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|Title: ||Propagation and scattering of lightwaves in cylindrical and spherical periodic structures|
|Other Titles: ||Guang zai zhu zhuang he qiu zhuang zhou qi jie gou zhong de chuan bo ji san she|
|Authors: ||Xie, Huan (谢环)|
|Department: ||Department of Mathematics|
|Degree: ||Doctor of Philosophy|
|Issue Date: ||2010|
|Publisher: ||City University of Hong Kong|
|Subjects: ||Light -- Scattering.|
|Notes: ||CityU Call Number: QC427.4 .X53 2010|
iv, 83 leaves : ill. 30 cm.
Thesis (Ph.D.)--City University of Hong Kong, 2010.
Includes bibliographical references (leaves -83)
|Abstract: ||In the last two decades, photonic crystals (PhCs) have attracted much attention because
of their amazing ability to manipulate and control light. Typical PhCs are periodic
structures with unit cells containing circular cylinders, spheres or other simple geometries.
To understand the basic physical properties of a PhC and to design PhC devices
for various applications, efficient numerical methods are needed. Mathematically, we
encounter eigenvalue problems and boundary value problems.
Recently, various two-dimensional PhC structures with cylindrical inclusions have
been analyzed using efficient numerical methods that rely on cylindrical wave expansions
and the Dirichlet-to-Neumann (DtN) or Neumann-to-Dirichlet (NtD) maps
of the unit cells. So far, the DtN or NtD map method has only been developed for
PhCs composed of isotropic materials. In this thesis, we extend the DtN map method
to anisotropic PhCs, based on cylindrical wave expansions for circular cylinders of
anisotropic media. For three-dimensional PhC structures with spherical inclusions,
there exists a few accurate numerical methods based on spherical wave expansions. In
this thesis, we present an improved spherical wave least squares method for calculating
transmission and reflection spectra of periodic arrays of spheres. The electromagnetic
fields inside and outside the periodic arrays are approximated by vector spherical
waves and plane waves, respectively, and they are matched at the interfaces in the least
squares sense. Finally, we extend the spherical wave least squares method to infinite
and periodic linear chains of dielectric spheres and calculate travelling electromagnetic
waves around the chains.
Keywords: Photonic crystals, Anisotropic media, Dirichlet-to-Neumann map, Least
squares method, Spherical scatterer.|
|Online Catalog Link: ||http://lib.cityu.edu.hk/record=b3947535|
|Appears in Collections:||MA - Doctor of Philosophy |
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