Boundary integral equation method for resonances in gradient index cavities designed by conformal transformation optics

TL;DR

This paper introduces a boundary integral equation method leveraging conformal transformation optics to efficiently compute resonant modes in 2D gradient index cavities, validated against finite element results.

Contribution

The authors develop a novel boundary integral approach using a fictitious space and Green's functions for accurate resonance calculations in gradient index cavities.

Findings

Resonant modes in limaçon-shaped cavities were successfully computed.

Mode patterns and far-field distributions matched finite element method results.

The method offers an efficient alternative for resonance analysis in complex optical cavities.

Abstract

In the case of two-dimensional gradient index cavities designed by the conformal transformation optics, we propose a boundary integral equation method for the calculation of resonant mode functions by employing a fictitious space which is reciprocally equivalent to the physical space. Using the Green's function of the interior region of the uniform index cavity in the fictitious space, resonant mode functions and their far-field distributions in the physical space can be obtained. As a verification, resonant modes in lima\c{c}on-shaped transformation cavities were calculated and mode patterns and far-field intensity distributions were compared with those of the same modes obtained from the finite element method.