Single scattering and effective medium description of multilayer cylinder metamaterials: Application to graphene- and to metasurface-coated cylinders

Coated and multicoated cylinder systems constitute an appealing metamaterial category, as they allow a very rich and highly tunable response, resulting from the interplay of the many different geometrical and material parameters involved. Here we derive and propose an effective medium approach for the detailed description and analysis of the electromagnetic wave propagation in such systems. In particular, we investigate infinitely-long multilayered cylinders with additional electric and magnetic surface conductivities at each interface. Our effective medium approach is based on the well known in the solid state physics community coherent potential approximation (CPA) method, combined with a transfer matrix-based formulation for cylindrical waves. Employing this effective medium scheme, we investigate two realistic systems, one comprising of cylindrical tubes made of uniform tunable graphene sheets and one of cylinders/tubes formed of metasurfaces exhibiting both electric and magnetic sheet conductivities. Both systems show a rich palette of engineerable electromagnetic features, including tunable hyperbolic response, double negative response, and epsilon-near-zero and mu-near-zero response regions.