Finite-difference time-domain simulation of the Maxwell-Schrödinger system
Ryu, Christopher Jayun
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https://hdl.handle.net/2142/88032
Description
Title
Finite-difference time-domain simulation of the Maxwell-Schrödinger system
Author(s)
Ryu, Christopher Jayun
Issue Date
2015-07-14
Director of Research (if dissertation) or Advisor (if thesis)
Chew, Weng C.
Department of Study
Electrical & Computer Engineering
Discipline
Electrical & Computer Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
M.S.
Degree Level
Thesis
Keyword(s)
finite-difference method
finite-difference time-domain (FDTD)
Maxwell-Schrödinger system
light-matter interaction
vector potential
perfectly matched layers (PML)
Abstract
A thorough study on the finite-difference time-domain (FDTD) simulation of the Maxwell-Schrödinger system is given in this thesis. This system is a very effective tool to simulate and study the light-matter interaction between electromagnetic (EM) radiation and a charged particle in the semi-classical regime. The system is divided into two parts: Maxwell's equations and the Schrödinger equation. For the Maxwell part, an alternate approach involving the vector and scalar potentials (A and Φ) is used instead of Maxwell's equations involving the fields (E and H). This new approach is more suitable for this system since it is stable in the long wavelength regime and gets rid of an additional step of extracting the potentials from the fields. A few important FDTD techniques such as the perfectly matched layers (PML) and the plane wave excitation technique are discussed in detail. For the Schrödinger part, the technique of extracting the eigenfunctions in the time-domain through FDTD simulations is explained. Then, the Schrödinger equation is modified to take the EM radiation into account, and the particle current term, which couples the two systems, is explained. The FDTD stability condition for the whole system is analyzed and derived. The FDTD simulation of the Maxwell-Schrödinger system is shown to agree with the theory of quantum coherent states.
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