Finite-difference time-domain simulation of the Maxwell-Schrödinger system

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.

Name thesis:degree_name

M.S.

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Electrical & Computer Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Ryu, Christopher Jayun

Contributors dc:contributor

• Chew, Weng C.

• finite-difference method
• finite-difference time-domain (FDTD)
• Maxwell-Schrödinger system
• light-matter interaction
• vector potential
• perfectly matched layers (PML)

Statement dc:rights

• Copyright 2015 Christopher J. Ryu

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/88032

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/88032