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We survey functional analytic methods for studying subwavelength resonator systems. In particular, rigorous discrete approximations of Helmholtz scattering problems are derived in an asymptotic subwavelength regime. This is achieved by…

Analysis of PDEs · Mathematics 2024-10-02 Habib Ammari , Bryn Davies , Erik Orvehed Hiltunen

We discuss the properties of the transmission function in the k-space for a generic multi-layered structure. In particular we analytically demonstrate that a transmission greater than one in the evanescent spectrum (amplification of the…

We present a rigorous spectral analysis of plasmonic resonances in the nonlocal regime of spatially dispersive media. We adopt the quasi-static approximation of the hydrodynamic Drude model, which provides an analytically tractable setting…

Analysis of PDEs · Mathematics 2026-04-21 Hyundae Lee , Matias Ruiz , Sanghyeon Yu

The document covers the fundamental algorithm of backward propagation from the point of view of reconstructing the wavefield captured by a "screen" in an imaging system. Owing to a property of the Helmholtz equation, wavefields have an…

Image and Video Processing · Electrical Eng. & Systems 2020-04-20 Anurag Pallaprolu

In this paper, we develop a mathematical framework for generating strong customized field concentration locally around the inhomogeneous medium inclusion via surface transmission resonance. The purpose of this paper is twofold. Firstly, we…

Numerical Analysis · Mathematics 2024-09-24 Yueguang Hu , Hongyu Liu , Xianchao Wang , Deyue Zhang

Optical embedded eigenstates are localized modes of an open structure that are compatible to radiation yet they have infinite lifetime and diverging quality factors. Their realization in nanostructures finite in all dimensions is inherently…

Optics · Physics 2018-06-13 Alex Krasnok , Andrea Alu

Recent works dealt with the optical transmission on arrays of subwavelength holes perforated in a thick metallic film. We have performed simulations which quantitatively agree with experimental results and which unambiguously evidence that…

Materials Science · Physics 2007-05-23 P. Lalanne , J. C. Rodier , J. P. Hugonin

The experimental demonstration and characterization is made of the plasmon-mediated resonant transmission through an embedded undulated continuous thin metal film under normal incidence. 1D undulations are shown to enable a spatially…

Localized 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…

Analysis of PDEs · Mathematics 2015-06-03 Habib Ammari , Pierre Millien , Matias Ruiz , Hai Zhang

We consider several intriguingly connected topics in the theory of wave propagation: geometrical characterizations of radiationless sources, non-radiating incident waves, interior transmission eigenfunctions, and their applications to…

Analysis of PDEs · Mathematics 2021-03-23 Emilia Blåsten , Hongyu Liu

We consider the quasi-static problem governing the localized surface plasmon modes and permittivity eigenvalues $\epsilon$ of smooth, arbitrarily shaped, axisymmetric inclusions. We develop an asymptotic theory for the dense part of the…

Optics · Physics 2018-10-17 Ory Schnitzer

We predict and study theoretically a new nonlinear electromagnetic phenomenon in a sample of layered superconductor of finite length placed in a waveguide with ideal walls. Two geometries are considered here: when the superconducting layers…

Superconductivity · Physics 2015-06-15 T. N. Rokhmanova , S. S. Apostolov , Z. A. Maizelis , V. A. Yampol'skii , Franco Nori

This paper is concerned with the inverse scattering and the transmission eigenvalues for anisotropic periodic layers. For the inverse scattering problem, we study the Factorization method for shape reconstruction of the periodic layers from…

Analysis of PDEs · Mathematics 2020-01-10 Isaac Harris , Dinh-Liem Nguyen , Jonathan Sands , Trung Truong

The present paper deals with the wave propagation in a particular two dimensional structure, obtained from a localized perturbation of a reference periodic medium. This reference medium is a ladder like domain, namely a thin periodic…

Analysis of PDEs · Mathematics 2017-09-20 Bérangère Delourme , Sonia Fliss , Patrick Joly , Elizaveta Vasilevskaya

Metasurfaces, with intrinsically planar nature and subwavelength thickness, provide us unconventional methodologies to not only mold the flow of propagating waves but also manipulate near-field waves. Plasmonic metasurfaces with topological…

We 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.…

Analysis of PDEs · Mathematics 2020-09-09 Habib Ammari , Yat Tin Chow , Hongyu Liu

In this work, we present a new solution representation for the Helmholtz transmission problem in a bounded domain in $\mathbb{R}^2$ with a thin and periodic layer of finite length. The layer may consists of a periodic pertubation of the…

Analysis of PDEs · Mathematics 2017-06-23 Adrien Semin , Bérangère Delourme , Kersten Schmidt

We theoretically demonstrated and experimentally verified high-order radial spoof localized surface plasmon resonances supported by textured metal particles. Through an effective medium theory and exact numerical simulations, we show the…

Plasmonic sensing in the infrared region employs the direct interaction of the vibrational fingerprints of molecules with the plasmonic resonances, creating surface-enhanced sensing platforms that are superior than the traditional…

The ability to engineer localized surface plasmon resonances at large scale usually relies on precise nanoscale patterning. Here, we demonstrate that mid-infrared plasmonic responses can instead emerge in unpatterned polysilicon films…