Dynamics of ultrashort pulses in birefringent media

A system of equations is proposed that describes the dynamics of a laser pulse containing a few optical cycles (ultrashort pulse) in the transparency region of a medium with induced birefringence. In this case, the approximation of slowly varying envelopes, which is standard in the case of monochromatic signals, is inapplicable. An approximate solution is found for the case when the dispersion spreading length is much smaller than the length of the polarisation ellipse beating. It has the form of a travelling soliton-like bound state of ordinary and extraordinary components. The conditions for the stability of this pulse with respect to self-focusing are determined.