Theory of Four-Wave Mixing of Cylindrical Vector Beams in Optical Fibers

TL;DR

This paper develops a theoretical framework for four-wave mixing of cylindrical vector beams in optical fibers, revealing how angular momentum is conserved and enabling generation of entangled photon pairs in these modes for quantum communication.

Contribution

It derives coupled amplitude equations for CV beams in FWM, establishing selection rules and demonstrating angular momentum conservation in mode conversion.

Findings

FWM conserves total angular momentum of CV modes.

Photon pairs can be generated and entangled in CV modes.

The equations enable prediction of mode interconversion in optical fibers.

Abstract

Cylindrical vector (CV) beams are a set of transverse spatial modes that exhibit a cylindrically symmetric intensity profile and a variable polarization about the beam axis. They are composed of a non-separable superposition of orbital and spin angular momentum. Critically, CV beams are also the eigenmodes of optical fiber and, as such, are of wide-spread practical importance in photonics and have the potential to increase communications bandwidth through spatial multiplexing. Here, we derive the coupled amplitude equations that describe the four-wave mixing (FWM) of CV beams in optical fibers. These equations allow us to determine the selection rules that govern the interconversion of CV modes in FWM processes. With these selection rules, we show that FWM conserves the total angular momentum, the sum of orbital and spin angular momentum, in the conversion of two input photons to two output photons. When applied to spontaneous four-wave mixing, the selection rules show that photon pairs can be generated in CV modes directly and can be entangled in those modes. Such quantum states of light in CV modes could benefit technologies such as quantum key distribution with satellites.