Guided electromagnetic waves propagating in a two-layer cylindrical dielectric waveguide with inhomogeneous nonlinear permittivity (Q277757)

This work concerns the electromagnetic wave propagation in a circular-cylindrical waveguide directed in the \(z\)-axis and stratified in the radial direction. The permeability is, naturally, assumed to be constant while the permittivity has three different values defining the stratification of the waveguide in the radial direction. The particular feature here is that the value of the permittivity in the central part of the stratification is a nonlinear perturbation of a constant, called the Kerr law, with a small multiplicative parameter.NEWLINENEWLINEThe authors are interested in deriving existence of TM waves guided by such nonlinear stratifications.NEWLINENEWLINEPlugging the TM-form of the electromagnetic waves in the original Maxwell system, the problem reduces to a 1D nonlinear eigenvalue problem. To derive the existence of such eigenvalues, they first characterize the ones of the linearized eigenvalue problem. Second, under some natural conditions on the small multiplicative parameter, they derive existence and estimations of these eigenvalues in terms of those of the linearized problem. The authors also propose a numerical study of such eigenmodes.