Symmetry in optics and photonics: a group theory approach

TL;DR

This paper reviews how group theory can be applied to optics and photonics, highlighting recent quantum-inspired symmetry principles and encouraging further research to develop new photonic devices using symmetry analysis.

Contribution

It provides a comprehensive overview of applying group theory in optics, emphasizing recent developments and potential for future innovations in photonic device design.

Findings

Group theory offers a powerful framework for analyzing symmetries in optics.

Recent quantum-inspired symmetry principles have been introduced in photonics.

The review encourages further exploration of group theory to innovate in photonic device development.

Abstract

Group theory (GT) provides a rigorous framework for studying symmetries in various disciplines in physics ranging from quantum field theories and the standard model to fluid mechanics and chaos theory. To date, the application of such a powerful tool in optical physics remains limited. Over the past few years however, several quantum-inspired symmetry principles (such as parity-time invariance and supersymmetry) have been introduced in optics and photonics for the first time. Despite the intense activities in these new research directions, only few works utilized the power of group theory. Motivated by this status quo, here we present a brief overview of the application of GT in optics, deliberately choosing examples that illustrate the power of this tool in both continuous and discrete setups. We hope that this review will stimulate further research that exploits the full potential of GT for investigating various symmetry paradigms in optics, eventually leading to new photonic devices.