Orbital angular momentum spectrum of Bessel-Gaussian modes, as generated by spontaneous parametric down-conversion

TL;DR

This paper derives a general expression for the probability of detecting specific Bessel-Gaussian modes generated via spontaneous parametric down-conversion, revealing conditions for a broad orbital angular momentum spectrum.

Contribution

It introduces a new theoretical framework for calculating the modal spectrum of Bessel-Gaussian modes in SPDC processes, extending understanding of their orbital angular momentum properties.

Findings

Broad OAM spectrum achievable under certain conditions

Derived general expression for mode detection probability

Applied theory to collinear, degenerate down-conversion

Abstract

The Bessel-Gaussian modal spectrum, generated in spontaneous parametric down-conversion of a Gaussian pump beam, is considered. This is done by first deriving a general expression for the true probability of detecting specific transverse spatial modes for the pairs of photons generated in a spontaneous parametric down-conversion process. These expressions are applied for Bessel-Gaussian modes in type I phase matching with collinear, degenerate down-converted beams. The result shows that a broad orbital angular momentum spectrum can be obtained for Bessel-Gaussian modes under certain conditions.