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We discuss the propagation of electromagnetic waves on a rectangular lattice of polarizable point dipoles. For wavelengths long compared to the lattice spacing, we obtain the dispersion relation in terms of the lattice spacing and the…

Astrophysics · Physics 2007-05-23 D. Gutkowicz-Krusin , B. T. Draine

We consider the Sommerfeld problem of diffraction by an opaque half-plane with a real wavenumber interpreting it as the limiting case, as time tends to infinity, of the corresponding time-dependent diffraction problem. We prove that the…

Mathematical Physics · Physics 2019-08-06 A. Merzon , P. Zhevandrov , J. E. De la Paz Méndez , T. J. Villalba Vega

The scattering of wave packets from a single slit and a double slit with the Schr\"odinger equation, is studied numerically and theoretically. The phenomenon of diffraction of wave packets in space and time in the backward region,…

Quantum Physics · Physics 2008-11-26 G. Kälbermann

A 2D problem of acoustic wave scattering by a segment bearing impedance boundary conditions is considered. In the current paper (the first part of a series of two) some preliminary steps are made, namely, the diffraction problem is reduced…

Analysis of PDEs · Mathematics 2015-12-24 Andrey V. Shanin , Andrey I. Korolkov

When a plane electromagnetic wave impinges upon a diffraction grating or other periodic structures, reflected and transmitted waves propagate away from the structure in different radiation channels. A diffraction anomaly occurs when the…

Computational Physics · Physics 2022-10-05 Zitao Mai , Ya Yan Lu

Linear and nonlinear mechanisms for conical wave propagation in two-dimensional lattices are explored in the realm of phononic crystals. As a prototypical example, a statically compressed granular lattice of spherical particles arranged in…

Pattern Formation and Solitons · Physics 2016-02-17 C. Chong , P. G. Kevrekidis , M. J. Ablowitz , Yi-Ping Ma

Diffraction tomography is a noninvasive technique that estimates the refractive indices of unknown objects and involves an inverse-scattering problem governed by the wave equation. Recent works have shown the benefit of nonlinear models of…

Image and Video Processing · Electrical Eng. & Systems 2021-07-09 Tao Hong , Thanh-an Pham , Eran Treister , Michael Unser

The behavior of a 2-D model of an extended hemielliptic silicon lens of a size typical for THz applications is accurately studied for the case of a plane E-wave illumination. The full-wave analysis of the scattering problem is based on the…

Traditionally, the diffraction of a scalar wave satisfying Helmholtz equation through an aperture on an otherwise black screen can be solved approximately by Kirchhoff's integral over the aperture. Rubinowicz, on the other hand, was able to…

Classical Physics · Physics 2011-12-16 Yi-Chuan Lu

In this paper, we use a straightforward numerical method to solve scattering models in one-dimensional lattices based on a tight-binding band structure. We do this by using the wave packet approach to scattering, which presents a more…

Physics Education · Physics 2022-07-06 M. Staelens , F. Marsiglio

We derive and establish a solution concept for the linear mountain wave problem in two dimensions. After linearizing the governing equations and a change of variables, the problem can be stated as a Dirichlet boundary value problem for a…

Analysis of PDEs · Mathematics 2026-03-24 Adrian Constantin , Jörg Weber

The utility of lattice discretization technique is demonstrated for solving nonrelativistic quantum scattering problems and specially for the treatment of ultraviolet divergences in these problems with some potentials singular at the origin…

High Energy Physics - Theory · Physics 2008-11-26 Sadhan K. Adhikari , T. Frederico , R. M. Marinho

We consider scalar lattice differential equations posed on square lattices in two space dimensions. Under certain natural conditions we show that wave-like solutions exist when obstacles (characterized by "holes") are present in the…

Dynamical Systems · Mathematics 2013-10-21 A. Hoffman , H. J. Hupkes , E. Van Vleck

We address the direct scattering problem for a penetrable obstacle in an infinite elastic two--dimensional Kirchhoff--Love plate. Under the assumption that the plate's thickness is small relative to the wavelength of the incident wave, the…

Analysis of PDEs · Mathematics 2026-02-20 Rafael Ceja Ayala , Isaac Harris , Tonatiuh Sánchez-Vizuet

Wave motion in two- and three-dimensional periodic lattices of beam members supporting longitudinal and flexural waves is considered. An analytic method for solving the Bloch wave spectrum is developed, characterized by a generalized…

Materials Science · Physics 2017-03-13 A. A. Kutsenko , A. J. Nagy , X. Su , A. L. Shuvalov , A. N. Norris

The Half-Space Matching (HSM) method has recently been developed as a new method for the solution of 2D scattering problems with complex backgrounds, providing an alternative to Perfectly Matched Layers (PML) or other artificial boundary…

Numerical Analysis · Mathematics 2022-03-15 Anne-Sophie Bonnet-Ben Dhia , Simon N. Chandler-Wilde , Sonia Fliss

This paper is divided in two parts. In the first part, the inverse spectral problem for tight-binding hamiltonians is studied. This problem is shown to have an infinite number of solutions for properly chosen energies. The space of such…

Quantum Physics · Physics 2016-03-30 E. Rivera-Mociños , E. Sadurní

In this paper, we investigate a class of semilinear wave equations in non-cylindrical time-dependent domains, subject to exterior homogeneous Dirichlet conditions. Under mild regularity and monotonicity assumptions on the evolving spatial…

Analysis of PDEs · Mathematics 2026-01-28 Mauro Bonafini , Van Phu Cuong Le , Riccardo Molinarolo

Wave fields obeying the 2D Helmholtz equation on branched surfaces (Sommerfeld surfaces) are studied. Such surfaces appear naturally as a result of applying the reflection method to diffraction problems with straight scatterers bearing…

Mathematical Physics · Physics 2021-02-09 Raphael C. Assier , Andrey V. Shanin

We investigate inverse diffraction problems for penetrable gratings in a piecewise constant medium. In the TE polarization case, it is proved that a binary grating profile together with the refractive index beneath it can be uniquely…

Analysis of PDEs · Mathematics 2021-11-24 Jianli Xiang , Guanghui Hu