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 $\ensuremath{\epsilon}$ 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 $\ensuremath{\epsilon}$ 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 $\ensuremath{\epsilon}$ 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 $\ensuremath{\epsilon}$ transition. We also describe several realistic metamaterial implementations of the studied problems, based on standard metallic waveguides, microstrip line configurations, and wire media.