SIMULATION OF WAVE PROPAGATION WITH ACTIVE MATERIALS EMBEDDED IN PHOTONIC CRYSTALS USING FDTD METHOD

Abstract

We implement a four-level two-electron Finite-Difference Time-Domain (FDTD) computational model for electrodynamics simulation of complex material media. This model allows us to study the medium carrier density dynamics together with its influence on propagating electromagnetic signal. We show the rate equation for the four-level model and incorporate Pauli Exclusion Principle into the rate equation. The two electrons model allows us to investigate optical pumping and probing in semiconductor devices. This FDTD model is sufficiently complex and, yet, computationally efficient, which allows us to simulate nano-photonic devices with complex electromagnetic structures requiring simultaneous solution of the medium-field dynamics in space and time. Applications include direct-gap semiconductors, ultrafast optical phenomena, and multimode microdisk lasers. This model is modified from an existing UNIX package developed by MIT, namely the MIT Electromagnetic Equation Propagation (MEEP). Examples of Scheme and C++ program to configure the desired waveguide form and electromagnetic dynamics are shown to illustrate the usage of MEEP. Details on the implementation of the four-level two-electron model are explained as well as the test cases that illustrates the end results.