Unified space-time description of pulsed twin beams

TL;DR

This paper derives a comprehensive mathematical model for multimode parametric down-conversion, unifying various experimental observations over 20 years into a single framework applicable across different gain regimes and levels.

Contribution

It presents a new, rigorous derivation of a quasi-stationary model from fundamental 3D+1 equations, improving upon heuristic approaches and enabling a unified description of pulsed twin beams.

Findings

Model valid in any gain regime

Applicable at quantum and classical levels

Unifies diverse experimental results

Abstract

This work provides a mathematical derivation of a quasi-stationary model for multimode parametric down-conversion, which was presented in [Gatti et al., Sci. Rep. 13, 16786] with heuristic arguments. The model is here derived from the 3D+1 propagation equation of the quantum fields in a nonlinear crystal, and its approximations discussed thoroughly. Thanks to its relative simplicity, and to the fact that it is valid in any gain regime, both at a quantum and classical level, it allows a unified description of disparate experimental observations conducted over the last 20 years, often described in the past by means of limited ad hoc models.