Three-dimensional analysis of a nonlinear directional coupler

Abstract

The propagating beam method is used to carry out a fully 3-D analysis of a nonlinear optical waveguide and a directional coupler formed from a pair of nonlinear waveguides. It is shown that for interesting levels of the index nonlinearity a beam in a monomode waveguide can undergo self-focusing and self-phase modulation. The latter effect results in an apparent shifting of the propagation constant. Both effects make it difficult to describe the field accurately in terms of modes. In the light of this behavior it is not surprising that the propagating beam method and coupled-mode theory predict different characteristics for the nonlinear coupler. The self-focusing induced in the waveguides is interesting of itself because it occurs at powers several orders of magnitude below the threshold for self-focusing in an unguided medium.