Closed-Form Expressions for Nonlinearity Coefficients in Multimode Fibers

TL;DR

This paper derives simple, approximate closed-form expressions for nonlinear coupling coefficients in multimode fibers, depending only on a few design parameters, aiding fiber design and performance prediction.

Contribution

It introduces novel approximate formulas for Manakov nonlinear coefficients in multimode fibers, simplifying analysis and design for space-division multiplexing.

Findings

Coefficients depend only on fiber design parameters.

Nonlinearity decreases with increasing core radius.

Coefficients are nearly constant with refractive index changes.

Abstract

We derive novel approximate closed-form expressions for the nonlinear coupling coefficients appearing in the Manakov equations for multimode fibers for space-division multiplexing in the two regimes of strong and weak coupling. The expressions depend only on few fiber design parameters. In particular, the Manakov coefficients are shown to be simple rational numbers which depend solely on the number of guided modes. The overall nonlinearity coefficients are found to decrease with increasing core radius and to stay nearly constant with increasing refractive index difference between core and cladding. Validation is performed through a numerical approach. The consequences of the findings onto fiber design are discussed in terms of achievable data rates. The analysis is mainly focused on the trenchless parabolic graded-index profile, but considerations on the use of realistic trenches and non-parabolic indices, and on the step-index profile are given.