A Finite-Difference Time-Domain Method for the Simulation of Gain Materials With Carrier Diffusion in Photonic Crystals

In this paper, we present a finite-difference time-domain formulation for active gain materials. Our scheme is based on a frequency-dependent conductivity. Experimental material gain is fitted with high accuracy to a multipole Lorentzian model using a semideterministic fitting algorithm. Because our model is an approximation to the full vectorial Maxwell´s system of equations, we include carrier diffusion into the rate equations for a two-level system. The material gain is included into the standard set of Maxwell´s equations by linking the frequency-dependent conductivity to the rate equations. Lasing is demonstrated for a vertical-cavity-surface-emitting-laser structure and photonic crystal lasers.