Numerical comparison of spectral properties of volume-integral-equation formulations

We study and compare spectral properties of various volume-integral-equation formulations. The equations are written for the electric flux, current, field, and potentials, and discretized with basis functions spanning the appropriate function spaces. Each formulation leads to eigenvalue distributions of different kind due to the effects of discretization procedure, namely, the choice of basis and testing functions. The discrete spectrum of the potential formulation reproduces the theoretically predicted spectrum almost exactly while the spectra of other formulations deviate from the ideal one. It is shown that the potential formulation has the spectral properties desired from the preconditioning perspective. (C) 2016 Elsevier Ltd. All rights reserved.Peer reviewe

On the Spectrum and Preconditioning of Electromagnetic Volume Integral Equations

Spectral properties of current-based volume integral equation of electromagnetic scattering are investigated in the case of isotropic and bi-isotropic objects. Using Helmholtz decomposition the spectrum is derived separately for the solenoidal, irrotational, and harmonic subspaces. Based on this analysis, preconditioning strategies of the matrix equation are discussed.Peer reviewe

Discretization of Electric Current Volume Integral Equation With Piecewise Linear Basis Functions

Peer reviewe

Positive and negative extinction of active particles

Using analytical Lorenz--Mie scattering formalism and numerical methods, we analyze the response of active particles to electromagnetic waves. The particles are composed of homogeneous, non-magnetic, and dielectrically isotropic medium. Spherical scatterers and sharp and rounded cubes are treated. The absorption cross-section of active particles is negative, thus showing gain in their electromagnetic response. Since the scattering cross-section is always positive, their extinction can be either positive, negative, or zero. We construct a five-class categorization of active and passive dielectric particles. We point out the enhanced backscattering phenomenon that active scatterers display, and also discuss extinction paradox and optical theorem. Finally, using COMSOL Multiphysics and an in-house Method-of-Moments code, the effects of the non-sphericity of active scatterers on their electromagnetic response are illustrated.Comment: preprint, 17 pages, 19 figure

Resonances in small scatterers with impedance boundary

With analytical (generalized Mie scattering) and numerical (integral-equation-based) considerations we show the existence of strong resonances in the scattering response of small spheres with lossless impedance boundary. With increasing size, these multipolar resonances are damped and shifted with respect to the magnitude of the surface impedance. The electric-type resonances are inductive and magnetic ones capacitive. Interestingly, these subwavelength resonances resemble plasmonic resonances in small negative-permittivity scatterers and dielectric resonances in small high-permittivity scatterers. The fundamental dipolar mode is also analyzed from the point of view of surface currents and the effect of the change of the shape into a non-spherical geometry

Realization of a spherical boundary by a layer of wave-guiding medium

In this paper the concept of wave-guiding medium, previously introduced for planar structures, is defined for the spherically symmetric case. It is shown that a quarter-wavelength layer of such a medium serves as a transformer of boundary conditions between two spherical interfaces. As an application, the D'B'-boundary condition, requiring vanishing of normal derivatives of the normal components of D and B field vectors, is realized by transforming the DB-boundary conditions. To test the theory, scattering from a spherical DB object covered by a layer of wave-guiding material is compared to the corresponding scattering from an ideal D'B' sphere, for varying medium parameters of the layer

On the applicability of discrete dipole approximation for plasmonic particles

It has been recognized that the commonly used discrete dipole approximation (DDA) for calculating the optical properties of plasmonic materials may exhibit slow convergence for a certain region of the complex refractive index. In this work we investigate the quantitative accuracy of DDA for particles of different shapes, with silver as the plasmonic material. As expected, the accuracy and convergence of the method as a function of the number of dipoles is relatively good for solid spheres and rounded cubes whose size is of the same order as the wavelength of the localized surface plasmon resonance in silver. However, we find that for solid particles much smaller than the resonance wavelength, and for silver-silica core-shell particles in particular, DDA does not converge to the correct limit even for 10(6) dipoles. We also find that the slow convergence tends to be accompanied by strong, discretization dependent oscillations in the particle's internal electric field. We demonstrate that the main factor behind the slow convergence of the DDA is due to inaccuracies in the plasmonic resonances of the dipoles at the surface of the particles. (C) 2015 Elsevier Ltd. All rights reserved.Peer reviewe