  In this work, we investigate the detailed theory of the supercoupling,
anomalous tunneling effect, and field confinement originally identified in [M.
Silveirinha, N. Engheta, Phys. Rev. Lett. 97, 157403, (2006)], where we
demonstrated the possibility of using materials with permittivity 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 new applications of the
tunneling effect in relevant waveguide scenarios (e.g., the "perfect" or
"super" waveguide coupling), study the effect of metal losses in the metallic
walls, and the possibility of using epsilon-near zero 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 epsilon-near zero 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 epsilon-near zero transition. We also
describe several realistic metamaterial implementations of the studied
problems, based on standard metallic waveguides, microstrip line
configurations, and wire media.
