Loss compensation by gain and spasing

We present a theory of the effective dielectric response of metamaterials containing gain. We demonstrate analytically that the conditions of spaser generation and the full loss compensation in a dense resonant plasmonic-gain metamaterial are identical. Consequently, attempting the full compensation or overcompensation of losses by gain will lead to an instability and a transition to a spaser state. This will limit (clamp) the inversion and eliminate the net gain. As a result, the full loss compensation (overcompensation) in such metamaterials is impossible. The criterion of the loss overcompensation, leading to the instability and spasing, is given in an analytical and a universal (independent from system geometry) form. Comparison with existing experiments is carried out.