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URN etd-0728114-134124
Author Chin-Min Chang Chien
Author's Email Address No Public.
Statistics This thesis had been viewed 5356 times. Download 359 times.
Department Electro-Optical Engineering
Year 2013
Semester 2
Degree Master
Type of Document
Language zh-TW.Big5 Chinese
Title 2D Compact Frequency-Domain Stencils for Dielectric Media with an Interface
Date of Defense 2014-07-14
Page Count 64
Keyword
  • numerical method
  • Fourier Bessel series
  • finite-difference
  • local plane wave expansion
  • connected local fields
  • Helmholtz equation
  • dielectric interfaces
  • Abstract For opto-electromagnetic passive devices, our primary concerns are in their steady-state behaviors or narrow-band characteristics. We use mainly the frequency-domain methods, like frequency- domain finite-difference (FD-FD) methods for the Helmholtz equation. In recent years, we proposed the method of Connected Local Fields (CLF) to solve Helmholtz equation problems. CLF method is the semi-analytical numerical method like FD method but with a whole new approach.
    The concept of CLF method is to use analytic solutions of the Helmholtz equation for the local fields defined by a basic cell (defined inside the red perimeter) as illustrated in Figure 1 showing a basic cell with a horizontal dielectric interface.  The classical FD-FD methods in handling media with dielectric interfaces are not really ideal. In this thesis, we use the concept of CLF to study how to obtain CLF-equivalent compact stencils for cells with dielectric interfaces.
    This thesis is divided into two parts: First, we review methods in handling media with dielectric interfaces: To obtain a compact stencil the simplest method is the straight forward implementation of the interface condition (such as continuity of normal derivative) by finite-difference approximation of the. We could also apply “material averaging” method to modify the Helmholtz equation near a dielectric interface. In the second half of the thesis we will adopt the local plane wave expansion, (LPWE) approach to obtain CLF-worthy compact stencils. To derive compact stencils with dielectric interfaces, we use some linear combination of incident waves with their reflected and transmitted waves to expand the local fields near the interface. Finally we will also look into Fourier Bessel series (FBS) approach to construct these special compact CLF stencils.
    We shall also present numerical performance comparisons of above methods. It is based on numerically exact, semi-analytical solutions of incident-reflected-transmitted plane wave triplet.
    Advisory Committee
  • N. H. Sun - chair
  • Hidenori Taga - co-chair
  • Tzyy-Sheng Horng - co-chair
  • Hung-wen Chang - advisor
  • Files
  • etd-0728114-134124.pdf
  • Indicate in-campus at 2 year and off-campus access at 2 year.
    Date of Submission 2014-09-01

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