Transverse electric waves in three-layered waveguide structure with a parabolic spatial profile of the dielectric constant, optical linear and nonlinear layers

Abstract

A three-layered waveguide structure containing the Kerr nonlinear medium separated by an optical linear interlayer from a parabolic graded-index layer is considered. Exact solutions of the wave equation corresponding to several types of transverse electric waves existing in different ranges of values of the effective refractive index are found. The types of waves differ from each other by the presence or absence of oscillations in the interlayer and in the graded-index layer, as well as the form of attenuation in a nonlinear medium. The wave types obtained can be divided into two main groups. The first group includes such waves that can propagate with an arbitrarily varying effective refractive index in the allowable range of values. The second one includes such waves that can propagate at certain discrete values of the effective refractive index. Such values of the effective refractive index of waveguide modes are determined by the wavelength of the incident ray, difference between the dielectric constants of a parabolic graded-index layer, and its width. Even and odd waveguide modes are described separately. Field oscillations can be observed only in the interlayer for waves of the first group. Field oscillations can also be observed in the graded-index layer for waves of the second group. The field profile is a self-focusing nonlinear medium flatter than in a defocusing one for all types of waves. An increase in the same parameters has a different effect on the profiles of the different types of waves. The possibility of controlling the distribution of the wave energy between the layers of the waveguide structure by changing the angle of incidence is shown.