Mode Basis Construction for Circular Dielectric Waveguide by Integral Equation Approach

Abstract

A new method based on the integral equation approach is proposed for mode basis construction for a circular dielectric waveguide in free space. The expressions for mode and norm functions are obtained in closed form. The rapid convergence of the expansion of frequency domain mode over obtained basis is shown. The field change in time and longitudinal coordinate is described by the system of integro-differential evolutionary equations for coefficients of the field expansion over basis. It is shown that the system of integro-differential equations can be reduced to the system of matrix differential equations by the method of moments. Solution of this system for a harmonic wave gives dispersion curves for a circular dielectric waveguide. The validity of the method proposed is confirmed by the coincidence of the dispersion curves obtained by the given approach with the known solutions in the frequency domain.