Abstract

Spatiotemporal chaos is one of the most attractive problem in physics presently. In the case of passive nonlinear optical systems, a nonlinear medium with a feedback mirror¹ appears to be a very interesting configuration and several impressive observations on pattern formation were reported. The first experimental² and theoretical^1,3 analysis showed the occurrence of an instability whose frequency is on order of c/4d where d is the distance between the nonlinear medium and the feedback mirror. Actually, a more recent experiment done in our laboratory and performed with a rubidium cell showed the occurrence of a spatiotemporal instability with emission of new waves having a polarization orthogonal to that of the incident waves and frequencies for the in stability smaller than c/4d by several orders of magnitude and occurring in the 10 kHz-1 MHz range. The only physical quantities that evolve with time constants having the right order of magnitude are the observables of the ground state. Because the nonlinearity in this experiment arises from optical pumping, the occurrence of such frequencies is not totally surprising; but no model describing how these frequencies appear in this spatiotemporal instability or the physical origin of the polarization of the instability has to our knowledge been presented so far. It is the aim of this paper to present an explanation of the occurrence of these low frequencies and of the polarization of the instability. The analytical model presented here provides a very simple approach to an instability that involves polarization, spatial, and temporal degrees of freedom. More precisely, we show by a self-consistent method the occurrence above threshold of a drift instability whose temporal frequency is determined by the optical pumping process.

© 1994 IEEE