Is Foster's Reactance Theorem Satisfied in Double-Negative and Single-Negative Media?

In this Letter, we address the issue of Foster's reactance theorem for the material media in which one or both of the material parameters ε and μ may possess negative real parts. We demonstrate that this theorem is indeed satisfied for a one-port termination filled with a lossless metamaterial with negative real permittivity and permeability, known as a "double-negative (DNG)" medium, or with a lossless metamaterial with either negative real permittivity or negative real permeability, which can be named as a "single-negative (SNG)" medium. However, in the case of DNG media when the reactive input impedance of such a termination is compared with that of its counterpart filled with a conventional lossless "double-positive (DPS)" material, it is found that the two reactances have opposite signs. Similar conclusions can be made for a termination filled with a lossless epsilon-negative (ENG) material when it is compared with that of its mu-negative (MNG) counterpart. Therefore, if a one-port termination filled with a lossless DPS or ENG material possesses inductive input reactance, when the same termination is filled instead with a lossless DNG or MNG material, its input reactance may be capacitive.