Second Kind Integral Equation Formulation for the Mode Calculation of Optical Waveguides

TL;DR

This paper introduces a second kind integral equation method for accurately computing electromagnetic modes in complex optical waveguides, including those with irregular geometries and multiple inclusions, enhancing design capabilities in photonics.

Contribution

The paper presents a well-conditioned, highly accurate integral equation formulation for mode calculation in complex optical waveguides with irregular geometries and multiple inclusions.

Findings

Capable of handling large, complex geometries.

Accurately computes bound, leaky, and complex modes.

Validated against semi-analytical and published results.

Abstract

We present a second kind integral equation (SKIE) formulation for calculating the electromagnetic modes of optical waveguides, where the unknowns are only on material interfaces. The resulting numerical algorithm can handle optical waveguides with a large number of inclusions of arbitrary irregular cross section. It is capable of finding the bound, leaky, and complex modes for optical fibers and waveguides including photonic crystal fibers (PCF), dielectric fibers and waveguides. Most importantly, the formulation is well conditioned even in the case of nonsmooth geometries. Our method is highly accurate and thus can be used to calculate the propagation loss of the electromagnetic modes accurately, which provides the photonics industry a reliable tool for the design of more compact and efficient photonic devices. We illustrate and validate the performance of our method through extensive numerical studies and by comparison with semi-analytical results and previously published results.