Manipulation of Semiclassical Laguerre-Gaussian Modes: a Model Case

TL;DR

This paper explores a simplified one-dimensional model for manipulating Laguerre-Gaussian photon modes, providing insights into their behavior and potential experimental applications in quantum communication.

Contribution

It demonstrates how a one-dimensional operator can effectively model two-dimensional Laguerre-Gaussian modes and improves the semiclassical Wigner transform analysis.

Findings

The one-dimensional model captures the flow of intensity distributions along elliptic curves.

Enhanced semiclassical Wigner transform treatment improves understanding of mode manipulations.

The model offers a practical approach for experimental manipulation of photon states.

Abstract

We continue the study, from a semiclassical viewpoint, of Calvo and Picon's operators, as manipulating photon states in quantum communication. In a previous paper, we defined a one-dimensional model operator and studied it analytically before moving on to Calvo and Picon's full two-dimensional operators. In the present paper, we show how the one-dimensional operator may also be useful as an experimental model, since it allows manipulations of two-dimensional Laguerre-Gaussian modes; the intensity distributions (in physical space) of the Laguerre-Gaussian modes then approximately flow along the elliptic curves studied earlier. Since the Wigner transform is fundamental in the study of Laguerre-Gaussian modes, we give a slightly expanded and improved treatment of the semiclassical Wigner transform, which was only briefly mentioned in the previous paper.