Abstract

We study the propagation modes in nonlinear planar and circular media that have a transverse parabolic index profile.¹ The first mode profiles, as well as their dispersion curves, are calculated numerically. In particular, one observes a splitting of some linear degenerate modes and cutoff of nonlinear modes because of self-focusing limits. A numerical scheme (beam propagation method) is also used to study near-modal propagation under the paraxial approximation. Those results are compared with an approximate analytical calculation based on the variational principle.² This approach is not limited to small nonlinearities; it describes quite well the amplitude-dependent quasiperiodic propagation observed numerically. Furthermore, it reproduces the modal dispersion curves in a simple way. These results can also be applied to the study of nonlinear radiation modes of the free three-dimensional paraxial wave equation.

© 1990 Optical Society of America