# Dissipative cnoidal waves (Turing rolls) and the soliton limit in microring resonators

## TL;DR

This paper investigates the stability and accessibility of cnoidal waves in microresonators, revealing their robustness and the conditions under which they can be deterministically accessed, with implications for frequency comb generation.

## Contribution

It provides a comprehensive analysis of cnoidal wave stability in microresonators using advanced computational tools, highlighting their relation to solitons and the challenges in deterministic access.

## Key findings

- Cnoidal waves are robust and accessible in microresonators.
- Their bandwidth can match that of single solitons, forming frequency combs.
- Stable regions for solitons overlap with those of certain cnoidal waves.

## Abstract

Single solitons are a special limit of more general waveforms commonly referred to as cnoidal waves or Turing rolls. We theoretically and computationally investigate the stability and accessibility of cnoidal waves in microresonators. We show that they are robust and, in contrast to single solitons, can be easily and deterministically accessed in most cases. Their bandwidth can be comparable to single solitons, in which limit they are effectively a periodic train of solitons and correspond to a frequency comb with increased power. We comprehensively explore the three-dimensional parameter space that consists of detuning, pump amplitude, and mode circumference in order to determine where stable solutions exist. To carry out this task, we use a unique set of computational tools based on dynamical system theory that allow us to rapidly and accurately determine the stable region for each cnoidal wave periodicity and to find the instability mechanisms and their time scales. Finally, we focus on the soliton limit, and we show that the stable region for single solitons almost completely overlaps the stable region for both continuous waves and several higher-periodicity cnoidal waves that are effectively multiple soliton trains. This result explains in part why it is difficult to access single solitons deterministically.

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Source: https://tomesphere.com/paper/1905.07086