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

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.