Off-axial pulse propagation in graded-index materials with Kerr nonlinearity - A variational approach

Abstract

We analyze off-axial, self-focused pulse propagation in graded-index Kerr materials with the variational method. Equations which determine the characteristics of the beam, namely the optical path, the wavefront curvature, the beam width, and the pulse duration are derived and solved. We show that continuously adjustable negative group-velocity dispersion can be generated by off-axial propagation, and for pulse energy smaller than a critical value, negative group-velocity dispersion and Kerr nonlinearity warrant the existence of stable spatio-temporal solitary pulses.