 9, 513 (1984)].
DOI
10.1364/ol.11.000727

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The phase-conjugate reflectivity produced by degenerate four-wave mixing in a Kerr medium in the Bragg scattering regime is shown to be unstable when the intensity of the external pump beams is greater than a threshold value that can be predicted analytically. Below this threshold, a single branch of the reflectivity curve is stable, eliminating any possibility for bistability. A numerical simulation indicates that the unstable regime is characterized by fast oscillations with a period related to the transit time in the nonlinear medium. A finite relaxation time of the nonlinearity eliminates the high-frequency oscillations but can increase the amplitude of the low-frequency components. The insertion of a phase-conjugate mirror into an optical cavity leads to an instability whose threshold can be evaluated analytically. The temporal evolution of the field intensity in the cavity is shown to change from a stable regime to periodic oscillations and then to quasi-periodic oscillations as the pump intensity is increased.
The effect of transverse intensity variation on the various instabilities associated with optical bistability seems to be catastrophic in the case of pure absorptive bistability1,2 but benign in the mixed absorptive-dispersive case.2,3 In particular, recent results of Lugiato et al.2 indicate that the mean-field single-mode instability is not destroyed by the assumption of a Gaussian transverse intensity profile, and that it should be observable for experimentally accessible parameter values. Stimulated by these results, we have looked for and observed self-pulsing due to the single-mode instability in the predicted region of parameter space.
We present a fully nonlinear theory of a phase-conjugate resonator in which the phase-conjugate mirror is a diffusive Kerr medium with an arbitrary ratio of cavity round-trip time to medium response time. The model is restricted to the Raman–Nath scattering regime but includes pump depletion and transverse coupling, which is provided by diffraction inside the cavity and diffusion inside the phase-conjugate mirror. A transverse linear-stability analysis of steady-state solutions is performed. The case of a sluggish medium is studied numerically in both low- and high-diffraction geometries.
We present here instabilities observed in the transverse profile of a continuous-wave light beam that crosses a sample of sodium vapor twice by means of a feedback mirror. The wave front and the intensity of the beam are spatially modulated by the intensity-dependent dispersive and absorptive action of the vapor. Experimental evidence indicates that the vapor acts as a phase-conjugate mirror, thus providing an active cavity when it is coupled with the feedback mirror. The instabilities develop as a consequence of sideband generation at the resonant modes of this cavity. The transverse-mode profiles of these sidebands are analyzed experimentally.