# Effect of saturable nonlinearity on cw stability in passively mode-locked lasers with fast saturable absorbers

## TL;DR

This paper investigates how saturable nonlinearity affects the stability and self-starting behavior of passively mode-locked lasers with fast saturable absorbers, providing analytical criteria for self-starting conditions.

## Contribution

It introduces a global map for laser self-starting criteria considering saturable nonlinearity, extending understanding of stability in different dispersion regimes.

## Key findings

- Saturable nonlinearity increases the input-field intensity needed for self-starting.
- Derived an analytical expression for the threshold input field in zero modulation-frequency regime.
- Evidence of self-starting in both normal and anomalous dispersion regimes.

## Abstract

The self-starting dynamics of a model for passively mode-locked lasers with saturable absorber, in which the optical amplifier has a saturable nonlinearity, is examined. The basic assumption is that the laser will operate in the mode-locked regime when the continuous-wave regime becomes unstable. Within the framework of the modulational-instability analysis, a global map for the laser self-starting criteria is constructed. According to this map, the saturable nonlinearity enhances the input-field intensity required for laser self-starting. Analytical expression of the zero modulation-frequency regime of this threshold input field is derived, which turns out to be valid in the normal as well as in the anomalous dispersion regime, where evidence of self-starting is also given.