Related papers: A Breakthrough in Resonance Analysis for Complex M…
In this paper, we present a mathematical study of wave scattering by a hard elastic obstacle embedded in a soft elastic body in three dimensions. Our contributions are threefold. First, we characterize subwavelength resonances using the…
Multi-layered structures are widely used in the construction of metamaterial devices to realize various cutting-edge waveguide applications. This paper makes several contributions to the mathematical analysis of subwavelength resonances in…
Subwavelength resonance is a vital acoustic phenomenon in contrasting media. The narrow bandgap width of single-layer resonator has prompted the exploration of multi-layer metamaterials as an effective alternative, which consist of…
This work analyzes the scattering resonances of general acoustic media in a one-dimensional setting using the propagation matrix approach. Specifically, we characterize the resonant frequencies as the zeros of an explicit trigonometric…
The need of mathematically formulate relations between composite materials' properties and its resonance response is growing. This is due the fast technological advancement in micro-material manufacturing, present in chips for instance. In…
We propose a multiscale approach for a nonlinear Helmholtz problem with possible oscillations in the Kerr coefficient, the refractive index, and the diffusion coefficient. The method does not rely on structural assumptions on 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…
In this paper, we consider the resonance problem for the cubic nonlinear Helmholtz equation in the subwavelength regime. We derive a discrete model for approximating the subwavelength resonances of finite systems of high-contrast resonators…
We present a diagrammatic theory for coherent backscattering from disordered dilute media in the nonlinear regime. The approach is non-perturbative in the strength of the nonlinearity. We show that the coherent backscattering enhancement…
On an example of the open nonlinear electrodynamic system - transverse non-homogeneous, isotropic, nonmagnetic, linearly polarized, nonlinear (a Kerr-like dielectric nonlinearity) dielectric layer, the algorithms of solution of the…
We consider wave propagation across an infinite waveguide of an arbitrary bounded cross-section, whose interior is blocked by two identical thick barriers with holes. When the holes are small, the waves over a broad range of frequencies are…
An S matrix approach is developed to describe elastic scattering resonances of systems where the scattered particle is asymptotically confined and the scattering potential lacks continuous symmetry. Examples are conductance resonances in…
This paper employs layer potential techniques to investigate wave scattering in two-dimensional elastic media exhibiting high contrasts in both Lam\'{e} parameters and density. Our contributions are fourfold. First, we construct an…
The presence of resonances modifies the passage of light or of electrons through a disordered medium. We generalize random matrix theory to account for this effect. Using supersymmetry, we calculate analytically the mean density of states,…
We consider the multiple scattering of a scalar wave in a disordered medium with a weak nonlinearity of Kerr type. The perturbation theory, developed to calculate the temporal autocorrelation function of scattered wave, fails at short…
Motivated by applications to acoustic imaging, the present work establishes a framework to analyze scattering for the one-dimensional wave, Helmholtz, Schr\"odinger and Riccati equations that allows for coefficients which are more singular…
We develop a diagrammatic theory for transport of waves in disordered media with weak nonlinearity. We first represent the solution of the nonlinear wave equation as a nonlinear Born series. From this, we construct nonlinear ladder and…
We use dynamical mean field theory to find an exact solution for inelastic light scattering in strongly correlated materials such as those near a quantum-critical metal-insulator transition. We evaluate the results for $\textbf{q}=0$…
This paper investigates a novel quasi-Minnaert resonance phenomenon in acoustic wave propagation through high-contrast medium in both two and three dimensions, occurring in the sub-wavelength regime. These media are characterized by…
Superresolution, extraordinary transmission, total absorption, and localization of electromagnetic waves are currently attracting growing attention. These phenomena are related to different physical objects and are usually studied within…