INCORPORATING DISPERSIVE DIELECTRIC OBJECTS INTO POTENTIAL-BASED FDTD METHODS

New classes of electromagnetic modeling problems are arising in the design of quantum information processing technologies. In many cases, these problems involve looking at controlling individual quantum systems with electromagnetic fields at optical frequencies. Since the optical control fields in these applications are essentially classical fields, one promising modeling approach is to perform a semiclassical analysis where the optical fields are treated classically, but the quantum system’s dynamics are modeled quantum mechanically. Typically referred to as Maxwell-Schrödinger models, there is growing interest in these applications to solve the “Maxwell” part of the system directly in terms of the electromagnetic potentials that are used in the Schrödinger equation rather than using the more conventional electric and magnetic fields. To date, the most popular numerical method used to discretize this system of equations is the finite-difference time-domain (FDTD) method. However, these prior works are missing the necessary utilities to consider the modeling of integrated photonic systems when using FDTD methods formulated directly in terms of the magnetic vector and electric scalar potentials. In particular, these potential-based FDTD methods have not been able to model dispersive dielectric materials, which are critical in integrated photonic systems. In this work, we introduce a kind of auxiliary differential equation method for incorporating a Drude-Lorentz-Sommerfeld material model into potential-based FDTD methods. This work also shows the functionality of an absorbing boundary condition for the first time within a potential-based FDTD model to replace the particularly complex implementation of perfectly matched layers within this modeling framework. As such, the methods described in this thesis are intended to help improve the modeling capabilities of potential-based FDTD methods so that they can be used in Maxwell-Schrödinger modeling of more realistic integrated quantum photonic technologies in the future.