Modeling light-sound interaction in nanoscale cavities and waveguides

The interaction of light and sound waves at the micro and nanoscale has attracted considerable interest in recent years. The main reason is that this interaction is responsible for a wide variety of intriguing physical phenomena, ranging from the laser-induced cooling of a micromechanical resonator down to its ground state to the management of the speed of guided light pulses by exciting sound waves. A common feature of all these phenomena is the feasibility to tightly confine photons and phonons of similar wavelengths in a very small volume. Amongst the different structures that enable such confinement, optomechanical or phoxonic crystals, which are periodic structures displaying forbidden frequency band gaps for light and sound waves, have revealed themselves as the most appropriate candidates to host nanoscale structures where the light-sound interaction can be boosted. In this review, we describe the theoretical tools that allow the modeling of the interaction between photons and acoustic phonons in nanoscale structures, namely cavities and waveguides, with special emphasis in phoxonic crystal structures. First, we start by summarizing the different optomechanical or phoxonic crystal structures proposed so far and discuss their main advantages and limitations. Then, we describe the different mechanisms that make light interact with sound, and show how to treat them from a theoretical point of view. We then illustrate the different photon-phonon interaction processes with numerical simulations in realistic phoxonic cavities and waveguides. Finally, we introduce some possible applications which can take enormous benefit from the enhanced interaction between light and sound at the nanoscale.