Few-cycle solitary wave formation from elliptically polarized ultrashort laser pulse in a medium with frequency dispersion

In this work we study numerically the quasi-solitary propagation of ultrashort elliptically polarized laser pulses in isotropic medium with cubic nonlinearity, under condition, when the frequency spectrum of the propagating light does not overlap with one-photon resonances and multi-photon non-Raman resonances. For that we use the modification of finite-difference time-domain method with auxiliary differential equation. It is shown that proper choice of initial conditions results in the formation of elliptically polarized solitary wave, which propagates then for a long distance. For the few-oscillation incident pulse its shape and the oscillation character practically do not change at distances of the order of hundreds of wavelengths, and the direction of the oscillations uniformly rotates in the course of propagation. The retardation of the nonlinear response of the medium limits the possibility of the solitary wave formation for few-cycle elliptically polarized pulses, and affects the carrier frequency shift of the incident elliptically polarized pulse. It is established that for any polarization state of the pulse its carrier frequency shift is almost proportional to the reciprocal duration of the pulse in forth degree.