Characterization of EM wave propagation in metamaterial environments

In this thesis, analytical and numerical solutions of the electromagnetic wave propagation in certain environments loaded with metamaterial (MTM) are presented. Finite Difference Time Domain (FDTD) algorithm is one of the most popular numerical techniques applicable to this problem area provided that it is augmented with Auxiliary Differential Equation (ADE) or Partial Linear Recursive Convolution (PLRC) methods to account for the dispersive characteristics of the MTM. To investigate the electromagnetic wave propagation in dispersive media Maxwell's curl and wave equation based FDTD algorithms are developed. FDTD update equations are obtained using ADE and also PLRC FDTD formulations for MTM medium described by Lorentz models. Numerical results obtained using the proposed FDTD algorithm are compared with the analytical results. FDTD algorithm based on the wave equation for double-negative (DNG) medium is also obtained using ADE approach, and its performance in terms of computational time and memory requirements is compared with the curl equation based formulations. Another issue discussed in this thesis is the novel formulation of Mur's ABC developed for truncating the DNG media for 1D and 2D problems using PLRC-FDTD algorithm. Efficient and simple FDTD update equations for first and second order Mur's absorbing boundary conditions (ABC) are obtained from frequency domain one-way wave equation using PLRC method and coefficient parameters are given for both Lorentz and Drude models. To demonstrate the validity and stability of the proposed Mur formulations, its absorption performance and computational advantages are compared with modified Uniaxial Perfectly Matched Layer (UPML). Finally, electromagnetic wave propagation is investigated in a rectangular waveguide partially loaded with DNG materials along a transverse or along the axial directions. Properties of eigen-solutions in waveguide environments partially loaded with Lorentz type DNG materials, modelled by lossless/lossy, identical/non-identical electric and magnetic parameters are investigated. The phase and group velocities are calculated and drawn for several problem scenarios. Modal cutoff phenomena associated with surface waves, transitions between evanescent/propagating, forward/backward waves and their dependence on frequency, filling factor and material parameters are also investigated. Novel conditions are given for existence of surface waves and for emergence of complex eigenvalues in the absence of losses. Analytic solutions of reflection and transmission coefficients are obtained for single mode supporting waveguide sections fully/partially loaded with DNG slabs in one transverse direction using Mode Matching Method. Floquet mode formalism is extended and applied to description of propagating fields in a waveguide loaded along the axial direction with air-DNG slabs in a quasiperiodic fashion. Eigenvalue and band-edge equations are obtained and representative solutions for dispersion and band edge diagrams are presented. Scattering characteristics and their dependence on the number of unit cells and the termination strategy used in the truncated structure are also investigated. Frequency dependence of reflection and transmission factors are calculated using frequency domain approach and compared with the results obtained from FDTD method.