TM Standing Wave Solution of Maxwell Equations in a Self-Defocusing Kerr Media and its Application to a Thin-Film Waveguide

Abstract

We applied the dielectric function method to solve analytically L-NL-L structure problems with negative Kerr nonlinearity. A damped wave in linear and a periodic standing wave in non-linear media had to be matched at boundaries. We gave a formulation of boundary conditions that did not explicitly include a film thickness. The boundary-value of a dielectric function can be expressed through the constant of non-trivial integral of motion. Using it, one generates a family of matched solutions satisfying boundary conditions. Then arbitrary film thickness can be checked against this family of solutions in search of matches. As a result, all fitted solutions are determined straightforwardly.

A thin-film waveguide problem with positive Kerr nonlinearity and its TM standing wave solution

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In the previous work [1], we applied the scattering-type TM standing wave solution to a slab waveguide with negative Kerr nonlinearity. In this work, we analyzed a waveguide problem with positive Kerr nonlinearity.

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“…This is a satisfactory condition. Squares of , Ah in (55) are determined through boundary 0 x  = value by formula (1). It means that a parameter cnst can be seen as a function of…”