{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/88032"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/88032","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Finite-difference time-domain simulation of the Maxwell-Schrödinger system","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Ryu, Christopher Jayun"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Electrical & Computer Engineering","degree_department":null,"school":null,"contributors":["Chew, Weng C."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-29T20:38:22Z","date_published":"2015-09-29T20:38:22Z","updated_at":"2026-07-22T22:26:31Z","subjects":["finite-difference method","finite-difference time-domain (FDTD)","Maxwell-Schrödinger system","light-matter interaction","vector potential","perfectly matched layers (PML)"],"languages":["en"],"rights":["Copyright 2015 Christopher J. Ryu"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/88032","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Chew, Weng C."]},{"key":"dc:creator","label":"Author","values":["Ryu, Christopher Jayun"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-29T20:38:22Z","2015-08","2015-07-14","2015-8"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Electrical & Computer Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["finite-difference method","finite-difference time-domain (FDTD)","Maxwell-Schrödinger system","light-matter interaction","vector potential","perfectly matched layers (PML)"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2015 Christopher J. Ryu"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/88032"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2015-09-29 without embargo terms","The student, Christopher Ryu, accepted the attached license on 2015-07-13 at 20:03.","The student, Christopher Ryu, submitted this Thesis for approval on 2015-07-13 at 20:05.","This Thesis was approved for publication on 2015-07-14 at 12:20.","DSpace SAF Submission Ingestion Package generated from Vireo submission #8436 on 2015-09-29 at 13:22:42","Made available in DSpace on 2015-09-29T20:38:22Z (GMT). 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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.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2015-09-29 without embargo terms","The student, Christopher Ryu, accepted the attached license on 2015-07-13 at 20:03.","The student, Christopher Ryu, submitted this Thesis for approval on 2015-07-13 at 20:05.","This Thesis was approved for publication on 2015-07-14 at 12:20.","DSpace SAF Submission Ingestion Package generated from Vireo submission #8436 on 2015-09-29 at 13:22:42","Made available in DSpace on 2015-09-29T20:38:22Z (GMT). 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