Rayleigh series for dielectric waveguides of complex cross-section

Abstract

With the use of the Rayleigh series in cylindrical Junctions for the longitudinal components of the electromagnetic field and the Green’s theorem, an algebraic formulation of the problem of calculating the modes of three-dimensional open dielectric waveguides of complex cross-section is obtained. The effectiveness of the approach is demonstrated by examples of calculating dielectric waveguides with elliptical cross-sections. The illustrations of the internal convergence of the method are given, and the obtained dispersion characteristics of the modes are compared with the data of other less general numerical approaches.