Confinement of hybridized light modes in nonlinear-optical superpotentials

Abstract

In this work, we present a spatial and temporal light trapping mechanism induced by coherent frequency conversion. We consider a wave-mixing process, where a pumped nonlinearity mediates a frequency-domain beamsplitter interaction between two signal modes. When these wave modes are counterpropagating, temporally trapped eigenmodes emerge at the zero of the nonlinearity profile. We establish that such spatio-temporal trapping has a direct connection to supersymmetric quantum mechanics, which ensures the existence and robustness of the trapped modes and allows us to derive analytic solutions of the bound eigenmodes. Backwards sum-frequency conversion may thus enable a unique class of active photonic memory devices, whose design parameters are compatible with the state of the art in integrated nonlinear photonics. We propose proof-of-principle experiments to study this nonlinear-optical trapping effect on thin-film lithium niobate. In addition, as a case study, we show how the temporal trap can be used alongside parametric gain. Our work unveils potential applications ranging from classical integrated photonics to multimode quantum nonlinear photonics.