Stable Mode Sorting by Two-Dimensional Parity of Photonic Transverse Spatial States

TL;DR

This paper presents a stable, efficient mode sorter for two-dimensional parity of transverse spatial states of light using a Sagnac interferometer, enabling advanced quantum information processing with single photons.

Contribution

It introduces a novel out-of-plane Sagnac interferometer for sorting spatial modes based on two-dimensional parity, enhancing stability and functionality over traditional methods.

Findings

Sorts Hermite-Gauss modes by parity of n+m

Sorts Laguerre-Gauss modes by orbital angular momentum parity

Enables stable measurement of single-photon orbital angular momentum

Abstract

We describe a mode sorter for two-dimensional parity of transverse spatial states of light based on an out-of-plane Sagnac interferometer. Both Hermite-Gauss (HG) and Laguerre-Gauss (LG) modes can be guided into one of two output ports according to the two-dimensional parity of the mode in question. Our interferometer sorts HG_nm input modes depending upon whether they have even or odd order n+m; it equivalently sorts LG modes depending upon whether they have an even or odd value of their orbital angular momentum. It functions efficiently at the single-photon level, and therefore can be used to sort single-photon states. Due to the inherent phase stability of this type of interferometer as compared to those of the Mach-Zehnder type, it provides a promising tool for the manipulation and filtering of higher order transverse spatial modes for the purposes of quantum information processing. For example, several similar Sagnacs cascaded together may allow, for the first time, a stable measurement of the orbital angular momentum of a true single-photon state. Furthermore, as an alternative to well-known holographic techniques, one can use the Sagnac in conjunction with a multi-mode fiber as a spatial mode filter, which can be used to produce spatial-mode entangled Bell states and heralded single photons in arbitrary first-order (n+m=1) spatial states, covering the entire Poincare sphere of first-order transverse modes.