Condition for minimum scattering antennas

The concept of a minimum-scattering antenna was introduced by Dicke more than 60 years ago, and Khan and Kurss redefined it. The theory of minimum-scattering antennas was considerably extended later. The minimum-scattering antenna is one which does not scatter electromagnetic fields when its feeding ports are terminated in a suitable set of reactances. Modeling an antenna as a minimum-scattering antenna simplifies antenna analysis. P. G. Rogers demonstrated that lossless antennas whose scattering behavior is dominated by a single characteristic mode can become minimum-scattering antennas (P. G. Rogers, IEEE Trans. Antennas Propag., vol. 34, no. 10, pp. 1223-1228, Oct. 1986). To the best of our knowledge, there is no literature that derives a condition where lossy antennas become minimum-scattering antennas. In this study, we investigate whether lossy antennas can become minimum-scattering antennas and determine a condition where antennas become minimum-scattering antennas.