# Stochastic numerical simulations of a fully spatio-temporal Hong-Ou-Mandel dip

## TL;DR

This paper presents a comprehensive stochastic numerical model for simulating spatio-temporal multimode spontaneous parametric down conversion and two-photon interference in a Hong-Ou-Mandel interferometer, revealing detailed coherence properties.

## Contribution

It introduces a fully spatio-temporal stochastic simulation framework for analyzing the Hong-Ou-Mandel effect with spatially and temporally multimode biphoton states.

## Key findings

- Spatio-temporal properties of two-photon interference are characterized.
- Full spatio-temporal HOM dip is demonstrated.
- Coherence properties can be measured without temporal resolution.

## Abstract

We develop a fully spatio-temporal numerical model, based on stochastic simulations, simulating the generation of spatio-temporal multimode spontaneous parametric down conversion, the propagation of the signal and idler beams through a Hong-Ou-Mandel interferometer and the detection of the outgoing beams with two separate detectors arrays. Spatial and temporal properties of the two-photon interference are investigated by measuring the spatial distribution of the momenta coincidence counts between the time integrated outgoing far-field images and a full spatio-temporal HOM dip is exhibited. Numerical results also demonstrate that the spatio-temporal coherence properties of bi-photon wave packets can be fully characterized with detectors arrays with no temporal resolution.