Nonlinear Transverse Magnetic Wave Propagation in a Layer Revisited

The paper focused on the problem of propagation of a monochromatic transverse magnetic (TM) wave (E, H)e(-i omega t) in a plane dielectric waveguide filled with nonlinear isotropic non-magnetic medium; here E, H are electric and magnetic fields, omega is the circular frequency. The waveguide is sandwiched between two half-spaces filled with isotropic non-magnetic homogeneous media with constant permittivities. The waveguide's permittivity is a monotonically increasing unbounded function with respect to vertical bar E vertical bar(2) ; such a function describes a lot of important nonlinearities like Kerr law, polynomial and power nonlinearities. The main problem is to determine propagation constants (PCs) of the TM guided waves. For the first time, the dispersion equation and results of its solvability are presented for an arbitrary nonlinearity. In particular, it is shown that in contrast to the linear problem in the nonlinear problem there exists an infinite number of PCs. It is also shown that only a finite number of these PCs have linear counterparts.