In this study, Finite Difference Time Domain (FDTD) is employed to model and simulate both dielectric materials and metamaterials. Interestingly, the metamaterials own very peculiar characteristics that are related to the simultaneous negative permittivity and permeability. Based on FDTD technique, we can simulate the electromagnetic devices with the inclusion of the simultaneous electric and magnetic fields over time. The striking features of metamaterials illustrate the increase and backward propagation as well as the energy absorption in one-dimensional (1D) or two-dimensional (2D) systems. These systems could have potential applications, such as metamaterial superlens.