Study on the gain media using FDTD and four energy level model

In order to investigate the gain media which were widely used in metamaterial, a four energy level model is proposed. We solve three groups of coupled equations: Maxwell equations, rate equations of electronic population and polarization equation. Population inversion and lasing threshlod were observed using numerical experiments based on a novel finite-difference time-domain (FDTD) treatment of the optical field. These results show good agreement with lasing theories and our numerical model can be used as an efficient tool for pursuing novel laser devices.