# Intermodal Four-Wave-Mixing and Parametric Amplification in km-long Fibers

## TL;DR

This paper investigates how random birefringence and core radius variations affect intermodal four-wave mixing and parametric amplification in long fibers, providing insights for designing multimode optical devices.

## Contribution

It introduces a theoretical and numerical analysis of intermodal four-wave mixing in km-long fibers considering random birefringence and core variations, highlighting regimes and bandwidth limitations.

## Key findings

- Random birefringence fluctuations significantly influence four-wave mixing regimes.
- Core radius variations are a major source of bandwidth impairment.
- The classical Manakov model's limits are delineated for long-haul fiber applications.

## Abstract

We theoretically and numerically investigate intermodal four-wave-mixing in km-long fibers, where random birefringence fluctuations are present along the fiber length. We identify several distinct regimes that depend on the relative magnitude between the length scale of the random fluctuations and the beat-lengths of the interacting quasi-degenerate modes. In addition, we analyze the impact of polarization mode-dispersion and we demonstrate that random variations of the core radius, which are typically encountered during the drawing stage of the fiber, can represent the major source of bandwidth impairment. These results set a boundary on the limits of validity of the classical Manakov model and may be useful for the design of multimode parametric amplifiers and wavelength converters, as well as for the analysis of nonlinear impairments in long-haul spatial division multiplexed transmission.