Extraction of material parameters in 1-D fractal metamaterial

Abstract

In this paper, we develop a transfer matrix-based homogenization approach applicable to self-similar fractal structures. With this method, we derive the material parameters of a layered metamaterial comprising two different dielectrics with permittivities equal to ε1 and ε2, respectively, in which the layers are distributed based on a fractal set. The band dispersion diagram and effective permittivity obtained analytically are verified with numerical simulations.

Keywords

• Metamaterials
• Fractals
• Material parameters