Type I parametric down conversion of highly focused Gaussian beams in finite length crystals

TL;DR

This paper investigates the correlations of photon pairs generated by type I spontaneous parametric down conversion using Gaussian beams, providing analytic expressions to optimize the process with highly focused beams.

Contribution

It introduces simple analytic formulas for the angular spectra of photon pairs in SPDC, aiding the optimization of highly focused Gaussian beams in nonlinear crystals.

Findings

Analytic expressions match numerical and experimental results.

Optimization parameters identified for generating photon pairs with desired wave vector properties.

Enhanced feasibility of using highly focused beams in quantum optics applications.

Abstract

We study the correlations in wave vector space of photon pairs generated by type I spontaneous parametric down conversion using a Gaussian pump beam. We analyze both moderate focused and highly focused regimes taking special attention to the angular spectrum and the conditional angular spectrum. Simple analytic expressions are derived that allow us to study in detail the dependence of these spectra on the waist of the source and the length of the nonlinear crystal. These expressions are in good agreement with numerical expectations and reported experimental results. They are used to make a systematic search of optimization parameters that improve the feasibility of using highly focused Gaussian beams to generate idler and signal photons with predetermined mean values and spread of their transverse wave vectors.