Finite Element Analysis of Dielectric and Plasmonic Periodic Structures
Date Issued
2009
Date
2009
Author(s)
Lee, Chi-Hong
Abstract
Periodic structures are successfully modeled by the implementations of periodic boundary conditions (PBCs) in the finite element method (FEM) for single and double periodicity. With a novel algorithm of PBCs, fast and precise calculations can be executed to investigate dispersion diagrams and modal characteristics ofoubly periodic structures composed of either frequency-dependent and frequency-independent material dielectric constants. Interesting and advantageous phenomena are discovered for the H-polarization situations for which surface plasmons are meantime excited. Starting from one-dimensional polaritonic and metallic photonic crystals, essential characters of dispersion relations are presented. Apparent dissimilarities between lossless and lossy photonic crystals are revealed and examined. In comparisonith analytical solutions, the correctness and behavior of numerical convergence can be accurately verified. Afterward we analyze the nano-plasmonic waveguides in the forms of circular and elliptical cylinders for guiding electromagnetic waves with plasmon resonances below the diffraction limit. Outstanding high-resolution dispersioniagrams of such subwavelength structures are performed by the real-ω FEM. The complex modes possessing complex Bloch-wave vectors are as well discovered in these systems and have been extensively discussed. The developed algorithm of PBCs for doubly periodic systems is then employedo analyze two-dimensional dielectric and metallic photonic crystals. Complete information about the propagating, complex, and evanescent modes are disclosed. Eminently high precision is shown in the calculations of dielectric photonic crystals. And excellent agreement between the Dirichlet-to-Neumann map and the multiple multipole method are shown for metallic photonic crystals. Furthermore, weemonstrate modal characteristics correlated with surface plasmons in detail.
Subjects
finite element
plasmonic
periodic structures
Type
thesis
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