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This article addresses a number of issues associated with the problem ofcalculating contributions from the electromagnetic quantum induced energy andstress in a stationary material with an inhomogeneous polarizability. Afterbriefly reviewing the conventional approaches developed by Lifshitz el al andmore recent attempts by others, we emphasize the need to accommodate theeffects due to the classical constitutive properties of the material in anyexperimental attempt to detect such contributions. Attention is thenconcentrated on a particular system composed of an ENZ-type (epsilon-near-zero)meta-material, chosen to have an anisotropic and inhomogeneous permittivityconfined in an infinitely long perfectly conducting open waveguide. Thispermits us to deduce from the source-free Maxwell's equations a complete set ofharmonic electromagnetic evanescent eigen-modes and eigen-frequencies. Sincethese solutions prohibit the existence of asymptotic scattering states in theguide an alternative regularization scheme, based on the Euler-Maclaurinformula, enables us to prescribe precise criteria for the extraction of finitequantum expectation values from regularized mode sums together with errorbounds on these values. This scheme is used to derive analytic results forregularized energy densities in the guide. The criteria are exploited toconstruct a numerical scheme that is bench-marked by comparing its output withthe analytic results derived from the special properties of the inhomogeneousENZ medium.

Aspects of Quantum Energy and Stress in Inhomogeneous Unbounded Dielectric Continua