Quasinormal mode theory of elastic Purcell factors and Fano resonances of optomechanical beams

TL;DR

This paper develops a quasinormal mode theory for elastic optomechanical resonators, emphasizing the role of complex mode volume and phase, and demonstrates its application to Fano resonances and Purcell factors in mechanical beams.

Contribution

It introduces a generalized quasinormal mode framework for elastic resonators, fixing previous normal mode theories and applying it to coupled modes and Fano resonances.

Findings

Generalized elastic Purcell factor theory with complex mode volume

Observation of Fano resonances from coupled quasinormal modes

Validation through 3D simulations of optomechanical beams

Abstract

We introduce a quasinormal mode theory of mechanical open-cavity modes for optomechanical resonators, and demonstrate the importance of using a generalized (complex) effective mode volume and the phase of the quasinormal mode. We first generalize and fix the normal mode theories of the elastic Purcell factor, and then show a striking example of coupled quasinormal modes yielding a pronounced Fano resonance. Our theory is exemplified and confirmed by full three-dimensional calculations on optomechanical beams, but the general findings apply to a wide range of mechanical cavity modes. This quasinormal mechanical mode formalism, when also coupled with a quasinormal theory of optical cavities, offers a unified framework for describing a wide range of optomechanical structures where dissipation is an inherent part of the resonator modes.