Abstract
An approach for modeling the dynamic saturable absorption of graphene using the finite-difference time-domain method is presented. In particular, this paper focuses on sub-picosecond pulse formation in a passively mode-locked semiconductor laser. The dynamics and the saturability of the gain and absorption are described by a carrier rate equation. The carrier dynamics are coupled to the electromagnetic field through an effective current density. All parameters of the graphene dynamics are obtained from reported experimental measurements. Using this numerical method, the dependence of output intensity and pulse width on input current density, graphene location, and cavity size is investigated. We find that pulse widths in the range 100–200 fs can be reliably generated with peak output intensities of around 0.15 mW/ $\mu \text{m}^{2}$ . The optimal placement of the graphene layer in the cavity is strongly dependent on the standing wave pattern near the mirror. We found that cavities as small as 30 $\mu \text{m}$ still support stable pulse formation.
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