We investigate the electrodynamics of structures incorporating nanocomposites with negative dielectric permittivity and magnetic permeability, the popular 'left-handed metamaterials'. We obtain analytical solutions to the Helmholtz equation for gradient-index interfaces between the positive and negative index part. We derive expressions for the field intensity as well as for the transmission- and reflection-coefficients, assuming that the graded region across the interface is smaller than the operating wavelength. We then compare the analytical results with the numerical results obtained by the Transfer Matrix Method (TMM). The model allows for arbitrary frequency dependencies and lossy media.

Tensors, Relativity, and Cosmology, Second Edition, combines relativity, astrophysics, and cosmology in a single volume, providing a simplified introduction to each subject that is followed by detailed mathematical derivations. The book includes a section on general relativity that gives the case for a curved space-time, presents the mathematical background (tensor calculus, Riemannian geometry), discusses the Einstein equation and its solutions (including black holes and Penrose processes), and considers the energy-momentum tensor for various solutions. In addition, a section on relativistic astrophysics discusses stellar contraction and collapse, neutron stars and their equations of state, black holes, and accretion onto collapsed objects, with a final section on cosmology discussing cosmological models, observational tests, and scenarios for the early universe.

This paper presents the design and microfabrication of a two-dimensional metal-dielectric metamaterial structure based on an array of pillars with submicrometer diameters and heights. The diameters of pillars periodically vary along one axis in a sawtooth fashion and are constant along the other. The electromagnetic field distribution within this graded metamaterial was considered utilizing an accurate analytical approach. The pillar arrays were fabricated in photoresist and subsequently covered with a sputter-deposited aluminum film. Structures were defined by direct laser writing in photoresist film. Controlled overexposure has been applied in order to make pillar features smaller than the nominal resolution of the equipment. The structures were characterized by optical and atomic force microscopy and by angle-dependent Fourier Transform infrared spectroscopy. The produced graded frequency-selective surfaces may be used e.g. in sensing.

The transmission and reflection properties of lossy structures involving left-handed materials with graded permittivity and permeability have been investigated. We present an exact analytical solution to Helmholtz' equation for a lossy case with the graded real parts of permittivity and permeability profile changing according to a hyperbolic tangent function along the direction of propagation. The simple analytical solutions and graphical results for the field intensity along the graded structure are presented. The model straightforwardly allows for arbitrary temporal dispersion.