Four-wave mixing and enhanced analog Hawking effect in a nonlinear optical waveguide

We study the scattering of light on a soliton propagating in a waveguide. When not applying the rotating wave approximation, we show that the linearized wave equation governing perturbations has the same structure as that governing phonon propagation in an atomic Bose condensate. By taking into account the full dispersion relation, we then show that the scattering coefficients encoding the analogue Hawking effect are amplified by a resonance effect related to the modulation instability occurring in the presence of a continuous wave. When using a realistic example of a silicon nitride waveguide on a silica substrate, we find that the typical values of the pair creation rates are about six orders of magnitude larger than those found in earlier works. Specifically, we find that a soliton of duration 10 fs would spontaneously emit about one photon pair for every cm it travels. This result is confirmed by numerically solving the equation encoding the Kerr nonlinearity and governing the evolution of the full field (soliton plus perturbations).