Coherence in parametric fluorescence

TL;DR

This paper analyzes spontaneous four wave mixing in a resonator array, deriving analytic expressions and exploring how the structure influences photon pair generation and biphoton wave function shape, revealing superradiance-like scaling effects.

Contribution

It provides new analytic formulas for photon pair generation and biphoton wave functions in a resonator array, and discusses conditions for super-SFWM and superradiance effects.

Findings

Photon pair generation scales super-linearly with the number of resonators.

The shape of the biphoton wave function depends on pump pulse duration and resonator count.

Super-SFWM can be observed under specific conditions.

Abstract

We investigate spontaneous four wave mixing (SFWM) in a single-channel side-coupled integrated spaced sequence of resonators (SCISSOR). Analytic expressions for the number of photon pairs generated, as well as the biphoton wave function (joint spectral amplitude) describing the pairs, are derived and numerically computed for different pump pulse durations and numbers of ring resonators. In the limit of a long input pump pulse, we show a strong analogy between super-linear scaling of generation efficiency with respect to the number of rings in the structure and Dicke superradiance. More generally, we discuss in detail the factors that influence the shape of the biphoton wave function, as well as the conditions for observing super-SFWM.