\"Passive quasi-one-dimensional random media exhibit one of the three regimes of transport - ballistic, diffusive, or Anderson localization - depending on system size. The ballistic and diffusion approximations assumes particle transport, whereas Anderson Localization occurs when wave self-interference effects are dominant. When the system contains absorption or gain, then how the regimes can be characterized becomes unclear. By investigating theoretically and numerically the ratio of transmission to energy in a random medium in one dimension, we show this parameter can be used to characterize localization in random media with gain. Non-conservative media implies a second dimension for the transport parameter space, namely gain/absorption. By studying the relations between the transport mean free path, the localization length, and the gain or absorption lengths, we enumerate fifteen regimes of wave propagation through quasi-one-dimensional nonconservative random media. Next a criterion characterizing the transition from diffusion to Anderson localization is developed for random media with gain or absorption. The position-dependent diffusion coefficient, which is closely related to the ratio of transmission to energy stored in the system, is investigated using numerical models. In contrast to random structures, deterministic aperiodic structures (DAS) offer predictable and reproducible transport behaviors while exhibiting a variety of unusual transport properties not found in either ordered or random media. By manipulating structural correlations one may design and fabricate artificial photonic nanomaterials with prescribed transport properties. The Thue-Morse structure is a prime example of deterministic aperiodic systems with singular-continuous spatial Fourier spectra. The non-periodic nature of the system makes it notoriously difficult to characterize theoretically especially in dimensions higher than one. The possibility of mapping the two-dimensional aperiodic Thue-Morse pattern of micro-cavities onto a square lattice is demonstrated, making it amenable to the tight-binding description\"--Abstract, page iv.
","abstract_html":"<p>"Passive quasi-one-dimensional random media exhibit one of the three regimes of transport - ballistic, diffusive, or Anderson localization - depending on system size. The ballistic and diffusion approximations assumes particle transport, whereas Anderson Localization occurs when wave self-interference effects are dominant. When the system contains absorption or gain, then how the regimes can be characterized becomes unclear. By investigating theoretically and numerically the ratio of transmission to energy in a random medium in one dimension, we show this parameter can be used to characterize localization in random media with gain. Non-conservative media implies a second dimension for the transport parameter space, namely gain/absorption. By studying the relations between the transport mean free path, the localization length, and the gain or absorption lengths, we enumerate fifteen regimes of wave propagation through quasi-one-dimensional nonconservative random media. Next a criterion characterizing the transition from diffusion to Anderson localization is developed for random media with gain or absorption. The position-dependent diffusion coefficient, which is closely related to the ratio of transmission to energy stored in the system, is investigated using numerical models. In contrast to random structures, deterministic aperiodic structures (DAS) offer predictable and reproducible transport behaviors while exhibiting a variety of unusual transport properties not found in either ordered or random media. By manipulating structural correlations one may design and fabricate artificial photonic nanomaterials with prescribed transport properties. The Thue-Morse structure is a prime example of deterministic aperiodic systems with singular-continuous spatial Fourier spectra. The non-periodic nature of the system makes it notoriously difficult to characterize theoretically especially in dimensions higher than one. The possibility of mapping the two-dimensional aperiodic Thue-Morse pattern of micro-cavities onto a square lattice is demonstrated, making it amenable to the tight-binding description"--Abstract, page iv.</p>","abstract_has_math":false,"creators":["Payne, Benjamin Henry"],"institution":"Missouri University of Science and Technology","degree_name":"Ph. D. in Physics","degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-02-10T08:00:00Z","date_published":"2016-02-10T08:00:00Z","updated_at":"2026-07-24T03:19:30Z","subjects":["Correlated disorder","Random disorder","Wave transport","Physics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarsmine.mst.edu/doctoral_dissertations/1957","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Payne, Benjamin Henry"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2016-02-10T08:00:00Z"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation - Open Access"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph. D. in Physics"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Missouri University of Science and Technology"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Correlated