Spontaneous four-wave mixing in lossy microring resonators

TL;DR

This paper presents a comprehensive Hamiltonian framework for analyzing spontaneous four-wave mixing in lossy microring resonators, accounting for scattering losses and nonlinear effects, with practical computation methods and spectral analysis results.

Contribution

It introduces a general Hamiltonian approach that includes losses and parasitic nonlinearities, providing a new way to analyze photon pair generation in microring resonators.

Findings

Derived an expression for joint spectral intensity of photon pairs.

Provided a method to compute system output for arbitrary parameters.

Analyzed the singles-to-coincidences ratio in the weak pump limit.

Abstract

We develop a general Hamiltonian treatement of spontaneous four-wave mixing in a microring resonator side-coupled to a channel waveguide. The effect of scattering losses in the ring is included, as well as parasitic nonlinear effects including self- and cross-phase modulation. A procedure for computing the output of such a system for arbitrary parameters and pump states is presented. For the limit of weak pumping an expression for the joint spectral intensity of generated photon pairs, as well as the singles-to-coincidences ratio, is derived.