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We give a comprehensive presentation of methods for calculating the Casimir force to arbitrary accuracy, for any number of objects, arbitrary shapes, susceptibility functions, and separations. The technique is applicable to objects immersed…
In this paper we consider the inverse electromagnetic scattering for a cavity surrounded by an inhomogeneous medium in three dimensions. The measurements are scattered wave fields measured on some surface inside the cavity, where such…
The paper is concerned with the inverse scattering problem for Maxwell's equations in three dimensional anisotropic periodic media. We study a new imaging functional for fast and stable reconstruction of the shape of anisotropic periodic…
In this paper, we consider a sorting scheme for potentially spurious scattering resonant pairs in one- and two-dimensional electromagnetic problems and in three-dimensional acoustic problems. The novel sorting scheme is based on a…
The scattering of electromagnetic wave by a periodic array of nanowires is calculated by the boundary element method. The method is extended to the infinite grating near the interface between two dielectrics. A special Green function is…
Traditional boundary integral methods suffer from the singularity of Green's kernels. The paper develops, for a model problem of 2D scattering as an illustrative example, singularity-free boundary difference equations. Instead of converting…
In this paper we study the scattering problem for the initial value problem of the generalized Korteweg-de Vries (gKdV) equation. The purpose of this paper is to achieve two primary goals. Firstly, we show small data scattering for (gKdV)…
A generalization of the S-parameter retrieval method for finite three-dimensional inhomogeneous objects under arbitrary illumination and observation conditions is presented. The effective permittivity of such objects may be rigorously…
In this paper, we study time-harmonic electromagnetic scattering in two scenarios, where the anomalous scatterer is either a pair of electromagnetic sources or an inhomogeneous medium, both with compact supports. We are mainly concerned…
In this paper, we investigate on the direct and inverse scattering problem by an unbounded penetrable rough surface in a lossless medium. The cases that the transmission coefficient $\mu\neq1$ and $\mu=1$, which creates certain difficulties…
The polarization-sensitive propagation in the anisotropic metamaterial (AMM) with double-sheeted hyperboloid dispersion relation is investigated from a purely wave propagation point of view. We show that TE and TM polarized waves present…
We develop a framework for the multiple scattering of a polarized wave. We consider particles with spin propagating in a medium filled with scatterers. We write the amplitudes of each spin eigenstate in a local, mobile frame. One of the…
This paper presents a fast high-order method for the solution of two-dimensional problems of scattering by penetrable inhomogeneous media, with application to high-frequency configurations containing (possibly) discontinuous refractivities.…
The multiple scattering of scalar waves in diffusive media is investigated by means of the radiative transfer equation. This approach, which does not rely on the diffusion approximation, becomes asymptotically exact in the regime of most…
Using the traditional surface integral methods, the computation of scattering from a dielectric object requires two equivalent current densities on the boundary of the dielectric. In this paper, we present an approach that requires only a…
A new numerical method is introduced for calculating the polarizability of an arbitrary dielectric object with position dependent complex permittivity. Three separate numerical approaches are provided to calculate the dipole moment of a…
This paper introduces a boundary integral equation for time-harmonic electromagnetic scattering by composite dielectric objects. The formulation extends the classical M\"uller equation to composite structures through the global multi-trace…
The diffraction of electromagnetic waves at the surface periodic structures accompanied by strong anomalous effects in different diffraction orders is considered in great detail for high-contrast interfaces. We restrict our discussion to…
This paper studies time-dependent electromagnetic scattering from metamaterials that are described by dispersive material laws. We consider the numerical treatment of a scattering problem in which a dispersive material law, for a causal and…
We derive from first principles the expression for the angular/wavelength distribution of the intensity diffracted by a blazed reflective grating, according to a scalar theory of diffraction. We considered the most common case of a groove…