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Mathematical analysis of plasmonic resonances for nanoparticles: the full Maxwell equations
(2015)SAM Research ReportIn this paper we use the full Maxwell equations for light propagation in order to analyze plasmonic resonances for nanoparticles. We mathematically define the notion of plasmonic resonance and analyze its shift and broadening with respect to changes in size, shape, and arrangement of the nanoparticles, using the layer potential techniques associated with the full Maxwell equations. We present an effective medium theory for resonant plasmonic ...Report -
Subwavelength resonances of encapsulated bubbles
(2018)SAM Research ReportThe aim of this paper is to derive a formula for the subwavelength resonance frequency of an encapsulated bubble with arbitrary shape in two dimensions. Using Gohberg-Sigal theory, we derive an asymptotic formula for this resonance frequency, as a perturbation away from the resonance of the uncoated bubble, in terms of the thickness of the coating. The formula is numerically verified in the case of circular bubbles, where the resonance ...Report -
Subwavelength resonances in 1D high-contrast acoustic media
(2022)SAM Research ReportWe propose a mathematical theory of acoustic wave scattering in one-dimensional finite high-contrast media. The system considered is constituted of a finite alternance of high-contrast segments of arbitrary lengths and interdistances, called the ``resonators'', and a background medium. We prove the existence of subwavelength resonances, which are the counterparts of the well-known Minnaert resonances in 3D systems. Our main contribution ...Report -
Transmission properties of space-time modulated metamaterials
(2022)SAM Research ReportWe prove the possibility of achieving exponentially growing wave propagation in space-time modulated media and give an asymptotic analysis of the quasifrequencies in terms of the amplitude of the time modulation at the degenerate points of the folded band structure. Our analysis provides the first proof of existence of k-gaps in the band structures of space-time modulated systems of subwavelength resonators.Report -
Asymptotic Floquet theory for first order ODEs with finite Fourier series perturbation and its applications to Floquet metamaterials
(2021)SAM Research ReportOur aim in this paper is twofold. Firstly, we develop a new asymptotic theory for Floquet exponents. We consider a linear system of differential equations with a time-periodic coefficient matrix. Assuming that the coefficient matrix depends analytically on a small parameter, we derive a full asymptotic expansion of its Floquet exponents. Based on this, we prove that only the constant order Floquet exponents of multiplicity higher than one ...Report -
Super-resolution in recovering embedded electromagnetic sources in high contrast media
(2020)SAM Research ReportThe purpose of this work is to provide a rigorous mathematical analysis of the expected super-resolution phenomenon in the time-reversal imaging of electromagnetic (EM) radiating sources embedded in a high contrast medium. It is known that the resolution limit is essentially determined by the sharpness of the imaginary part of the EM Green's tensor for the associated background. We first establish the close connection between the resolution ...Report -
Mathematical modelling of plasmonic strain sensors
(2020)SAM Research ReportWe provide a mathematical analysis for a metasurface constructed of plasmonic nanoparticles mounted periodically on the surface of a microcapsule. We derive an effective transmission condition, which exhibits resonances depending on the inter-particle distance. When the microcapsule is deformed, the resonances are shifted. We fully characterise the dependence of these resonances on the deformation of the microcapsule, enabling the detection ...Report -
Localized sensitivity analysis at high-curvature boundary points of reconstructing inclusions in transmission problems
(2020)SAM Research ReportIn this paper, we are concerned with the recovery of the geometric shapes of inhomogeneous inclusions from the associated far field data in electrostatics and acoustic scattering. We present a local resolution analysis and show that the local shape around a boundary point with a high magnitude of mean curvature can be reconstructed more easily and stably. In proving this, we develop a novel mathematical scheme by analyzing the generalized ...Report -
Robust reconstruction of fluorescence molecular tomography with an optimized illumination pattern
(2019)SAM Research ReportFluorescence molecular tomography (FMT) is an emerging powerful tool for biomedical research and drug development. The reconstruction quality of the unknown fluorescence distribution is the focus of many FMT studies. There are two important factors that influence the quality of reconstruction most effectively. The first one is the regularization techniques used in the inverse model. Traditional methods such as Algebraic Reconstruction ...Report -
Perturbed Block Toeplitz matrices and the non-Hermitian skin effect in dimer systems of subwavelength resonators
(2023)SAM Research ReportThe aim of this paper is fourfold: (i) to obtain explicit formulas for the eigenpairs of perturbed tridiagonal block Toeplitz matrices; (ii) to make use of such formulas in order to provide a mathematical justification of the non-Hermitian skin effect in dimer systems by proving the condensation of the system's bulk eigenmodes at one of the edges of the system; (iii) to show the topological origin of the non-Hermitian skin effect for dimer ...Report