Search
Results
-
Mathematical framework for multi-frequency identification of thin insulating and small conductive inhomogeneities
(2015)SAM Research ReportWe are aiming to identify the thin insulating inhomogeneities and small conductive inhomogeneities inside an electrically conducting medium by using multi-frequency electrical impedance tomography (mfEIT). The thin insulating inhomogeneities are considered in the form of tubular neighborhood of a curve and small conductive inhomogeneities are regarded as circular disks. Taking advantage of the frequency dependent behavior of insulating ...Report -
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 -
Phased and phaseless domain reconstruction in inverse scattering problem via scattering coefficients
(2015)Research ReportIn this work we shall review the (phased) inverse scattering problem and then pursue the phaseless reconstruction from far-field data with the help of the concept of scattering coefficients. We perform sensitivity, resolution and stability analysis of both phased and phaseless problems and compare the degree of ill-posedness of the phased and phaseless reconstructions. The phaseless reconstruction is highly nonlinear and much more severely ...Report -
Super-resolution in imaging high contrast targets from the perspective of scattering coefficients
(2015)SAM Research ReportIn this paper we consider the inverse scattering problem for high-contrast targets. We mathe- matically analyze the experimentally-observed phenomenon of super-resolution in imaging the target shape. This is the first time that a mathematical theory of super-resolution has been established in the context of imaging high contrast inclusions. We illustrate our main findings with a variety of numerical examples. Our analysis is based on the ...Report -
Mathematical analysis of plasmonic nanoparticles: the scalar case
(2015)SAM Research ReportLocalized surface plasmons are charge density oscillations confined to metallic nanoparticles. Excitation of localized surface plasmons by an electromagnetic field at an incident wavelength where resonance occurs results in a strong light scattering and an enhancement of the local electromagnetic fields. This paper is devoted to the mathematical modeling of plasmonic nanoparticles. Its aim is threefold: (i) to mathematically define the ...Report