Quasinormal-mode theory and design of elastic Purcell factors, mechanical cavity modes and Fano resonances in optomechanical beams

Abstract

In optomechanical systems, the radiation forces exerted by photons are exploited to manipulate and measure mechanical motion, finding applications is optics, nanophotonics, mechanics, and gravitational wave detection. To understand and design such structures, the optical and mechanical mode behavior must be well understood and characterized. For example, one should have a good idea of how the design parameters of a system affect the underlying modes, how the modes interact with their surroundings (dissipation), and how the modes interact with each other. The recent development of quasinormal-mode (QNM) theory in cavity optics, which allows for a quantitatively accurate model of realistic cavities subject to energy losses and interference, has proven to be very powerful in nanophotonics design and simulations. In this thesis, we introduce a QNM theory of mechanical open-cavity modes, and use it to study the elastic mode behavior of optomechanical resonators subject to intrinsic loss and mode coupling, including a quantitative description of the elastic Purcell effect. In addition, we present controllable designs of exceptionally high quality-factor mechanical modes for coupled optomechanical cavities. Our semi-analytical theory is exemplified and confirmed by full three-dimensional numerical calculations on optomechanical beams, and the general findings apply to a wide range of mechanical cavity modes. This QNM formalism, when also coupled with a QNM 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.