Computational model of solid-state, molecular, or atomic media for FDTD simulation based on a multi-level multi-electron system governed by Pauli exclusion and Fermi-Dirac thermalization with application to semiconductor photonics

We report a general computational model of complex material media for electrodynamics simulation using the Finite-Difference Time-Domain (FDTD) method. It is based on a multi-level multi-electron quantum system with electron dynamics governed by Pauli Exclusion Principle, state filling, and dynamical Fermi-Dirac Thermalization, enabling it to treat various solid-state, molecular, or atomic media. The formulation is valid at near or far off resonance as well as at high intensity. We show its FDTD application to a semiconductor in which the carriers' intraband and interband dynamics, energy band filling, and thermal processes were all incorporated for the first time. The FDTD model is sufficiently complex and yet computationally efficient, enabling it to simulate nanophotonic devices with complex electromagnetic structures requiring simultaneous solution of the mediumfield dynamics in space and time. Applications to direct-gap semiconductors, ultrafast optical phenomena, and multimode microdisk lasers are illustrated.