Creating stable gain in active metamaterials

The question of losses in metamaterials that are based upon magnetic resonances deriving from split-ring arrays is addressed through the use of active inclusions designed from diode arrays. A full discussion of the way in which the current-voltage characteristics of the inclusions are deployed to produce gain is given, and the question of the overall stability of the new material is investigated in a quantitative way that is linked to absolute and convective instability. It is shown that instability associated with the inclusion of negative resistance devices can be avoided through a scheme that is approximately scalable from gigahertz to at least the low terahertz regimes. Furthermore, absolute instabilities that potentially complicate any active gain media can be controlled through a suitable choice of the system parameters. The latter step reduces the working frequency window over which spatial gain is available, leading to the need for compromise. Full numerical details are given with the conclusion that construction of such arrays of diode inclusions is possible and that a practical gain window is accessible.