{"id":{"repo_id":"toronto-retro","oai_identifier":"oai:utoronto.scholaris.ca:1807/80790"},"canonical_url":"https://search.dev.ndltd.org/etd/toronto-retro/oai:utoronto.scholaris.ca:1807/80790","repository":{"repo_id":"toronto-retro","name":"University of Toronto","base_url":"https://utoronto.scholaris.ca/server/oai/request"},"display":{"title":"Response of periodic systems to electromagnetic fields: multipole expansion, microscopic charge-current density, polarization and magnetization","abstract":"Polarization and magnetization fields are central concepts in the theory of light-matter interaction, because they describe the distribution of charges and currents induced in the material medium due to an application of electromagnetic fields. Here I develop strategies to treat polarization and magnetization fields in periodic structures and I analyze the radiation spectrum emitted by them. The methods are based on the multipole expansion of charge-current distributions and on its extensions to account for the motion of charges between lattice sites. In the first part of this thesis I treat the optical response of 2d nanoparticle arrays, with the focus on collective effects that arise due to higher order multipolar response. First, I evaluate the interaction constants that describe the collective radiative interactions between nanoparticles in magneto-electric quadrupolar arrays, in an approach that gives the radiative damping in an exact analytic form. Then I find the radiation spectrum from an array of gold spheres with large electric quadrupolar response. The spectrum is dominated by surface-lattice resonances (SLRs) which are of a mixed multipolar character, with significant contributions from multipoles that would be negligible if the sphere was isolated. I link the SLRs to an excitation of the normal modes of the array, and propose a simplified model of the normal mode dispersion relations to explain the SLR properties. In the second part of this thesis I develop strategies to describe charges and currents and polarization and magnetization fields in regular solids. The formalism is based on gauge-invariant dynamical equations of electron Green functions. I derive and categorize the descriptions of dynamics introduced via Peierls transformation of the Green function. Then I apply the formalism to treat the linear response of an insulator to electromagnetic fields. I find the microscopic charge and current densitites in a form such that their expansion around lattice sites follows in a natural way. Restricting myself to static and uniform fields I introduce microscopic polarization and magnetization fields, and derive all the response coefficients within one formalism that makes no reference to energy or thermodynamic potentials.","abstract_html":"Polarization and magnetization fields are central concepts in the theory of light-matter interaction, because they describe the distribution of charges and currents induced in the material medium due to an application of electromagnetic fields. Here I develop strategies to treat polarization and magnetization fields in periodic structures and I analyze the radiation spectrum emitted by them. The methods are based on the multipole expansion of charge-current distributions and on its extensions to account for the motion of charges between lattice sites. In the first part of this thesis I treat the optical response of 2d nanoparticle arrays, with the focus on collective effects that arise due to higher order multipolar response. First, I evaluate the interaction constants that describe the collective radiative interactions between nanoparticles in magneto-electric quadrupolar arrays, in an approach that gives the radiative damping in an exact analytic form. Then I find the radiation spectrum from an array of gold spheres with large electric quadrupolar response. The spectrum is dominated by surface-lattice resonances (SLRs) which are of a mixed multipolar character, with significant contributions from multipoles that would be negligible if the sphere was isolated. I link the SLRs to an excitation of the normal modes of the array, and propose a simplified model of the normal mode dispersion relations to explain the SLR properties. In the second part of this thesis I develop strategies to describe charges and currents and polarization and magnetization fields in regular solids. The formalism is based on gauge-invariant dynamical equations of electron Green functions. I derive and categorize the descriptions of dynamics introduced via Peierls transformation of the Green function. Then I apply the formalism to treat the linear response of an insulator to electromagnetic fields. I find the microscopic charge and current densitites in a form such that their expansion around lattice sites follows in a natural way. Restricting myself to static and uniform fields I introduce microscopic polarization and magnetization fields, and derive all the response coefficients within one formalism that makes no reference to energy or thermodynamic potentials.","abstract_has_math":false,"creators":["Swiecicki, Sylvia Dianna"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Physics","school":null,"contributors":[],"advisors":["Sipe, John E"],"committee_chairs":[],"committee_members":[],"year":2017,"date_issued":"2017-11","date_published":"2017-11","updated_at":"2026-07-27T21:27:56Z","subjects":["metamaterials","multipole expansion","optical properties of materials","periodic systems","polarization and magnetization"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/1807/80790","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Sipe, John E"]},{"key":"dc:contributor.department","label":"Department","values":["Physics"]},{"key":"dc:creator","label":"Author","values":["Swiecicki, Sylvia