A new method for the computation of eigenmodes in dielectric waveguides

Abstract

A new method for the computation of eigenmodes in isotropic cylindrical loss-free dielectric waveguides is proposed. Such Waveguide Is a cylindrical structure with the refractive index n not varied along the generatrix of cylinder. It is assumed that the waveguide is infinitely long and is in unbounded space with the constant index of refraction n, > 0. Besides, man > n. . Eigenmodes are generator-free electromagnetic waves which satisfy the homogenous Maxwell equations. We consider surface waves. Origlnal problem formulated in unbounded domain is reduced to a linear generalized spectral problem in the circle R containing the domain of the cross-section of the waveguide. To approximate obtained problem Finite Element Method is used. Our method allows computing of waveguides of different cross- sections such as clrcle, square, rectangle, threecircle, etc. I. INTRODUCTION In this work a new method for the computation of eigenmodes in isotropic cylindrical loss-free dielectric waveguides is prbposed. Such waveguide is a cylindrical structure with the refractive index n being the function of transverse coordinates n = n(x,,x,) not varied along the generatrix of cylinder. It is assumed that the waveguide is infinitely long and is in unbounded space with the constant index of refraction n. > 0. Besides, n+ = max n > n, . Eigenmodes are generator-free electromagnetic waves propagating along the waveguide. They satisfy the homogenous Maxwell equations and have the form