Electromagnetic field energy density in artificial microwave materials with strong dispersion and loss

An approach to define and calculate the stored reactive field energy density in passive linear artificial microwave materials is established. The introduced formulas for the energy density account for dispersion and absorption effects in such 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. Results of this Letter are necessary for understanding potential applications of metamaterials, recently suggested in the literature. This is crucial especially for applications in small antennas, because the stored field energy determines the antenna bandwidth.