Full vectorial analysis of a nonlinear slab waveguide based on the nonlinear hybrid vector finite-element method

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Abstract
We propose a new nonlinear hybrid vector finite-element method to study the propagation of an optical beam in a nonlinear waveguide in three space dimensions. The new method is a combination of the edge-element and finite-difference methods; the former applies to the waveguide cross section and the latter to the propagation direction. To validate our method, a planar nonlinear waveguide (consisting of a linear substrate, a linear film, and a Kerr-type cladding) that is end-fire excited by the TE0 and TM0 modes is studied numerically. We demonstrate that the external excitation of a nonlinear slab waveguide can produce sequential threshold behavior by means of multisoliton emission from the waveguide.