Numerical proposal to solve Maxwell’s equations in a toroidal waveguide

Abstract

In this contribution, we propose a numerical solution to the Maxwell equations to determine the electromagnetic fields in a toroidal dielectric wave-guide. Analyzing the relationship between the size of the cross-section of the toroid and its bending radius. We considered a sinusoidal time dependence of the electromagnetic field, then we just solve the Helmholtz equation in the waveguide. We propose a numerical way to solve this equation and analyze for to find the power radiation in each synchronous mode. We show a numerical method by calculating the frequencies and the loss factors for any mode in square, triangular, and round waveguides.