Modeling and Theory of Nonlinear or Gyrotropic Negative Phase Velocity Metamaterials

Negative phase velocity metamaterials are engineered media that are currently enjoying a surge of interest due to their interesting properties and potential applications, such as cloaking to make things invisible. The literature is alive with papers devoted to the design of suitable metamaterials and there is a particular desire to create photonic applications that will operate at THz frequencies and above. At one level, the modeling of curious artificial molecules is straightforward. Nevertheless, the approximations involved need to be able to inspire confidence for optical frequency operation. Nonlinear behaviour is intrinsic to the Holy Grail quest for power control but this topic is only just being explored. With the introduction of power come the possibility of competition with damping, gain and the creation of auto- or dissipative solitons. Functionality comes not only through power control, however, but also through other externally imposed influences such as gyromagnetic effects and external stresses. Some novel possibilities that embrace these will be presented and a new generalized theory of metamaterial behaviour, based upon a nonlinear Lorentz lemma will be outlined. The outcomes of extensive computations will be used, throughout, to illustrate all the concepts in a dramatic fashion