Electromagnetic TM wave propagation in a layer with Kerr nonlinearity: Analytical results

Abstract

The paper is devoted to a transmission eigenvalue problem for Maxwell's equations with cubic nonlinearity that describes the propagation of transverse magnetic waves along the boundaries of a dielectric layer filled with nonlinear (Kerr) medium. It is shown that the Kerr nonlinearity creates a nonperturbative ‘purely’ nonlinear effect. This effect consists in the existence of infinitely many guided modes even for small values of the nonlinearity coefficient, whereas the corresponding linear problem always has a finite number of solutions. This fact implies theoretical existence of a novel type of eigenwaves that do not reduce to the linear ones in the limit in which the nonlinear coefficient reduces to zero.