Study On The Effective Model Of The Wire Medium By Using The Finite-difference Time-domain Method

As a type of basic and important metamaterial, the wire medium consisting of an arrayof parallel thin metallic wires has been widely used in many electromagnetic applications,such as the design of novel antennas and sub-wavelength imaging, and so on. Ahomogenization effective EM model with high accuracy and wide effective range is thetarget in the study of wire medium, because it helps us to have a deeper understanding ofthe physical phenomena in this metamaterial and thus guides us in designing in manyapplications.In this thesis, the half-wavelength canonical structure of the wire medium and itseffective models are studied by using the finite-difference time-domain method (FDTD).The major contents and contributions of the thesis are listed as follows：1. By using our in-house FDTD code incorporating the sub-cell technique of thin wire,the half-wavelength canonical structure of wire medium is simulated with high efficiencyand accuracy. The validity of conventional effective model based on the2th orderdispersion equation was examined numerically by the transmission coefficients of thephysical structure. The effectiveness of the effective model was studied in a quantitativemanner. The reason of the discrepancy in the scattering between the effective model and thephysical structure occurs was discussed.2. Based on the close-form of the dispersion equation in the canonical structure of thewire medium，a new effective model with the4th order dispersion equation was proposedin the framework of the homogenized uniaxial medium by using the transmissioncoefficients data. Compared with the FDTD results of the half-wavelength wire medium,the proposed model has demonstrated significant improvement in numerical accuracy incharacterizing the EM behavior for high transversal spatial harmonics in this type of wiremedium. It has also been validated that this proposed model is applicable for generalizedcases, i.e., for wave incidence with arbitrary incident direction and with various type ofwire media.3. In respect of algorithm, a resonance perfectly matched layer (RPML) was proposedfor truncating the physical structure of the wire medium with controllable reflections inFDTD modeling. Through setting up a resonant state similar to the internal domain ofperiodic structure, the convergence time of FDTD results and the computational domain can be significantly reduced by using the RPML. The optimization of RPML is alsodiscussed and the efficiency of the RPML is validating by a FDTD simulation of the2-Dimaging. Besides, some important details in the FDTD simulation of wire medium aregiven in the thesis. For example, the impact of grid resolution in FDTD, the reason of theinstability when PML and periodic boundary condition are combined in the FDTDsimulation, and the treating of the instability.