Poynting theorem constraints on the signs of the imaginary parts of the electromagnetic constitutive parameters.

In time harmonic analysis, media composed of sub-wavelength metallic or dielectric inclusions are described by complex and dispersive effective constitutive parameters. A study of such parameters based on the conservation law of energy and causality is presented. We derive a set of general constraints on the real and imaginary parts of the constitutive parameters for lossy and lossless media in terms of electric and magnetic loss tangents. It is shown that a passive medium can indeed have a negative imaginary part of either the permeability or permittivity over a range of frequencies. These findings are consistent with the principles of causality and energy conservation.