Dianna"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2017-11"]},{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2017-12-19T00:01:57Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2017-12-19T00:01:57Z"]},{"key":"dc:date.issued","label":"Date","values":["2017-11"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["metamaterials","multipole expansion","optical properties of materials","periodic systems","polarization and magnetization"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/1807/80790"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Polarization and magnetization fields are central concepts in the theory of light-matter interaction, because they describe the distribution of charges and currents induced in the material medium due to an application of electromagnetic fields. Here I develop strategies to treat polarization and magnetization fields in periodic structures and I analyze the radiation spectrum emitted by them. The methods are based on the multipole expansion of charge-current distributions and on its extensions to account for the motion of charges between lattice sites. In the first part of this thesis I treat the optical response of 2d nanoparticle arrays, with the focus on collective effects that arise due to higher order multipolar response. First, I evaluate the interaction constants that describe the collective radiative interactions between nanoparticles in magneto-electric quadrupolar arrays, in an approach that gives the radiative damping in an exact analytic form. Then I find the radiation spectrum from an array of gold spheres with large electric quadrupolar response. The spectrum is dominated by surface-lattice resonances (SLRs) which are of a mixed multipolar character, with significant contributions from multipoles that would be negligible if the sphere was isolated. I link the SLRs to an excitation of the normal modes of the array, and propose a simplified model of the normal mode dispersion relations to explain the SLR properties. In the second part of this thesis I develop strategies to describe charges and currents and polarization and magnetization fields in regular solids. The formalism is based on gauge-invariant dynamical equations of electron Green functions. I derive and categorize the descriptions of dynamics introduced via Peierls transformation of the Green function. Then I apply the formalism to treat the linear response of an insulator to electromagnetic fields. I find the microscopic charge and current densitites in a form such that their expansion around lattice sites follows in a natural way. Restricting myself to static and uniform fields I introduce microscopic polarization and magnetization fields, and derive all the response coefficients within one formalism that makes no reference to energy or thermodynamic potentials."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph.D."]},{"key":"dc:title","label":"Title","values":["Response of periodic systems to electromagnetic fields: multipole expansion, microscopic charge-current density, polarization and magnetization"]}]}],"canonical_facts":{"dc:contributor.advisor":["Sipe, John E"],"dc:contributor.department":["Physics"],"dc:creator":["Swiecicki, Sylvia Dianna"],"dc:date":["2017-11"],"dc:date.accessioned":["2017-12-19T00:01:57Z"],"dc:date.available":["2017-12-19T00:01:57Z"],"dc:date.issued":["2017-11"],"dc:description.abstract":["Polarization and magnetization fields are central concepts in the theory of light-matter interaction, because they describe the distribution of charges and currents induced in the material medium due to an application of electromagnetic fields. Here I develop strategies to treat polarization and magnetization fields in periodic structures and I analyze the radiation spectrum emitted by them. The methods are based on the multipole expansion of charge-current distributions and on its extensions to account for the motion of charges between lattice sites. In the first part of this thesis I treat the optical response of 2d nanoparticle arrays, with the focus on collective effects that arise due to higher order multipolar response. First, I evaluate the interaction constants that describe the collective radiative interactions between nanoparticles in magneto-electric quadrupolar arrays, in an approach that gives the radiative damping in an exact analytic form. Then I find the radiation spectrum from an array of gold spheres with large electric quadrupolar response. The spectrum is dominated by surface-lattice resonances (SLRs) which are of a mixed multipolar character, with significant contributions from multipoles that would be negligible if the sphere was isolated. I link the SLRs to an excitation of the normal modes of the array, and propose a simplified model of the normal mode dispersion relations to explain the SLR properties. In the second part of this thesis I develop strategies to describe charges and currents and polarization and magnetization fields in regular solids. The formalism is based on gauge-invariant dynamical equations of electron Green functions. I derive and categorize the descriptions of dynamics introduced via Peierls transformation of the Green function. Then I apply the formalism to treat the linear response of an insulator to electromagnetic fields. I find the microscopic charge and current densitites in a form such that their expansion around lattice sites follows in a natural way. Restricting myself to static and uniform fields I introduce microscopic polarization and magnetization fields, and derive all the response coefficients within one formalism that makes no reference to energy or thermodynamic potentials."],"dc:description.degree":["Ph.D."],"dc:identifier.uri":["http://hdl.handle.net/1807/80790"],"dc:subject":["metamaterials","multipole expansion","optical properties of materials","periodic systems","polarization and magnetization"],"dc:title":["Response of periodic systems to electromagnetic fields: multipole expansion, microscopic charge-current density, polarization and magnetization"],"dc:type":["Thesis"]},"updated_at":"2026-07-27T21:27:56Z"}