Abstract

In a Kerr medium with instantaneous response, pure counterpropagation of scalar plane waves is dynamically stable because of conservation laws. Inclusion of diffraction provides extra degrees of freedom, and both plane waves and Gaussian beams become unstable against transverse modulation when counterpropagating in a Kerr medium, even with no explicit feedback. The spontaneous spatial patterns which emerge may be dynamic or static but are frequently metastable, often persisting for hundreds of transit times before changing. Stability analysis leads to an interpretation as a generalization of phase conjugate oscillation to the Raman-Nath regime, in which formed and backward four-wave mixing terms are important, and can lead to lower thresholds than in the Bragg regime. Thresholds are also often lower than for the plane wave instabilities found when, e.g., finite response time or field polarization are incorporated, so that these theories will often be incomplete without transverse effects. Some existing experimental observations may be ascribable to transverse instabilities, even in more complex configurations such as resonators.

© 1989 Optical Society of America