Spatial and temporal characteristics of spontaneous parametric down-conversion with varying focal planes of interacting beams

TL;DR

This paper investigates how shifting the focal planes of interacting beams in spontaneous parametric down-conversion affects the spatial and temporal properties of photon pairs, highlighting implications for optimizing collection efficiency.

Contribution

It provides a detailed analysis of the effects of focal plane displacements on SPDC, emphasizing scenarios where precise focal plane positioning is crucial for experimental success.

Findings

Focal plane shifts can significantly alter photon pair properties.

Knowledge of exact focal plane positions is essential in certain SPDC arrangements.

Focal plane displacements can either enhance or reduce collection efficiency.

Abstract

Spontaneous parametric down-conversion (SPDC) is a widely used process to prepare entangled photon pairs. In SPDC, a second-order nonlinear crystal is pumped by a coherent laser beam to generate photon pairs. The photon pairs are usually detected by single-mode fibers (SMF), where only photons in a Gaussian mode can be collected. The collection modes possess typical Gaussian parameters, namely a beam waist and a focal plane position. The collection efficiency of photons highly depends on the choice of both parameters. The exact focal plane position of the pump beam relative to those of the detection modes is difficult to determine in a real experiment. Usually, theoretical and experimental studies assume that the focal plane positions of the pump and the generated beams are positioned in the center of the crystal. The displacement of beam focal planes can lead to deviations from expected results and the coupling efficiency into SMF can increase or decrease. In this work, we consider variable positions of focal planes and investigate how shifts of these focal planes influence the spatial and temporal properties of photon pairs. We present SPDC arrangements, in which the knowledge of the exact position of the focal planes is essential, as well as scenarios, where focal plane displacements do not contribute significantly to experimental outcomes. These findings are of particular interest for achieving higher efficiency in SPDC experiments.