# Optimization of conformal whispering gallery modes in lima\c{c}on-shaped transformation cavities

## TL;DR

This paper investigates how conformal transformation optics can optimize whispering gallery modes in limaçon-shaped dielectric cavities, enhancing bidirectionality and Q-factors for better resonant mode control.

## Contribution

It introduces a method to optimize whispering gallery modes in limaçon-shaped cavities using conformal transformation optics, revealing the relationship between system parameters, bidirectionality, and Q-factors.

## Key findings

- Bidirectionality factors are not directly proportional to Q-factors.
- Optimal parameters for high bidirectionality and Q-factor coexistence were identified.
- Anisotropic whispering gallery modes support total internal reflection.

## Abstract

In lima\c{c}on-shaped gradient index dielectric cavities designed by conformal transformation optics, the variation of Q-factors and emission directionality of resonant modes was traced in their system parameter space. For these cavities, their boundary shapes and refractive index profiles are determined in each case by a chosen conformal mapping which is taken as a coordinate transformation. Through the numerical exploration, we found that bidirectionality factors of generic high-Q resonant modes are not directly proportional to their Q-factors. The optimal system parameters for the coexistence of strong bidirectionality and a high Q-factor was obtained for anisotropic whispering gallery modes supported by total internal reflection.