{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/164598"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/164598","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Reciprocity and Normality in the Scattering Matrix of Disordered Media","abstract":"The scattering matrix formalism provides a practical characterization of wave transport in linear, source-free systems by relating a set of operationally defined input and output spatial channels. The matrix is structured as a block operator, with diagonal blocks encoding same-side reflection matrices (RMs) and off-diagonal blocks encoding transmission matrices (TMs) in opposing propagation directions. Under Helmholtz reciprocity, symmetry relations are imposed: RMs are symmetric, and forward and reverse TMs are mathematical transposes of each other. These relations were employed as constraints to correct system-induced aberrations in measured scattering matrices of complex optical media via a matrix-based gradient descent procedure. Resulting phase corrections corresponded closely with classical aberration modes without heuristic parameterizations, suggesting that these modes naturally arise to restore reciprocity-induced symmetry. Vectorial TMs were measured for single- and double-pass propagation through step-index MMFs and scattering samples, with corrected phase terms showing agreement across sample types. Furthermore, matrix normality was introduced as a descriptor of stable modal transport. Normal matrices admit unitary diagonalization, reflecting orthogonal eigenchannels and spectrally coherent propagation. Near-normal behavior was observed in fiber TMs, while RMs of scattering slabs remained strongly non-normal, as quantified by a normalized Henrici departure. Sufficient conditions for normality were identified in terms of the system Green’s function and its bi-compression onto the measurement basis. A complementary dispersion experiment investigated two regimes: nearly-normal MMFs, where the Wigner–Smith time-delay operator was jointly diagonalizable and supported accurate first-order spectral models; and mechanically compressed fibers, where loss of normality produced noncommuting operators and collapse of model fidelity. These results suggest that normality captures well-behaved modal transport, underpinning the validity of parametric models and other operator-based analyses of disordered media. Together, reciprocity and normality impose complementary constraints on wave transport: reciprocity governs global symmetry, while normality captures internal coherence of modal propagation. Relevance is noted for matrix-based imaging, inverse scattering theory, and non-Hermitian wave physics, where symmetry and modal stability remain central.","abstract_html":"The scattering matrix formalism provides a practical characterization of wave transport in linear, source-free systems by relating a set of operationally defined input and output spatial channels. The matrix is structured as a block operator, with diagonal blocks encoding same-side reflection matrices (RMs) and off-diagonal blocks encoding transmission matrices (TMs) in opposing propagation directions. Under Helmholtz reciprocity, symmetry relations are imposed: RMs are symmetric, and forward and reverse TMs are mathematical transposes of each other. These relations were employed as constraints to correct system-induced aberrations in measured scattering matrices of complex optical media via a matrix-based gradient descent procedure. Resulting phase corrections corresponded closely with classical aberration modes without heuristic parameterizations, suggesting that these modes naturally arise to restore reciprocity-induced symmetry. Vectorial TMs were measured for single- and double-pass propagation through step-index MMFs and scattering samples, with corrected phase terms showing agreement across sample types. Furthermore, matrix normality was introduced as a descriptor of stable modal transport. Normal matrices admit unitary diagonalization, reflecting orthogonal eigenchannels and spectrally coherent propagation. Near-normal behavior was observed in fiber TMs, while RMs of scattering slabs remained strongly non-normal, as quantified by a normalized Henrici departure. Sufficient conditions for normality were identified in terms of the system Green’s function and its bi-compression onto the measurement basis. A complementary dispersion experiment investigated two regimes: nearly-normal MMFs, where the Wigner–Smith time-delay operator was jointly diagonalizable and supported accurate first-order spectral models; and mechanically compressed fibers, where loss of normality produced noncommuting operators and collapse of model fidelity. These results suggest that normality captures well-behaved modal transport, underpinning the validity of parametric models and other operator-based analyses of disordered media. Together, reciprocity and normality impose complementary constraints on wave transport: reciprocity governs global symmetry, while normality captures internal coherence of modal propagation. Relevance is noted for matrix-based imaging, inverse scattering theory, and non-Hermitian wave physics, where symmetry and modal stability remain central.","abstract_has_math":false,"creators":["Bharadwaj, Shreyas K."],"institution":"Massachusetts Institute of Technology","degree_name":"Master","degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science","school":null,"contributors":[],"advisors":["Villiger, Martin"],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025-09","date_published":"2025-09","updated_at":"2026-07-22T22:21:59Z","subjects":[],"languages":[],"rights":["In Copyright - Educational Use Permitted","Copyright retained by author(s)"],"rights_urls":["https://rightsstatements.org/page/InC-EDU/1.0/"],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/1721.1/164598","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Villiger, Martin"]},{"key":"dc:contributor.department","label":"Department","values":["Massachusetts Institute of Technology. 