# Orbital Angular Momentum (OAM) Mode Mixing in a Bent Step Index Fiber in Perturbation Theory

## TL;DR

This paper develops an analytical perturbation theory framework to understand how fiber bends cause mixing of orbital angular momentum modes, affecting mode stability and crosstalk in multimode fibers.

## Contribution

It provides explicit analytic expressions for OAM mode mixing due to fiber bends, including the walk-off length, and demonstrates applications to mode crosstalk in fiber systems.

## Key findings

- Derived formulas for mode mixing and walk-off length.
- Numerical simulations show bend-induced crosstalk effects.
- Insights into dependence on bend radius and topological charge.

## Abstract

Within the framework of perturbation theory, we explore in detail the mixing of orbital angular momentum(OAM) modes due to a fiber bend in a step-index multimode fiber. Using scalar wave equation, we develop a complete set of analytic expressions for mode-mixing, including those for the $2\pi$ walk-off length, which is the distance traveled within the bent fiber before an OAM mode transforms into its negative topological charge counterpart, and back into itself. The derived results provide insight into the nature of the bend effects, clearly revealing the mathematical dependence on the bend radius and the topological charge. We numerically simulate the theoretical results with applications to a few-mode fiber and a multimode fiber, and calculate bend-induced modal crosstalk with implications for mode-multiplexed systems. The presented perturbation technique is general enough to be applicable to other perturbations like ellipticity and easily extendable to other fibers with step-index-like profile as in the ring fiber.