Circuit Model of Gain in Metamaterials

Metamaterials embody exciting prospects for a new generation of novel photonic devices. From their initial emergence as a physical construct in the GHz domain at the start of the 21st century [1–3], they have attracted a significant amount of global interest [4–13] with considerable effort being undertaken to extend their operation into the THz window and even optical regimes [14,15]. However, as they stand, early theoretical indications are that losses will cause potential problems for all possible frequencies and, in particular, kill any opportunity [16] for a useful metamaterial operating around and above 30THz. Such losses are inevitably closely linked to the resonant behaviour of the metaparticles and is addressed here by the placement of active diodes onto a form of metallic split-ring. The use of diodes to create a nonlinear magnetic response [16] and to create tunability [17] has already been discussed but active diodes [18] not only promise means of reducing losses but they can be deployed to produce an overall gain [19]. This behaviour is readily scalable from GHz to THz and even to nanowire [20] and nanoparticle-based metamaterials [21] operating in the optical frequency window. Nevertheless, it is highlighted here that instabilities could present a serious issue. From an investigation of the dispersion relation for a plane wave, a number of conditions are derived that identify the limits placed upon the system parameters, in order to ensure stable overall gain. Any examination of loss, or gain, must, however, be conducted from the perspective of the entire metamaterial, including the permittivity. Depending on the level of sophistication required in the fabrication technique, split-rings may be engineered with different shapes and deployed in a number of different arrays. The most popular have either a circular, or square shape. The term “split-ring” is treated here as a generic name and is not necessarily indicative of a specific shape.