  This article addresses a number of issues associated with the problem of
calculating contributions from the electromagnetic quantum induced energy and
stress in a stationary material with an inhomogeneous polarizability. After
briefly reviewing the conventional approaches developed by Lifshitz el al and
more recent attempts by others, we emphasize the need to accommodate the
effects due to the classical constitutive properties of the material in any
experimental attempt to detect such contributions. Attention is then
concentrated on a particular system composed of an ENZ-type (epsilon-near-zero)
meta-material, chosen to have an anisotropic and inhomogeneous permittivity
confined in an infinitely long perfectly conducting open waveguide. This
permits us to deduce from the source-free Maxwell's equations a complete set of
harmonic electromagnetic evanescent eigen-modes and eigen-frequencies. Since
these solutions prohibit the existence of asymptotic scattering states in the
guide an alternative regularization scheme, based on the Euler-Maclaurin
formula, enables us to prescribe precise criteria for the extraction of finite
quantum expectation values from regularized mode sums together with error
bounds on these values. This scheme is used to derive analytic results for
regularized energy densities in the guide. The criteria are exploited to
construct a numerical scheme that is bench-marked by comparing its output with
the analytic results derived from the special properties of the inhomogeneous
ENZ medium.
