Abstract

Over the last few years, different types of instability associated with counterpropa- gating waves in a bulk Kerrlike medium have been discovered.¹⁻³ Considering a finite response time for the nonlinearity, Silberberg and Bar-Joseph¹ first predicted temporal oscillations and chaos at high intensity. Taking into account the extra degree of freedom due to the polarization state of the fields, Gaeta et al.² have then shown that this polarization state is actually unstable above some intensity threshold. Finally, we have recently shown, using a linear stability analysis, that transverse instabilities also occur above another intensity threshold and an analytical expression has been given for this threshold.³ Here, we present a simple explicit analytical expression (in terms of the length of the medium and the tensor components of the susceptibility) for the polarization instability threshold in the case of equal beam intensities, considering only the first bifurcation. This instability can then be interpreted as a four-wave mixing self-oscillation. This result allows us to compare the different instability thresholds associated with contra- directional waves. It is shown that the transverse instability should dominate, not excluding however the possible onset of polarization instability at higher intensity.

© 1989 Optical Society of America