A Highly Efficient Computational Model for FDTD Simulations of Ultrafast Electromagnetic Interactions With Semiconductor Media With Carrier Heating/Cooling Dynamics

We report a new computational model to incorporate carrier heating/cooling effects for the finite-difference time-domain (FDTD) simulation of electromagnetic interactions with semiconductor media. The model is formulated to be computationally efficient enough to be applied to FDTD simulations of photonic devices of complex structural geometry. The model developed here is built on top of a previous multi-level multi-electron (MLME) model we presented and the new model is called MLME-dynamical temperature (MLMEDT) model. The key developments here include the following. 1) Intraband transition terms with electron and hole temperature parameters that vary with time and space are introduced. 2) Rate equations for the explicit update of carrier temperature are formulated. A computationally efficient method is used to evaluate these carrier temperature rate equations which circumvent iterative procedures as well as the need to dynamically compute the chemical potential by presolving the relational functions required using dimensionless fitting functions. The temporal update of these fitting functions only needs the total carrier number densities, which are already obtained in the MLME model computation. 3) The changes in the total carrier kinetic energy density and carrier number density due to all interband processes such as stimulated emission/absorption and intraband processes such as free carrier absorption are tracked to drive the carrier temperature rate equations. 4) The thermal relaxation of the electron and hole temperatures to the lattice temperature and the thermal relaxation between electrons and holes are also included. In order to validate the approach, simulations of thermalization of nonequilibrium carrier distributions and nonlinear gain and refractive index dynamics in semiconductor optical amplifiers (SOA) are presented. Quantitative agreement with nonlinear gain dynamics experiments of SOA directly verifies the accuracy of the current approach. Additionally, a 2-D simulation of a microdisk laser is presented to depict how FDTD can be used to visualize the spatial profile of carrier temperatures. The computational time of the MLMEDT model is found to be only ~10% more than that of the MLME model, thus showing high computational efficiency.