Steady-state self-focusing and filamentation in the presence of longitudinal inhomogeneity

This paper examines the effect of gradients in the linear and nonlinear susceptibilities along the propagation direction of intense light beams in weakly nonlinear media. A transformation of the generalised self-focusing equation (the cubic Schroedinger equation with time-dependent coefficients) is introduced which simplifies a broad class of nonlinear optics problems in the nonuniform media. The corresponding problem for beam filamentation (transverse modulation instability) is treated and applied to a cold, relativistic laser plasma problem. (author)