Design and function of a vertical micro-cavity optical parametric oscillator

Optical parametric oscillators (OPOs) have emerged as highly versatile platforms for signal processing, machine learning, and all-optical computation. In particular, integrated photonic circuits have demonstrated an efficient and scalable route to build OPO networks through time-multiplexing. However, for tasks requiring massive parallelism with low latency, spatial multiplexing with vertical micro-cavities is a more natural approach to overcome the shoreline density limits of edge-emitting photonics. To this end, we propose an approach to realizing vertical micro-cavity OPOs (VCOPOs) leveraging recent developments in micro-optical fabrication techniques. We consider thin film LiNbO3 (TFLN)-filled dielectric micro-cavities as a case study, but the approach taken here is readily extended to any χ(2) nonlinear medium. Based on conservative industrial fabrication tolerances, we predict a minimal foot-print of ca. 5×5µm2, while achieving oscillation thresholds in the microwatts range. Advanced fabrication methods open a path toward sub-µW oscillation threshold, with a ratio of single-photon non-linear coupling rate to dissipation rate g/κ > 5%. We propose a theoretical framework for the classical and quantum operation of two dimensional arrays of VCOPOs, and discuss potential applications such as surface emitting devices, spatially multi-mode parametric amplifiers and squeezers, as well as optical simulators of classical and quantum Hamiltonians.