The main focus of this dissertation is the development offull-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 (λ0 ~ 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.