High-order unified symplectic FDTD scheme for the metamaterials

A high-order unified symplectic finite-difference time-domain (US-FDTD) method, which is energy conserved, for modeling the metamaterials is proposed. The lossless Drude dispersive model is taken into account in US-FDTD scheme, and the detailed formulations of the proposed US-FDTD method are also provided. The high-order split perfectly matched layers (SPML) are used as the absorbing boundary conditions (ABCs) to terminate the computational domain. The analysis of Courant stability and numerical dispersion demonstrate that US-FDTD scheme is more efficient than the traditional time domain numerical methods. Focusing and refocusing of the electromagnetic wave in target detection is validated using the normal incident Gaussian beam with a matched slab. Oblique incidence results associated with the inverse Snell effect and the phase compensation effect of the composite slab further demonstrated the efficiency of the method. Numerical results for a more realistic structure are also included. All the results agree well with the theoretical prediction. The method proposed here can be directly put into using as a time-domain full-wave simulation tool for applications in metamaterials.