Kerr-enhanced amplification of three-wave mixing and emergent masing regimes

TL;DR

This paper develops an analytic theory showing how Kerr nonlinearities enhance three-wave mixing in microresonators, enabling gain in regimes where traditional amplifiers are subthreshold, with simulations confirming the threshold reduction.

Contribution

It introduces a comprehensive analytic model of Kerr-enhanced three-wave mixing in microresonators with combined $$ and $$ nonlinearities, revealing new amplification regimes.

Findings

Kerr dressing hybridizes optical sidebands and renormalizes couplings.

The system exhibits gain below traditional thresholds.

Simulations confirm practical design windows for experiments.

Abstract

Integrated optical microresonators exploiting either second-order ($\chi^{(2)}$) or third-order ($\chi^{(3)}$) nonlinearities have become key platforms for frequency conversion, low-noise microwave photonics, and quantum entanglement generation. Here, we present an analytic theory of Kerr-enhanced three-wave mixing amplification in an electro-optic microresonator with both $\chi^{(2)}$ and $\chi^{(3)}$ nonlinearities. We demonstrate that Kerr dressing hybridizes the optical sidebands, renormalizing the $\chi^{(2)}$ couplings and detunings. As a result the system exhibits gain in regions where analogous bare $\chi^{(2)}$ or $\chi^{(3)}$ amplifiers are subthreshold. Time-domain Langevin simulations confirm this threshold reduction, mapping a practical design window for experiments.