Analytic Expressions for Orbital Angular Momentum Modal Crosstalk in a Slightly Elliptical Fiber

TL;DR

This paper derives analytic formulas to quantify how ellipticity in fibers causes orbital angular momentum mode crosstalk, aiding the design of fibers for spatial mode multiplexing in optical communications.

Contribution

It provides a complete set of scalar perturbation theory expressions for OAM mode mixing in elliptical fibers, including crosstalk and walk-off length calculations, considering degeneracy and spin-orbit effects.

Findings

Derived explicit formulas for OAM mode crosstalk in elliptical fibers.

Validated expressions with applications to step-index fibers.

Analyzed the impact of ellipticity and spin-orbit interaction on mode mixing.

Abstract

Assuming weakly guiding approximation, we examine orbital angular momentum (OAM) mode mixing on account of ellipticity in a fiber and derive a complete set of analytic expressions for spatial crosstalk, using scalar perturbation theory that incorporates fully the existing degeneracy between a spatial OAM mode and its degenerate partner characterized by a topological charge of opposite sign. These expressions, consequently, include an explicit formula for calculating the 2 pi walk-off length over which an input OAM mode converts into its degenerate partner, and back into itself. We further explore the applicability of the derived expressions in the presence of spin-orbit interaction. The expressions constitute a useful mathematical tool in the analysis and design of fibers for spatially-multiplexed mode transmissions. Their utility is demonstrated with application to a few mode and a multimode step-index fiber.