Numerical study on the minimum modulation depth of a saturable absorber for stable fiber laser mode locking

We conducted a numerical study to investigate the minimum modulation depth of a saturable absorber that is essentially required for stable optical pulses to be generated from a passively mode-locked fiber laser cavity. More specifically, an extended nonlinear Schrodinger equation was numerically solved in order to analyze the impact of the cavity group velocity dispersion (GVD), cavity χ⁽³⁾ nonlinearity, and saturation gain of an active fiber on the minimum modulation depth that is required. The net cavity GVD is shown to significantly influence the required minimum modulation depth level of a saturable absorber. A cavity with little net anomalous dispersion was found to be readily mode locked through the use of a saturable absorber with a very small amount of modulation depth. Furthermore, the reason that a fiber laser cavity with a zero cavity GVD becomes unstable and needs a much higher modulation depth was investigated, and such a condition was found to be associated with the fiber χ⁽³⁾ nonlinearity. The minimum modulation depth was also shown to vary according to the saturation gain level of an active fiber.