Optimal Co-linear Gaussian Beams for Spontaneous Parametric Down-Conversion

TL;DR

This paper analyzes and optimizes the properties of co-linear Gaussian beam SPDC sources, providing analytical and numerical results to enhance photon pair quality and collection efficiency for advanced quantum optics applications.

Contribution

It offers a comprehensive optimization of SPDC parameters, including focusing conditions, to maximize collection probability, purity, and heralding ratio simultaneously.

Findings

Focusing conditions can optimize multiple SPDC properties simultaneously.

SPDC properties are nearly scale invariant, independent of crystal length.

Analytical and numerical results guide high-performance SPDC source design.

Abstract

I investigate the properties of spontaneous parametric down-conversion (SPDC) involving co-linear Gaussian spatial modes for the pump and the photon collection optics. Approximate analytical and numerical results are obtained for the peak spectral density, photon bandwidth, pair collection probability, heralding ratio, and spectral purity, as a function of crystal length and beam focusing parameters. I address the optimization of these properties individually as well as jointly, and find focusing conditions that simultaneously bring the pair collection probability, heralding ratio, and spectral purity to near-optimal values. These properties are also found to be nearly scale invariant, that is, ultimately independent of crystal length. The results obtained here are expected to be useful for designing SPDC sources with high performance in multiple categories for the next generation of SPDC applications.