Non-Hermitian Amplification via Four-Wave Mixing in Silicon Photonics

In nonlinear integrated optics, phase matching is a key requirement for practical device efficiency. Recently one new approach has been advanced, which goes beyond phase matching for amplification in nonlinear optical devices by harnessing the non-Hermitian properties of optical devices for four-wave mixing (FWM). Previously, we used parity-time (PT) symmetry breaking to show that by careful engineering of the dissipative spectral features in a nonlinear optical system, it is possible to achieve gain for the signal component in the absence of Hermitian phase-matching condition using a second or third-order nonlinear material by introducing optical losses to the idler component. In this work, our goal is to show numerically that a realistic device based on PT principles can be realized in a silicon-based material system. In particular, we investigate PT symmetry in FWM that provides signal gain while imposing idler loss in a waveguide-based directional coupler. The interaction of nonlinearity and non-Hermiticity can thus be applied to develop amplifiers and oscillators that do not require the stringent phase-matching condition between the different frequency components.