Related papers: Resonances in axially symmetric dielectric objects

Electromagnetic interaction between a sub-wavelength particle (the `probe') and a material surface (the `sample') is studied theoretically. The interaction is shown to be governed by a series of resonances corresponding to surface polariton…

Resonance plays critical roles in the formation of many physical phenomena, and several methods have been developed for the exploration of resonance. In this work, we propose a new scheme for resonance by solving the Dirac equation in…

Resonances are omnipresent in physics and essential for the description of wave phenomena. We present an approach for computing eigenfrequency sensitivities of resonances. The theory is based on Riesz projections and the approach can be…

A theoretical model based on the transverse resonance method is proposed for the description of cylindrical multilayer dielectric resonator sensors. From this model, the resonant frequency and the sensitivities with respect to geometrical…

Optical resonators are widely used in modern photonics. Their spectral response and temporal dynamics are fundamentally driven by their natural resonances, the so-called quasinormal modes (QNMs), with complex frequencies. For optical…

On an example of the open nonlinear electrodynamic system - transverse non-homogeneous, isotropic, nonlinear (a Kerr-like dielectric nonlinearity) dielectric layer, the algorithms of solution of the diffraction problem of a plane wave on…

This paper concerns the random source problems for the time-harmonic acoustic and elastic wave equations in two and three dimensions. The goal is to determine the compactly supported external force from the radiated wave field measured in a…

We develop a high-order, explicit method for acoustic scattering in three space dimensions based on a combined-field time-domain integral equation. The spatial discretization, of Nystr\"om type, uses Gaussian quadrature on panels combined…

This paper concerns the inverse source scattering problems of recovering random sources for acoustic and elastic waves. The underlying sources are assumed to be random functions driven by an additive white noise. The inversion process aims…

Differential equations may possess coefficients that vary on a spectrum of scales. Because coefficients are typically multiplicative in real space, they turn into convolution operators in spectral space, mixing all wavenumbers. However, in…

We present a Fourier-based approach for high-dimensional function approximation. To this end, we analyze the truncated ANOVA (analysis of variance) decomposition and learn the anisotropic smoothness properties of the target function from…

A Dirichlet-type problem is studied for an equation of even order with variable coefficients. A criterion for the uniqueness of a solution is given. The solution is built in the form of a Fourier series. When justifying the convergence of…

The diffraction spectrum of coherent waves scattered from fractal supports is calculated exactly. The fractals considered are of the class generated iteratively by successive dilations and translations, and include generalizations of the…

This work establishes a rigorous mathematical framework for the analysis of nonlinear dielectric resonances in wave scattering by high-index resonators with Kerr-type nonlinearities. We consider both two- and three-dimensional settings and…

Maxwell equations describe the propagation of electromagnetic waves and are therefore fundamental to understanding many problems encountered in the study of antennas and electromagnetics. The aim of this paper is to propose and analyse an…

We study the seismic inverse problem for the recovery of subsurface properties in acoustic media. In order to reduce the ill-posedness of the problem, the heterogeneous wave speed parameter to be recovered is represented using a limited…

In this paper a treatment of hypersingular integral equations, which have relevant applications in many problems of wave dynamics, elasticity and fluid mechanics with mixed boundary conditions, is presented. The main goal of the present…

We improve upon an Omega result due to Soundararajan with respect to general trigonometric polynomials having positive Fourier coefficients. Instead of Dirichlet's approximation theorem we employ the resonance method and this leads to…

Atomic-resolution imaging with scanning transmission electron microscopy is a powerful tool for characterizing the nanoscale structure of materials, in particular features such as defects, local strains, and symmetry-breaking distortions.…

Deep cosmic microwave background polarization experiments allow a very precise internal reconstruction of the gravitational lensing signal in pricinple. For this aim, likelihood-based or Bayesian methods are typically necessary, where very…