Theory of supercoupling, squeezing wave energy, and field confinement in narrow channels and tight bends using ε near-zero metamaterials

In this work, we investigate the detailed theory of the supercoupling, anomalous tunneling effect, and field confinement originally identified by Silveirinha and Engheta [Phys. Rev. Lett. 97, 157403 (2006)], where we demonstrated the possibility of using materials with permittivity epsilon near zero to drastically improve the transmission of electromagnetic energy through a narrow irregular channel with very subwavelength transverse cross section. Here, we present additional physical insights, describe applications of the tunneling effect in relevant waveguide scenarios (e.g., the perfect or super waveguide coupling), and study the effect of metal losses in the metallic walls and the possibility of using near-zero epsilon materials to confine energy in a subwavelength cavity with gigantic field enhancement. In addition, we systematically study the propagation of electromagnetic waves through narrow channels filled with anisotropic near-zero epsilon materials. It is demonstrated that these materials may have interesting potentials, and that for some particular geometries, the reflectivity of the channel is independent of the specific dimensions or parameters of near-zero epsilon transition. We also describe several realistic metamaterial implementations of the studied problems, based on standard metallic waveguides, microstrip line configurations, and wire media.