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The matrix is structured as a block operator, with diagonal blocks encoding same-side reflection matrices (RMs) and off-diagonal blocks encoding transmission matrices (TMs) in opposing propagation directions. Under Helmholtz reciprocity, symmetry relations are imposed: RMs are symmetric, and forward and reverse TMs are mathematical transposes of each other. These relations were employed as constraints to correct system-induced aberrations in measured scattering matrices of complex optical media via a matrix-based gradient descent procedure. Resulting phase corrections corresponded closely with classical aberration modes without heuristic parameterizations, suggesting that these modes naturally arise to restore reciprocity-induced symmetry. Vectorial TMs were measured for single- and double-pass propagation through step-index MMFs and scattering samples, with corrected phase terms showing agreement across sample types. Furthermore, matrix normality was introduced as a descriptor of stable modal transport. Normal matrices admit unitary diagonalization, reflecting orthogonal eigenchannels and spectrally coherent propagation. Near-normal behavior was observed in fiber TMs, while RMs of scattering slabs remained strongly non-normal, as quantified by a normalized Henrici departure. Sufficient conditions for normality were identified in terms of the system Green’s function and its bi-compression onto the measurement basis. A complementary dispersion experiment investigated two regimes: nearly-normal MMFs, where the Wigner–Smith time-delay operator was jointly diagonalizable and supported accurate first-order spectral models; and mechanically compressed fibers, where loss of normality produced noncommuting operators and collapse of model fidelity. These results suggest that normality captures well-behaved modal transport, underpinning the validity of parametric models and other operator-based analyses of disordered media. Together, reciprocity and normality impose complementary constraints on wave transport: reciprocity governs global symmetry, while normality captures internal coherence of modal propagation. Relevance is noted for matrix-based imaging, inverse scattering theory, and non-Hermitian wave physics, where symmetry and modal stability remain central."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["S.M."]},{"key":"dc:title","label":"Title","values":["Reciprocity and Normality in the Scattering Matrix of Disordered Media"]}]}],"canonical_facts":{"dc:contributor.advisor":["Villiger, Martin"],"dc:contributor.department":["Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science"],"dc:creator":["Bharadwaj, Shreyas K."],"dc:date.accessioned":["2026-01-20T19:47:49Z"],"dc:date.available":["2026-01-20T19:47:49Z"],"dc:date.issued":["2025-09"],"dc:description.abstract":["The scattering matrix formalism provides a practical characterization of wave transport in linear, source-free systems by relating a set of operationally defined input and output spatial channels. The matrix is structured as a block operator, with diagonal blocks encoding same-side reflection matrices (RMs) and off-diagonal blocks encoding transmission matrices (TMs) in opposing propagation directions. Under Helmholtz reciprocity, symmetry relations are imposed: RMs are symmetric, and forward and reverse TMs are mathematical transposes of each other. These relations were employed as constraints to correct system-induced aberrations in measured scattering matrices of complex optical media via a matrix-based gradient descent procedure. Resulting phase corrections corresponded closely with classical aberration modes without heuristic parameterizations, suggesting that these modes naturally arise to restore reciprocity-induced symmetry. Vectorial TMs were measured for single- and double-pass propagation through step-index MMFs and scattering samples, with corrected phase terms showing agreement across sample types. Furthermore, matrix normality was introduced as a descriptor of stable modal transport. Normal matrices admit unitary diagonalization, reflecting orthogonal eigenchannels and spectrally coherent propagation. Near-normal behavior was observed in fiber TMs, while RMs of scattering slabs remained strongly non-normal, as quantified by a normalized Henrici departure. Sufficient conditions for normality were identified in terms of the system Green’s function and its bi-compression onto the measurement basis. A complementary dispersion experiment investigated two regimes: nearly-normal MMFs, where the Wigner–Smith time-delay operator was jointly diagonalizable and supported accurate first-order spectral models; and mechanically compressed fibers, where loss of normality produced noncommuting operators and collapse of model fidelity. These results suggest that normality captures well-behaved modal transport, underpinning the validity of parametric models and other operator-based analyses of disordered media. Together, reciprocity and normality impose complementary constraints on wave transport: reciprocity governs global symmetry, while normality captures internal coherence of modal propagation. Relevance is noted for matrix-based imaging, inverse scattering theory, and non-Hermitian wave physics, where symmetry and modal stability remain central."],"dc:description.degree":["S.M."],"dc:identifier.uri":["https://hdl.handle.net/1721.1/164598"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["In Copyright - Educational Use Permitted","Copyright retained by author(s)"],"dc:rights.uri":["https://rightsstatements.org/page/InC-EDU/1.0/"],"dc:title":["Reciprocity and Normality in the Scattering Matrix of Disordered Media"],"dc:type":["Thesis"],"thesis:degree_name":["Master","Master of Science in Electrical Engineering and Computer Science"]},"updated_at":"2026-07-22T22:21:59Z"}