M.V. Davidovich – Dr.Sc.(Phys.-Math.), Professor, Department of Radiotechnique and Electrodynamics, Saratov State University named after N.G. Chernyshevsky
The metamaterials constituted of conducting rings included in the dielectric matrix and arranged randomly or periodically, forming a photon crystal in the latter case, are considered. Quasi-static models based on the law of electromagnetic induction and the parameters of the conducting ring are proposed, as well as electrodynamic models based on integral equations obtained using the method of periodic Green’s functions.
To obtain rigorous results it is necessary to solve the integral equation, obtain the dispersion equation, calculate the variance and the averaged fields and polarizations for given points on the isofrequency surface. The cases of dissipative structures and methods of cal-culation of dispersion and losses in this case are considered. The obtained models show that the magnetic response can be both di-amagnetic and paramagnetic, but in the non-resonant region, where a uniform magnetic permeability still makes sense, its value is close to one. The questions of the sense of magnetic permeability in the region of optical frequencies, where there are Bregg resonances of a photonic crystal and plasmon resonances in metal inclusions, about the possibility of obtaining isotropic artificial media with magnetic properties, including using only dielectric inclusions (metaatoms) are also considered.
It is shown that such induced magnetic permeability has limited physical meaning, and it can be omitted from introduction at all, having limited by the effective dielectric permeability tensor. It is also shown that in the resonance region in the case of an artificial medium made of rings, described by the effective magnetic permeability, negative values of the latter do not arise, and in the nonresonance region there is a weak diamagnetism or paramagnetism. In the description of the cubic photonic crystal of dielectric permittivity and magnetic permeability it is impossible to obtain a condition where both these quantities are negative. The question of negative magnetic permeability is usually associated with the possibility of propagation of backward waves in artificial media, if this also achieves negative dielectric permeability. The latter is quite simple to obtain in the area of plasmonics, where the dielectric permittivity of the metal is negative. However, in periodic artificial media, backward waves are possible regardless of which specific models of the medium are used and are determined only from the solution of the dispersion equation. In such environments there is a dissipation, and any input effective material parameters are complex. In addition, such media cannot be considered homogeneous and isotropic even in the case of a cubic photon crystal due to spatial dispersion. The results are obtained on the basis of homogenization carried out by averaging and using the Fresnel equation.
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