Search
Results
-
Wave interaction with subwavelength resonators
(2020)SAM Research ReportThe aim of this review is to cover recent developments in the mathematical analysis of subwavelength resonators. The use of sophisticated mathematics in the field of metamaterials is reported, which provides a mathematical framework for focusing, trapping, and guiding of waves at subwavelength scales. Throughout this review, the power of layer potential techniques combined with asymptotic analysis for solving challenging wave propagation ...Report -
High-order exceptional points and enhanced sensing in subwavelength resonator arrays
(2020)SAM Research ReportSystems exhibiting degeneracies known as exceptional points have remarkable properties with powerful applications, particularly in sensor design. These degeneracies are formed when eigenstates coincide, and the remarkable effects are exaggerated by increasing the order of the exceptional point (that is, the number of coinciding eigenstates). In this work, we use asymptotic techniques to study PT-symmetric arrays of many subwavelength ...Report -
Edge modes in active systems of subwavelength resonators
(2020)SAM Research ReportWave scattering structures with amplification and dissipation can be modelled by non-Hermitian systems, opening new ways to control waves at small length scales. In this work, we study the phenomenon of topologically protected edge states in acoustic systems with gain and loss. We demonstrate that localized edge modes appear in a periodic structure of subwavelength resonators with a defect in the gain/loss distribution, and explicitly ...Report -
A biomimetic basis for the perception of natural sounds
(2020)SAM Research ReportArrays of subwavelength resonators can mimic the biomechanical properties of the cochlea, at the same scale. We derive, from first principles, a modal time-domain expansion for the scattered pressure field due to such a structure and propose that these modes should form the basis of a signal processing architecture. We investigate the properties of such an approach and show that higher-order gammatone filters appear by cascading. Further, ...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 -
Quantum ergodicity and localization of plasmon resonances
(2020)SAM Research ReportWe are concerned with the geometric properties of the surface plasmon resonance (SPR). SPR is a non-radiative electromagnetic surface wave that propagates in a direction parallel to the negative permittivity/dielectric material interface. It is known that the SPR oscillation is topologically very sensitive to the material interface. However, we show that the SPR oscillation asympotically localizes at places with high magnitude of curvature ...Report -
Exceptional points in parity-time-symmetric subwavelength metamaterials
(2020)SAM Research ReportWhen sources of energy gain and loss are introduced to a wave scattering system, the underlying mathematical formulation will be non-Hermitian. This paves the way for the existence of exceptional points, whereby eigenmodes are linearly dependent. The main goal of this work is to study the existence and consequences of exceptional points in the setting of high-contrast subwavelength metamaterials. We begin by studying a system of two ...Report -
Quantitative estimates for stress concentration of the Stokes flow between adjacent circular cylinders
(2020)SAM Research ReportWhen two inclusions with high contrast material properties are located close to each other in a homogeneous medium, stress may become arbitrarily large in the narrow region between them. In this paper, we investigate such stress concentration in the two-dimensional Stokes flow when inclusions are the two-dimensional cross sections of circular cylinders of the same radii and the background velocity field is linear. We construct two ...Report -
Mathematical analysis of electromagnetic scattering by dielectric nanoparticles with high refractive indices
(2020)SAM Research ReportIn this work, we are concerned with the mathematical modeling of the electromagnetic (EM) scattering by arbitrarily shaped non-magnetic nanoparticles with high refractive indices. When illuminated by visible light, these particles can exhibit a very strong isotropic magnetic response, in addition to the electric resonance, resulting from the coupling of the incident wave with the circular displacement currents of the EM fields. We shall ...Report -
Modal expansion for plasmonic resonators in the time domain
(2020)SAM Research ReportWe study the electromagnetic field scattered by a metallic nanoparticle with dispersive material parameters placed in a homogeneous medium in a low frequency regime. We use asymptotic analysis and spectral theory to diagonalise a singular integral operator, which allows us to write the field inside and outside the particle in the form of a complete and orthogonal modal expansion. We find the eigenvalues of the volume operator to be ...Report