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oai:dspace.mit.edu:1721.1/1645982026-01-21T04:07:46Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023

Villiger, Martin Bharadwaj, Shreyas K. Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science 2026-01-20T19:47:49Z 2026-01-20T19:47:49Z 2025-09 2025-09-15T14:39:31.439Z https://hdl.handle.net/1721.1/164598 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. S.M. Massachusetts Institute of Technology In Copyright - Educational Use Permitted Copyright retained by author(s) https://rightsstatements.org/page/InC-EDU/1.0/ Reciprocity and Normality in the Scattering Matrix of Disordered Media Thesis application/pdf Master Master of Science in Electrical Engineering and Computer Science Publication unknown unknown <Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="aefa74cc-1516-43d0-88f0-fafddce97417"> <Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type> <Title>Reciprocity and Normality in the Scattering Matrix of Disordered Media</Title> <PublishedIn> <Publication> </Publication> </PublishedIn> <PublicationDate>2025-09</PublicationDate> <Authors> <Author> <DisplayName>Bharadwaj, Shreyas K.</DisplayName> <Affiliation> <OrgUnit> </OrgUnit> </Affiliation> </Author> </Authors> <Editors> </Editors> <Publishers> <Publisher> <DisplayName>Massachusetts Institute of Technology</DisplayName> <OrgUnit /> </Publisher> </Publishers> <License>https://rightsstatements.org/page/InC-EDU/1.0/</License> <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> <Access xmlns="http://purl.org/coar/access_right" > </Access> </Publication>