Dispersion-Engineered Super-Gain Parametric Amplification in Nanoscale Optical Cavities

The gain factor of the optical parametric amplification (OPA) process is known to be negligible in the small scale due to low-interaction-medium length. Hence, in the nanoscale, OPA is deemed as infeasible. Therefore, in small-scale-integrated optical devices, stimulated-emission-based amplifiers (lasers) are employed instead of OPAs. In contrast, the major advantage of OPAs over lasers is that unlike lasers which only provide amplification over a narrow spectral band, OPAs provide high-gain amplification over a very large, user-controlled spectral band. In this article, it is shown that OPA can yield wideband high-gain amplification over a nanoscale beam propagation distance through dispersion engineering. This is achieved by a proper tuning of the pump (source) wave frequency, which can maximize the effective medium nonlinearity by a few orders of magnitude, while concurrently maximizing the intracavity energy density, thereby compensating for the small co-propagation distance for the input (signal) and pump beams. In this study, it is shown that an input wave can be amplified by a factor ${10}^8$ in a nanoscale cavity via precise dispersion engineering. Both empirical and computational formulations are used for the investigation, which display a reasonable agreement.