Analysis of optical waveguides with arbitrary index profile using an immersed interface method

TL;DR

This paper presents a numerical method based on an immersed interface approach to accurately solve Maxwell's equations in optical waveguides with complex index profiles, handling discontinuities and singularities efficiently.

Contribution

It introduces a modified finite difference scheme tailored for interface problems in optical waveguides, including second and fourth order accuracy and adaptations for eigenvalue problems.

Findings

Effective handling of discontinuities in refractive index profiles.

Accurate computation of light confinement in complex geometries.

Applicable to various waveguide configurations with defects.

Abstract

A numerical technique is described that can efficiently compute solutions in interface problems. These are problems with data, such as the coefficients of differential equations, discontinuous or even singular across one or more interfaces. A prime example of these problems are optical waveguides and as such the scheme is applied to Maxwell's equations as they are formulated to describe light confinement in Bragg fibers. It is based on standard finite differences appropriately modified to take into account all possible discontinuities across the waveguide's interfaces due to the change of the refractive index. Second and fourth order schemes are described with additional adaptations to handle matrix eigenvalue problems, demanding geometries and defects.