Modeling Dispersive Coupling and Losses of Localized Optical and Mechanical Modes in Optomechanical Crystals

TL;DR

This paper analyzes how geometry influences dispersive coupling and losses in optomechanical crystals, providing design principles for high-Q optical and mechanical modes in nanostructures.

Contribution

It introduces a perturbation theory-based approach to optimize optomechanical properties by geometric design in 1D and 2D structures.

Findings

Mechanical Q-factors can reach over 10^7.

Optomechanical coupling lengths can be less than 5 microns.

Mechanical frequencies are in the 1-10 GHz range.

Abstract

Periodically structured materials can sustain both optical and mechanical excitations which are tailored by the geometry. Here we analyze the properties of dispersively coupled planar photonic and phononic crystals: optomechanical crystals. In particular, the properties of co-resonant optical and mechanical cavities in quasi-1D (patterned nanobeam) and quasi-2D (patterned membrane) geometries are studied. It is shown that the mechanical Q and optomechanical coupling in these structures can vary by many orders of magnitude with modest changes in geometry. An intuitive picture is developed based upon a perturbation theory for shifting material boundaries that allows the optomechanical properties to be designed and optimized. Several designs are presented with mechanical frequency ~ 1-10 GHz, optical Q-factor Qo > 10^7, motional masses meff 100 femtograms, optomechanical coupling length LOM < 5 microns, and a radiation-limited mechanical Q-factor Qm > 10^7.