Coupled Mode Theory of Optomechanical Crystals

TL;DR

This paper develops an exact coupled mode theory for the interaction of elastic and optical Bloch waves in optomechanical crystals, enabling precise analysis of mode conversion, power conservation, and non-reciprocal light transmission.

Contribution

It introduces a rigorous formulation of coupled mode theory accounting for infinite optical modes and elastic interactions in optomechanical waveguides and cavities.

Findings

Derived explicit coupling rates and mode profiles.

Established a conservation law for optical power among modes.

Demonstrated applications to non-reciprocal transmission and switches.

Abstract

Acousto-optic interaction in optomechanical crystals allows unidirectional control of elastic waves over optical waves. However, as a result of this nonlinear interaction, infinitely many optical modes are born. This article presents an exact formulaion of coupled mode theory for interaction between elastic and photonic Bloch waves moving along an optomechanical waveguide. In general, an optical wavefront is strongly diffracted by an elastic wave in frequency and wavevector, and thus infinite modes with different frequencies and wavevectors appear. We discuss resonance and mode conversion conditions, and present a rigorous method to derive coupling rates and mode profiles. We also find a conservation law which rules over total optical power from interacting individual modes. We present application examples to the theory to optomechanical waveguides and cavities, as well as non-reciprocal transmission of light and optomechanical switches.