Figure 2: The parameters for the four-level system are chosen as C2/kg (C stands for Coulomb), which is the strength of the coupling between the gain material and the host NRM, s−1 is related to the linewidth of the gain medium, s−1 is the central pumping frequency, determined by the frequency difference between state 3 and state 2, at which is satisfied without the gain (see Figure 1(a)), and the decay time of the gain level 2 is s. The value of the occupation density is set to be m−3. The pumping rates are assumed to be s−1 for insufficient pumping, s−1 for the appropriate pumping (to be discussed below), and s−1 for the excessive pumping, respectively. (a) The real part of the refractive index for different pumping amplitudes. A red shift of the frequency is observed at . (b) The imaginary part of the refractive index for different pumping amplitudes. Loss-free windows (intervals of amplification) are revealed by the curves. Increasing the pumping rate may compensate the losses, or even turn the material into an active medium.