disorder","Random disorder","Wave transport","Physics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarsmine.mst.edu/doctoral_dissertations/1957"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["\"Passive quasi-one-dimensional random media exhibit one of the three regimes of transport - ballistic, diffusive, or Anderson localization - depending on system size. The ballistic and diffusion approximations assumes particle transport, whereas Anderson Localization occurs when wave self-interference effects are dominant. When the system contains absorption or gain, then how the regimes can be characterized becomes unclear. By investigating theoretically and numerically the ratio of transmission to energy in a random medium in one dimension, we show this parameter can be used to characterize localization in random media with gain. Non-conservative media implies a second dimension for the transport parameter space, namely gain/absorption. By studying the relations between the transport mean free path, the localization length, and the gain or absorption lengths, we enumerate fifteen regimes of wave propagation through quasi-one-dimensional nonconservative random media. Next a criterion characterizing the transition from diffusion to Anderson localization is developed for random media with gain or absorption. The position-dependent diffusion coefficient, which is closely related to the ratio of transmission to energy stored in the system, is investigated using numerical models. In contrast to random structures, deterministic aperiodic structures (DAS) offer predictable and reproducible transport behaviors while exhibiting a variety of unusual transport properties not found in either ordered or random media. By manipulating structural correlations one may design and fabricate artificial photonic nanomaterials with prescribed transport properties. The Thue-Morse structure is a prime example of deterministic aperiodic systems with singular-continuous spatial Fourier spectra. The non-periodic nature of the system makes it notoriously difficult to characterize theoretically especially in dimensions higher than one. The possibility of mapping the two-dimensional aperiodic Thue-Morse pattern of micro-cavities onto a square lattice is demonstrated, making it amenable to the tight-binding description\"--Abstract, page iv.
"]},{"key":"dc:title","label":"Title","values":["Characterization of wave transport in non-conservative media with random and correlated disorder"]}]}],"canonical_facts":{"dc:creator":["Payne, Benjamin Henry"],"dc:date.available":["2016-02-10T08:00:00Z"],"dc:description.abstract":["\"Passive quasi-one-dimensional random media exhibit one of the three regimes of transport - ballistic, diffusive, or Anderson localization - depending on system size. The ballistic and diffusion approximations assumes particle transport, whereas Anderson Localization occurs when wave self-interference effects are dominant. When the system contains absorption or gain, then how the regimes can be characterized becomes unclear. By investigating theoretically and numerically the ratio of transmission to energy in a random medium in one dimension, we show this parameter can be used to characterize localization in random media with gain. Non-conservative media implies a second dimension for the transport parameter space, namely gain/absorption. By studying the relations between the transport mean free path, the localization length, and the gain or absorption lengths, we enumerate fifteen regimes of wave propagation through quasi-one-dimensional nonconservative random media. Next a criterion characterizing the transition from diffusion to Anderson localization is developed for random media with gain or absorption. The position-dependent diffusion coefficient, which is closely related to the ratio of transmission to energy stored in the system, is investigated using numerical models. In contrast to random structures, deterministic aperiodic structures (DAS) offer predictable and reproducible transport behaviors while exhibiting a variety of unusual transport properties not found in either ordered or random media. By manipulating structural correlations one may design and fabricate artificial photonic nanomaterials with prescribed transport properties. The Thue-Morse structure is a prime example of deterministic aperiodic systems with singular-continuous spatial Fourier spectra. The non-periodic nature of the system makes it notoriously difficult to characterize theoretically especially in dimensions higher than one. The possibility of mapping the two-dimensional aperiodic Thue-Morse pattern of micro-cavities onto a square lattice is demonstrated, making it amenable to the tight-binding description\"--Abstract, page iv.
"],"dc:identifier":["https://scholarsmine.mst.edu/doctoral_dissertations/1957"],"dc:subject":["Correlated disorder","Random disorder","Wave transport","Physics"],"dc:title":["Characterization of wave transport in non-conservative media with random and correlated disorder"],"dc:type":["Dissertation - Open Access"],"thesis:degree_name":["Ph. D. in Physics"],"thesis:institution_name":["Missouri University of Science and Technology"]},"updated_at":"2026-07-24T03:19:30Z"}