# Modulation Instability of Discrete Angular Momentum in Coupled Fiber Rings

## TL;DR

This paper analyzes how continuous-wave signals in coupled fiber ring arrays become unstable due to modulation instability, influenced by angular momentum, dispersion, coupling strength, and twisting, revealing tunable spectral properties.

## Contribution

It provides a novel analysis of modulation instability in fiber ring arrays considering discrete angular momentum, coupling, and twisting effects.

## Key findings

- Instability occurs for perturbations with discrete angular momentum.
- Frequency spectra depend on coupling strength and angular momentum.
- Twisting the ring tunes the instability spectra via the Peierls phase.

## Abstract

We present an analysis of temporal modulation instability in a ring array of coupled optical fibers. Continuous-wave signals are shown to be unstable to perturbations carrying discrete angular momenta, both for normal and anomalous group velocity dispersion. We find the frequency spectrum of modulation instability is different for each perturbation angular momentum and depends strongly on the coupling strength between fibers in the ring. Twisting the ring array also allows the frequency spectra to be tuned through the induced tunnelling Peierls phase.