Coupled-Ring Resonance and Unitary Groups

TL;DR

This paper explores the group-theoretic structure of coupled microring resonances, revealing the emergence of pseudo-unitary groups and providing exact solutions for tri-microring resonance conditions, with applications in resonance tuning.

Contribution

It introduces a novel group-theoretic framework for analyzing coupled microring resonances and provides exact solutions for tri-microring configurations, advancing the understanding of resonance control.

Findings

Emergence of pseudo-unitary group in microring resonance phenomena

Exact solution for tri-microring resonance condition

Application to resonance frequency tuning via coupling modulation

Abstract

The group-theoretic content of photonic coupled microrings resonance phenomena is shown, in particular, an interesting emergence of pseudo-unitary group. The application to the resonance condition in a tri-microring configuration is solved exactly. A practical application of this work will be in the resonance frequency tuning based on the coupling coefficient, in particular, the Mach-Zehnder interferometer approach was analyzed for the coupling modulation.