Is Foster's reactance theorem satisfied in double-negative and single-negative media?

In this paper, we address the issue of Foster's reactance theorem for the material media in which one or both of the material parameters epsilon and mu 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 called 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. (C) 2003 Wiley Periodicals, Inc.