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Theoretical description and mathematical modeling of electromagnetic field focusings in metamaterials

Keywords:

A.S. Kryukovsky – Dr. Sc. (Phys.-Math.), Professor, Dean of the Faculty of Information Systems and Computer Technologies, Russian New University (Moscow). E-mail: kryukovsky@rambler.ru


Theoretical and numerical modeling of wave field focusings extending from a point source in a metamaterial is executed by the bi-characteristic method. The basic concepts of metamaterial physics are considered. Bifurcations of ray and caustic structures arising at change of parameters, describing propagation of electromagnetic radiation in a layer with a negative parameter of refraction are investigated. The cases of propagation of waves in a homogeneous metamaterial layer and propagation in a non-homogeneous layer are considered. The cases are investigated, when the module of permittivity varies linearly lengthways metamaterial and symmetrically decreases or grows under the parabolic law in a cross direction. It is shown, that arising caustic structures, correspond to wave catastrophes of cuspoid and umbilic series. The processes resulting in topological reorganization of ray and caustic structures are investigated that is a basis for the further study of focusings in metamaterials by methods of the wave catastrophe theory.
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