  We present a theoretical analysis of the nonlinear response of a metamaterial
consisting of an array of split ring resonators coupled to a two level atomic
system (2LS) without inversion. We calculated the total complex susceptibility
and the linear, third and fifth-order nonlinear solution of the Maxwell Bloch
equations that describe the coupled system. We analyzed the impact of the
nonlinear effects on the dynamics of an active metamaterial/2LS compound in
dependence of the magnitude of the external electric field when the 2LS is
pumped by an external pump source and population inversion is achieved. We
observed that nonlinear damping in the active metamaterial/2LS compound
significantly reduces the effect of spiking. Finally, we investigated the
conditions under which the system can exhibit the phenomenon of optical
bistability. We observed that optical bistability can only be obtained when the
atomic volume density of the 2LS attains unphysically high values and thus is
not expected in the system under investigation.
