On the geometry of spatial biphoton correlation in spontaneous parametric down-conversion

TL;DR

This paper derives analytical expressions for the spatial correlation distribution of photon pairs generated by spontaneous parametric down-conversion, revealing elliptical patterns that depend on the detection geometry and phase-matching conditions.

Contribution

It provides the first analytical model linking the geometry of biphoton correlations with phase-matching in SPDC, validated by experimental data.

Findings

Correlation patterns form ellipses on detection planes.

Predictions match experimental measurements.

Geometry depends on phase-matching conditions.

Abstract

Analytical expressions are derived for the distribution rates of spatial coincidences in the counting of photons produced by spontaneous parametric down conversion (SPDC). Gaussian profiles are assumed for the wave function of the idler and signal light created in type-I SPDC. The distribution rates describe ellipses on the detection planes that are oriented at different angles according to the photon coincidences in either horizontal-horizontal, vertical-vertical, horizontal-vertical or vertical-horizontal position variables. The predictions are in agreement with the experimental data obtained with a type-I BBO crystal that is illuminated by a 100 mW violet pump laser as well as with the results obtained from the geometry defined by the phase-matching conditions.