# Dynamics of a class A nonlinear mirror mode-locked laser

## TL;DR

This paper models the complex dynamics of a class-A nonlinear mirror mode-locked laser using delay differential equations, revealing stability conditions, instabilities, and the formation of asymmetric mode-locked pulses.

## Contribution

It introduces a theoretical delay differential equation model to analyze the stability and pulse formation in a class-A nonlinear mirror mode-locked laser.

## Key findings

- CW regimes can be destabilized by modulational, Turing, and square-wave instabilities.
- Mode-locked pulses exhibit asymmetric exponential decay in their edges.
- Harmonic mode-locking arises from asymmetric pulse interactions.

## Abstract

Using a delay differential equation model we study theoretically the dynamics of a unidirectional class-A ring laser with a nonlinear amplifying loop mirror. We perform linear stability analysis of the CW regimes in the large delay limit and demonstrate that these regimes can be destabilized via modulational and Turing-type instabilities, as well as by an instability leading to the appearance of square-waves. We investigate the formation of square-waves and mode-locked pulses in the system. We show that mode-locked pulses are asymmetric with exponential decay of the trailing edge in positive time and faster-than-exponential (super-exponential) decay of the leading edge in negative time. We discuss asymmetric interaction of these pulses leading to a formation of harmonic mode-locked regimes.