Dirichlet L-series with real and complex characters and their application to solving double sums

A description of the properties of \L with complex characters is given. By using these, together with the more familiar \L with real characters, it is shown how certain two dimensional lattice sums, which previously could not be put into closed form, may now be expressed in this way.Comment: 21 pages, 1 tabl

On the applicability of non-resonant artificial diamagnetics

Artificial diamagnetics are prominent for achieving extraordinarily strong diamagnetism in a wide frequency range. However, as far as the magnetic fields outside the artificial medium are concerned, bulk conductors show a very similar pattern. The question arises whether the complicated internal structure of artificial diamagnetics can, to this end, be replaced by a simpler object. We analyse the figure of merit for the application of diamagnetics in magnetic levitation, and show that for an electrically small body, any internal structuring makes the figure of merit worse than that of a simple conducting object.Comment: 5 pages, 5 figure

Vortex-type elastic structured media and dynamic shielding

The paper addresses a novel model of metamaterial structure. A system of spinners has been embedded into a two-dimensional periodic lattice system. The equations of motion of spinners are used to derive the expression for the chiral term in the equations describing the dynamics of the lattice. Dispersion of elastic waves is shown to possess innovative filtering and polarization properties induced by the vortextype nature of the structured media. The related homogenised effective behavior is obtained analytically and it has been implemented to build a shielding cloak around an obstacle. Analytical work is accompanied by numerical illustrations.Comment: 24 pages, 13 figure

Active cloaking of finite defects for flexural waves in elastic plates

We present a new method to create an active cloak for a rigid inclusion in a thin plate, and analyse flexural waves within such a plate governed by the Kirchhoff plate equation. We consider scattering of both a plane wave and a cylindrical wave by a single clamped inclusion of circular shape. In order to cloak the inclusion, we place control sources at small distances from the scatterer and choose their intensities to eliminate propagating orders of the scattered wave, thus reconstructing the respective incident wave. We then vary the number and position of the control sources to obtain the most effective configuration for cloaking the circular inclusion. Finally, we successfully cloak an arbitrarily shaped scatterer in a thin plate by deriving a semi-analytical, asymptotic algorithm.Comment: 19 pages, 14 figures, 1 tabl

Electromagnetic surface states in structured perfect-conductor surfaces

Surface-bound modes in metamaterials forged by drilling periodic hole arrays in perfect-conductor surfaces are investigated by means of both analytical techniques and rigorous numerical solution of Maxwell's equations. It is shown that these metamaterials cannot be described in general by local, frequency-dependent permittivities and permeabilities for small periods compared to the wavelength, except in certain limiting cases that are discussed in detail. New related metamaterials are shown to exhibit exciting optical properties that are elucidated in the light of our simple analytical approach.Comment: 5 figure