Closed Form of the Biphoton K-Vector Spectrum for Arbitrary Spatio-Temporal Pump Modes

TL;DR

This paper derives a closed-form expression for the biphoton k-vector spectrum considering arbitrary pump modes, enabling optimization of biphoton flux and inclusion of crystal poling effects.

Contribution

It provides a novel closed-form solution for biphoton spectra with arbitrary pump modes, facilitating enhanced control and optimization in quantum optics experiments.

Findings

Derived a closed-form biphoton k-vector spectrum

Identified pump mode coefficients that maximize biphoton detection probability

Allows inclusion of crystal poling structures in biphoton flux optimization

Abstract

A closed form solution is derived for the biphoton k-vector spectrum for an arbitrary pump spatial mode. The resulting mode coefficients for the pump input that maximize the probability of biphoton detection in the far field are found. It is thus possible to include the effect of arbitrary crystal poling strucures, and optimize the resulting biphoton flux.