Metamaterials with gain and interpretation of transmission in pump-probe experiments*

We establish a new approach for pump-probe simulations of metallic metamaterials coupled to the gain materials. It is of vital importance to understand the mechanism of the coupling of metamaterials with the gain medium. Using a four-level gain system, we have studied light amplification of arrays of metallic split-ring resonators (SRRs) with a gain layer underneath. We find that that the differential transmittance $\Delta T/T$ can be negative for SRRs on the top of the gain substrate, which is not expected, and $\Delta T/T$ is positive for the gain substrate alone. These simulations agree with pump-probe experiments and can help to design new experiments to compensate the losses of metamaterials.We numerically investigate loss compensation and transmission in pump-probe experiments in resonant metamaterials with gain using an FDTD algorithm coupled to semiclassical rate equations. We explain experimentally observed negative differential transmission by gain-dependent impedance.