Development of Finite-Difference Frequency-Domain Eigenmode Analysis Algorithms for Anisotropic Optical Waveguides/Photonic Crystals and Periodic Plasmonic Structures
Date Issued
2009
Date
2009
Author(s)
Chen, Ming-yun
Abstract
We propose full-vectorial finite-difference frequency-domain (FDFD) method basedtandard eigenvalue algorithms for analyzing anisotropic optical waveguides andhotonic crystals (PCs). Using the established full-vectorial waveguide mode solver,e can easily and efficiently calculate allowed guided modes on anisotropic opticalaveguides with an arbitrary permittivity tensor, such as lithium niobate and liq-id crystal (LC) optical waveguides. We also incorporate perfectly matched layersPMLs) for anisotropic media into our formulation as the absorbing boundary condi-ion at the outer boundaries of the computational domain so that leaky waveguidesan be treated.or band diagram analysis of 2-D PCs with isotropic or in-plane anisotropic ma-erials under the in-plane wave propagation for which the waves can be decouplednto transverse-electric (TE) and transverse-magnetic (TM) modes, we formulate thecalar FDFD method based eigenvalue algorithm. We then develop a full-vectorialDFD based eigenvalue algorithm to analyze band diagrams of 2-D PCs with ar-itrary 3-D anisotropy, in which the TE and TM modes are coupled. The bandiagram analysis algorithm is further generalized to investigate 3-D PCs with anrbitrary permittivity tensor. The band diagrams of 3-D simple cubic PCs or PClab structures with isotopic and anisotropic media are examined and investigated.n addition to the algorithms for anisotropic waveguide modes and PC bandiagrams, we derive a standard eigenvalue algorithm for analyzing 2-D and 3-Durface plasmonic waveguides with 1-D periodicity and involving real metals ignoringhe losses. We are able to efficiently obtain dispersion band characteristics anduided mode patterns for 2-D and 3-D periodic waveguides.
Subjects
finite-difference frequency-domain method
anisotropic materials
surface plasmonic waveguide
Type
thesis
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