Optical guiding of laser beam in nonuniform plasma

A plasma channel produced by a short ionising laser pulse is axially nonuniform resulting from the self-defocusing. Through such preformed plasma channel, when a delayed pulse propagates, the phenomena of diffraction, refraction and self-phase modulation come into play. We have solved the nonlinear parabolic partial differential equation governing the propagation characteristics for an approximate analytical solution using variational approach. Results are compared with the theoretical model of Liu and Tripathi (Phys. Plasmas 1, 3100 (1994)) based on paraxial ray approximation. Particular emphasis is on both beam width and longitudinal phase delay which are crucial to many applications.