SEMILINEAR DESCRIPTION OF BEAM NONLINEAR PROPAGATION

It has recently been shown [1] that propagation in nonlinear Kerr medi a and propagation in linear media can be consistently interrelated by a transformation that scales a propagation distance, a radius of a pha se front curvature and an on-axis beam phase. The transformation is va lid for cases of arbitrary transverse dimension of the beam and for po wer levels up to a self-trapped propagation level Although the analysi s leads to an efficient tracing of the beam by complex rays or nonline ar ABCD matrices, an equivalent semi-linear description of nonlinear p ropagation in terms of four aberration nonlinear effects is possible a s well. These effects, i.e, an optical distance self-shortening, a bea m waist shift, a beam waist width modification and an on-axis phase sh ift are introduced and discussed in this paper. A generalization of th e method into higher-order mode propagation is also outlined.