Mathematical models for metamaterials
We investigate layered systems. The layers are filled with negative index materials (NIMs) and positive index materials (PIMs). For realistic modeling we use a single Lorentz contribution for the permittivity and permeability. The aim of our work is constructing the Green’s function, i.e., obtaining the analytical formula described the electromagnetic (EM) field of the point source. This formula leads to obtaining the expression of the EM field of the source of any size and shape.
Figure 1: An example of the layered system. The layered system is composed of (n+m+1) parallel alternated layers. The layers alternate with each other. All even layers (as well as the zero layer) are Δ1 in width, and filled with a NIM (grey color). All odd layers are Δ2 in width, and filled with a vacuum (white color). The point source is located at the y coordinate of the x axis in the zero NIM layer.
The second aim of our work is studying the photonic band gap structure of the layered systems. The permittivity and permeability of the layered systems are periodic functions. Thus, these systems are considered as photonic crystals (PCs), where for certain frequencies the propagation of EM waves can be forbidden.
Figure 2: The photonic band gap structure of the one dimensional PC. The forbidden bands are white, and the permitted bands are grey. Dot lines divide the space on areas of the radiative and evanescent regimes.