Abstract

There is great worldwide interest in nonlinear waveguide propagation.¹ To date, however, work in this area has concentrated on single interfaces² or planar waveguides,^3,4 where the wave is confined in only one lateral dimension, because a study of nonlinear waveguides with complicated cross sections requires the use of advanced computing techniques. A study is now presented for guides with two-dimensional lateral confinement with cross sections that are significant in integrated and fiber optics. Exact stationary states are calculated by using a finite-element method, yielding field component profiles and the total power flow down the guide for a range of possible material and wave parameters. Because the simplest cases to deal with conceptually are rectangular and rib waveguides, these are discussed in detail. It is shown that the finite-element method is ideally suited to the solution of waveguides with arbitrary cross sections such as, for instance, in-diffused guides of the type used in directional couplers. Structures in which the substrates, claddings, or the waveguiding medium itself are anisotropic, owing to low symmetry or magneto-optic effects, are easily incorporated into the general framework and several examples will be given. The rectangular waveguide will be used to show, in detail, how the nonlinear guided waves reduce to the now familiar TE- and TM-polarized states of a nonlinear planar waveguide, as one of the dimensions of the rectangular guide begins to dominate the other. It is shown that this benchmarking onto known results in simpler structures gives valuable insight into guiding by general cross-section guides. Finally, it is emphasized that the calculations reported here are a necessary precursor to an understanding of stability, and propagation evolution, of nonlinear waves in these general structures.

© 1990 Optical Society of America