Propagation characteristics of TE0 waves in three-layer optical waveguides with self focusing and self defocusing nonlinear layers

An expression for the optical field in a self defocusing nonlinear medium is proposed and used to analyse the propagation characteristics of TE₀ waves supported by a three-layer nonlinear waveguide with a self focusing nonlinear substrate and a self defocusing nonlinear film. Numerical results for propagation are illustrated for four kinds of guided waves whose fields in the film are expressed by different Jacobian elliptic functions. These reveal the relation between nonlinearity measure and normalised frequency for waves guided with various dielectric constant and nonlinear coefficient distributions. The properties of the propagation constant for waves with their peak of the field profile in the film or substrate are also discussed. Moreover, numerical results for dispersion relations of TE₀ waves are given, and the stability analysis using the beam propagation method is also presented