Mathematical theory of transverse-magnetic guided waves in a plane waveguide filled with nonhomogeneous nonlinear medium

Abstract The paper focuses on electromagnetic transverse-magnetic wave propagation in a plane waveguide sandwiched between two linear half-spaces and filled with nonlinear nonhomogeneous medium. The nonlinearity is described by an arbitrary positive twice differentiable function having power growth at infinity. Nonhomogeneity is presented by small perturbations of the linear part and nonlinear coefficient in the permittivity of the medium and is characterised by two perturbation coefficients. Developing a nonstandard perturbation approach we prove existence of nonlinear guided modes including nonlinearisable ones. Numerical calculations partly illustrate the found theoretical results as well as show some aspects of the problem that are not covered by this study.