Modeling Passive Mode-Locking via Saturable Absorption in Graphene Using the Finite-Difference Time-Domain Method

摘要

Graphene's electromagnetic properties have been broadly studied; however, incorporating those properties into electromagnetic simulation tools continues to be investigated. In the present submission, we should how graphene's nonlinear response can be incorporated into the finite-difference time-domain method. Specifically, we focus on graphene's saturable absorption. Saturable absorbers are those whose absorption decreases as the input intensity is increased. Generally this is associated with a reduction of carriers in the valence band (and a reduction of states in the conduction band) due to absorption of intense illumination. In this work we use a carrier rate equation to model the nonlinear dynamics of both the graphene and the gain regions. We show how experimentally measured values of graphene's nominal and saturable absorption can be incorporated into the carrier rate equation approach.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/ . 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 still support stable pulse formation.