Self-similar pulse-shape mode for femtosecond pulse propagation in medium with resonant nonlinearity

Abstract

We investigate the mode of laser pulse propagation in homogeneous medium with resonant nonlinearity, at which the shape of pulse is self-similar one along some distance of propagation. We take into account a laser pulse frequency detuning from resonant frequency. Both types of sign for frequency detuning are considered. This results in appearance of a refractive index grating which induced self-action of a laser pulse. I certain cases we develop analytical solution of corresponding nonlinear eigenfunction problem of laser pulse propagation in medium for multi-photon resonance. This solution is confirmed by computer simulation of an eigenfunction problem for Schrodinger equation with considered nonlinearity. Using computer simulation, one shows a validity of existence of such kind of laser pulse propagation in a medium with resonant nonlinear response.