How Kerr nonlinearity influences polarized electromagnetic wave propagation

摘要

The propagation of electromagnetic TE waves along boundaries of a plane dielectric layer filled with a Kerr medium is studied for all possible cases of the problem's parameters. The layer is located between two half-spaces with constant permittivities. The problem is reduced to a nonlinear transmission eigenvalue problem for Maxwell's equations, in which each eigenvalue is a propagation constant of a guided wave. The exact dispersion equation with respect to the eigenvalues (propagation constants) is derived and studied. It is proven that in the presence of the Kerr effect, several novel wave-guiding regimes arise, including regimes that have no counterparts in the linear theory. An infinite number of eigenvalues arise in the focusing case, even if the corresponding linear problem has no solutions (the linear problem always has no more than a finite number of solutions). In the defocusing case, only those solutions arise that tend to linear solutions when the nonlinearity coefficient vanishes. It is also proven that in the nonlinear case, an infinite number of eigenvalues do not reduce to the solutions of the corresponding linear problem, even if the nonlinearity coefficient tends to zero. Numerical illustrations for the results obtained are provided.