Electromagnetic scattering by periodic arrays of particles

Abstract

Employing self-consistency, the multiple-scattering problem is formulated for periodic arrays of particles having constitutive parameters distinct from those of the embedding material. A T-matrix description of individual particle scattering is employed, so that particles need not be spherical. Explicit analytical and numerical results are obtained for the effective complex dielectric constant ε̄ and permeability μ̄ in the quasistatic and infinitesimal lattice limits for several lattice geometries, and shown to agree with existing static computations under appropriate conditions. Random arrays are also considered briefly, and the role of single-particle resonance effects is examined. Finally, longitudinal electric and magnetic waves are predicted to exist at certain discrete frequencies where ε̄ or μ̄ vanish.

Metamaterials and the Landau–Lifshitz permeability argument: Large permittivity begets high-frequency magnetism

“…3 is but the first step in a calculation of the optical constants (22). If local-field effects can be ignored, that is, if E Ϸ ᑟ and B Ϸ ᑜ, we get for optically isotropic particles ( ij ϭ ␦ ij and ij ϭ ␦ ij ) ϭ H (1 ϩ 4 N␣) and ϭ H (1 ϩ 4 N␥).…”

“…The particles are immersed in a host medium of permittivity (permeability) H ( H ). There is a vast literature describing the many approaches to calculate effective-medium electromagnetic parameters (22)(23)(24), and many of the existing theories are closely related to models developed in the late 1800s and early 1900s. We note in particular the expressions for the effective permittivity obtained by Maxwell-Garnett (25) and by Bruggeman (26) that, in turn, are closely related to the much older Lorentz-Lorenz formula for time-dependent and the Clausius-Mosotti equation for static fields (27).…”

“…In selfconsistent methods (22), the first step to compute bulk parameters is the calculation of the induced electric and magnetic multipoles. Note that, unless the filling factor, that is, the ratio between the volumes of the particle and the unit cell, is very small, higher-order multipoles matter even if ᐉ Ͻ Ͻ (22).…”

A negative-index metamaterial design based on metal-core, dielectric shell resonators

“…A metal core dielectric shell resonator with core radius ac and dielectric shell radius a. [4,5,6] which has no restrictions on the volume packing fraction p (as with the Clausius-Mossotti formulation) but does assume a quasistatic host region. Following an iterative matrix approach as given in [4] and enforcing continuity in r E r , E , and E at the two radial boundaries a c and a (Fig.…”

Tailoring Effective Media by Mie Resonances of Radially-Anisotropic Cylinders

“…However, the paper of Lewin [16] from 1947 is nowadays much better known. Since then, many others have followed this approach [17][18][19][20][21][22][23][24][25][26]. Using only isotropic dielectric spheres, the DNG condition is very difficult to achieve.…”