# Soliton-comb structures in ring-shaped optical microresonators: generation, reconstruction and stability

## TL;DR

This paper investigates the formation, reconstruction, and stability of soliton-comb structures in optical microresonators across different dispersion regimes, revealing their internal structures and stability characteristics through analytical and numerical methods.

## Contribution

It introduces new analytical and numerical schemes for reconstructing soliton-comb structures and analyzes their stability via a novel eigenvalue problem, advancing understanding of their dynamics.

## Key findings

- Identification of stable and unstable modes in soliton-comb spectra
- Reconstruction schemes for soliton structures in microresonators
- Detection of structural defects in power spectra

## Abstract

Characteristic features of soliton-comb structures in optical microresonators are investigated in normal and anomalous dispersion regimes, when the detuning parameter is varied over a broad range of values. The study rests on the assumption that soliton combs are self-organized ensemble of co-propagating coherently entangled states of light, and depending on the group-velocity dispersion they can result from space-division multiplexing of single-bright and single-dark solitons. Their analytical and numerical reconstruction schemes are discussed, while a linear-stability analysis leads to a $2\times 2$ Lam\'e eigenvalue problem whose boundstate spectrum is composed of a Goldstone-type translation mode and stable internal modes, as well as unstable decaying modes and growing modes. A power-spectral analysis of the three distinct possible soliton crystals enables us probe their inner structures in the frequency domain, and unveil the existence of structural defects in their power spectra.