Finite-element solution of arbitrarily nonlinear, graded-index slab waveguides

Dispersion relations for TE modes in arbitrarily nonlinear, graded-index slab waveguides are solved numerically by the finite-element method. In this approach, self-consistent solutions can be obtained by a simple iteration. It is shown that a small deviation from the Kerr-type nonlinear effect gives rise to a drastic change in the power-dependent behaviour of guided waves. The dependence of dispersion relations on the refractive-index profile of the film is also examined.