Coupled-Ring Resonance and Unitary Groups

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.