# Model of point source for layered metamaterials

**By:**K.V. Pravdin, I. Yi. Popov

### Main Information

### Abstract

The multilayer system including negative index material (NIM) layers is examined. We deal with the NIM system composed of arbitrary finite number of parallel alternated layers filled with isotropic homogeneous NIM and vacuum. The Maxwell's equations for the point source are considered. The NIM layer has the electric permittivity and magnetic permeability, which are equal to -1 for the certain frequency (NIM frequency). We set the goal of obtaining expressions for the electric Green's function. The Laplace and Fourier transforms are used. The differential equations for the scalar s- and p- polarization parts of the electric Green's function are obtained. The solutions of the differential equations are obtained in the travelling wave form with unknown coefficients. With the standard boundary conditions for every layer, the recurrence relations for the coefficients are obtained. The solution is obtained by the generating function method. The expressions for the scalar s- and p- polarization and vector part of the electric Green's function are derived. Under some assumptions, we observe the reflection absence (for the main term of the solution asymptotics near the NIM frequency). The obtained results can be used in simulation or engineering of real objects, such as superlens systems and multilayer NIM coverings.

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