Sorting photons by radial quantum number

TL;DR

This paper introduces a fractional Fourier transform-based device for efficiently sorting photons by their radial quantum number, enabling complete characterization of their transverse optical modes with potential quantum applications.

Contribution

The paper presents a novel mode sorter based on the fractional Fourier transform for radial mode decomposition, complementing existing azimuthal mode sorters.

Findings

Successfully separates individual radial modes

Demonstrates superposition state decomposition

Achieves high efficiency potential

Abstract

The Laguerre-Gaussian (LG) modes constitute a complete basis set for representing the transverse structure of a {paraxial} photon field in free space. Earlier workers have shown how to construct a device for sorting a photon according to its azimuthal LG mode index, which describes the orbital angular momentum (OAM) carried by the field. In this paper we propose and demonstrate a mode sorter based on the fractional Fourier transform (FRFT) to efficiently decompose the optical field according to its radial profile. We experimentally characterize the performance of our implementation by separating individual radial modes as well as superposition states. The reported scheme can, in principle, achieve unit efficiency and thus can be suitable for applications that involve quantum states of light. This approach can be readily combined with existing OAM mode sorters to provide a complete characterization of the transverse profile of the optical field.