Electromagnetic field energy density in artificial microwave materials with negative parameters

General relations for the stored reactive field energy density in passive linear artificial microwave materials are established. These relations account for dispersion and absorption effects in these materials, and they are valid also in the regions where the real parts of the material parameters are negative. These relations always give physically sound positive values for the energy density in passive metamaterials. The energy density and field solutions in active metamaterials with non-dispersive negative parameters are also considered. Basic physical limitations on the frequency dispersion of material parameters of artificial passive materials with negative real parts of the effective parameters are discussed. It is shown that field solutions in hypothetical materials with negative and non-dispersive parameters are unstable.