Single Plane Spatial Mode Sorter

TL;DR

This paper introduces a single-plane device capable of sorting various spatial light modes with minimal cross-talk, validated experimentally, and applicable to quantum and classical optics, including mode generation and high efficiency.

Contribution

The paper provides an analytic derivation and experimental validation of a versatile, nearly cross-talk free mode sorter for multiple mode families, including a limit case for all modes of a family.

Findings

Achieved almost no cross-talk in mode sorting across diverse mode families.

Demonstrated the sorter reproduces the Fork grating for OAM modes.

Proved the power transmission scales as 1/M and is mathematically optimal.

Abstract

A mode sorter separates a set of M orthogonal spatial modes in a shared input channel into M different output channels. Here we present an analytic derivation and experimental validation of a single plane device for sorting spatial modes from a diverse variety of mode families, including Hermite-Gaussian (HG), Laguerre-Gaussian (LG), Bessel-Gaussian (BG), with almost no cross-talk. This sorting capability is required for a wide range of applications that employ classical or quantum light. We also show that applying this design in order to sort a set of Orbital Angular Momentum (OAM) modes with zero radial index reproduces the well-known Fork grating configuration. Furthermore, by taking the limit of M -> inf, we present an analytical expression for sorting all the modes of a given family. By operating this device in reverse, it can be used to generate arbitrary modes, by illuminating it with a Gaussian beam. The power transmission coefficient for this sorter goes as 1/M and we provide a mathematical proof that this is optimal for any typical arrangement of the detector positions. We further study the sorter sensitivity to wavelength and random phase noise.