Transverse instabilities in the polarizations and intensities of counterpropagating light waves

We present a theoretical analysis of the stability characteristics of each of the four eigenpolarization configurations of two light waves counterpropagating through a nonlinear medium. Our treatment generalizes previous treatments in that we allow the possibility of the development of transverse instabilities in either the intensities or the polarizations of the waves. Indeed, we find that under many conditions the instability develops in directions other than the symmetry axis of the interaction and that the instability can affect the intensity or the polarization of the waves. We also find through numerical computations that the polarizations of the waves can become unstable in the nonlinear regime at intensities above the threshold for the transverse amplitude instability but below the threshold predicted by linear stability analysis for the corresponding polarization instability. We conclude that in many cases the inclusion of the tensor properties of the nonlinear interaction is important in describing the dynamical behavior of counterpropagating waves.