Full-wave modeling and analysis of dispersion-engineered materials and plasmon waveguides

The main focus of this dissertation is the development of full-wave modeling and the analysis of dispersion-engineered materials and plasmon waveguides. Among dispersion-engineered structures, we in particular focus on slow-wave photonic crystals (PhCs) where the dispersion curve ω(k) is approximated as a cubic polynomial, a quartic polynomial, or a linear combination of a quadratic polynomial and a quartic polynomial. We propose and investigate new compact plasmon waveguides operating at optical communication band (λ 0 ∼ 1550 nm).;Slow-wave PhCs may consist of periodic arrangements of complex media such as ferromagnetic materials and anisotropic dielectrics. The dispersion curve is tailored by the choice of geometries and materials for each unit cell. We develop finite-difference time-domain (FDTD) algorithms suitable for the analysis of slow-wave PhCs. This will be performed by decoupling the time-marching update equations into two steps, viz. one associated with Maxwell’s equations and the other associated with the constitutive relations. The complex-frequency-shifted (CFS)-perfectly matched layer (PML) is employed to minimize spurious reflections from the outer boundary of the computational domain. We further extend the complex-envelope (CE)-alternating-direction-implicit (ADI)-FDTD algorithm to anisotropic media, in order to lift the Courant stability limit with no loss of accuracy.;Plasmon structures are based on metallic nanostructures and they are of great interest due to their extraordinary properties such as subwavelength guiding and highly localized field phenomena. By harnessing the extraordinary optical properties of plasmon structures, we propose two types of compact plasmon waveguides operating at optical communication band. The first plasmon waveguide is based on an ordered array of gold nanorings. Electromagnetic fields are guided along this nanoparticle-based plasmon waveguide by near-field coupling between closely spaced nanoparticles. The second plasmon waveguide is based on a surface plasmon (SP)-coplanar waveguide (CPW). The SP-CPW yields compact mode confinement and moderate propagation loss. The analysis and design of these two types of plasmon waveguides will be performed using the 3-D CFS-PML-FDTD algorithm extended for the Drude dispersion model.;Further algorithm improvements are described. We propose an efficient time-domain modeling for plasmon structures in the visible spectrum, based on the extension of the ADI-FDTD algorithm to the multispecies Drude-Lorentz dispersion model. We also introduce a novel locally-one-dimensional (LOD)-FDTD algorithm based on an iterative fixed-point correction to reduce the splitting error. Lastly, we investigate numerical artifacts of the CE-ADI-FDTD algorithm and discuss the way to reduce these numerical artifacts.