Electromagnetic simulation of quantum well structures.

We present an auxiliary differential equation Finite-difference Time-domain (ADE-FDTD) approach to numerically model the wave propagation within a gain or absorbing medium such as quantum well structures. Start from traditional quantum electronics theory, the macroscopic susceptibility of the semiconductor is derived and expressed by a multiple-Lorentz-like model based on Prony's method. With the auxiliary differential equation method each Lorentz-like model can be simulated in the time domain and the induced polarization is then determined by summing all the models. By incorporating the induced polarization into the time-domain Maxwell's equations, electromagnetic wave propagation in the quantum well medium can be accurately modeled using the FDTD method.