Spectral decomposition of entangled photons with an arbitrary pump

TL;DR

This paper provides a comprehensive method for calculating the bi-photon state generated by spontaneous parametric down conversion with arbitrary pump modes, highlighting the importance of pump-signal/idler width ratios in entanglement properties.

Contribution

It introduces a spectral decomposition approach for entangled photons with arbitrary pump profiles, extending previous models to include complex spatial pump modes without restrictions.

Findings

Pump to signal/idler width ratio significantly affects entangled field composition

The method allows calculation of maximally entangled states with complex pump profiles

No restrictions on angular or radial momenta of the modes

Abstract

We calculate the bi-photon state generated by spontaneous parametric down conversion in a thin crystal and under collinear phase matching conditions using a pump consisting of any superposition of Laguerre-Gauss modes. The result has no restrictions on the angular or radial momenta or, in particular, on the width of the pump, signal and idler modes. We demonstrate the strong effect of the pump to signal/idler width ratio on the composition of the down-converted entangled fields. Knowledge of the pump to signal/idler width ratio is shown to be essential when calculating the maximally entangled states that can be produced using pumps with a complex spatial profile.