POINT SOURCE IN THE LAYERED MEDIUM WITH METAMATERIALS: METHOD OF RECURRENT RELATIONS

Konstantin V. Pravdin, Igor Yu. Popov

2014 , VOLUME 14, NUMBER 3 ( MAY-JUNE )

ISSN 2226-1494 (print), ISSN 2500-0373 (online)

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Nikiforov
Vladimir O.
D.Sc., Prof.

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POINT SOURCE IN THE LAYERED MEDIUM WITH METAMATERIALS: METHOD OF RECURRENT RELATIONS

K. V. Pravdin, I. Y. Popov

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Article in Russian

Abstract

Multilayer systems with metamaterials are studied. A system comprising parallel alternated layers filled with metamaterial and vacuum is considered. The problem of obtaining expressions for electric part of the Green’s function is raised for the NIM situation. A NIM situation is a case when electric and magnetic permeabilities are equal –1 for metamaterial and +1 for vacuum. The Maxwell’s equations for a point source of electromagnetic field are considered. A differential equation for electric p-polarized scalar part of the Green’s function for every layer is obtained with standard boundary conditions. Solution is obtained with the fundamental system of solutions with unknown coefficients. For the unknown coefficients the recurrence relations method is chosen as evident in usage and easy in analysis of obtained solutions. The solutions of the recurrence relations are obtained in general form by the method of generating functions. As a result the formulae for required Green’s function are obtained for every layer in the condition of NIM situation. s-polarized part is obtained in a similar way. It is easy to obtain a vector form of the electric Green’s function with its scalar form and the standard alternations. Obtained results can be used by simulations of superlens systems and multilayer covers with metamaterials.

Keywords: metamaterials, negative refractive index, NIM, Maxwell’s equations, recurrence relations, Green’s function

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