Cavity optomechanics with Anderson-localized optical modes

Confining photons in cavities enables the modification of the interaction between light and different forms of matter.\ In optomechanics, cavities are used to enhance the radiation pressure, which in turn enables a wealth of phenomena ranging from optomechanically induced transparency to macroscopic objects cooled to their motional ground state.\ Previous work on cavity optomechanics employed devices where the ubiquitous structural disorder played no role beyond perturbing resonance frequencies and quality factors.\ More generally, the interplay between disorder, which must be described by statistical physics, and optomechanical effects has thus far been unexplored.\ Here we show that sidewall roughness in air-slot photonic-crystal waveguides can induce sufficiently strong backscattering of slot-guided light to create tightly confined Anderson-localized modes with quality factors above $10^5$ and estimated mode volumes below the diffraction limit.\ The interaction between these disorder-induced optical modes and in-plane mechanical modes of the slotted membrane is governed by a distribution of coupling rates, which can exceed $g_{\text{o}}/2\pi\sim 200$ kHz, leading to mechanical amplification up to self sustained oscillations via optomechanical backaction.\ Our work contributes to understand optomechanics in the multiple-scattering regime opening new perspectives for exploring complex systems with multitude mutually-coupled degrees of freedom.