以有限差分時域法分析以微共振腔及光子晶體為基礎之光濾波器

In this thesis, the finite-difference time-domain (FDTD) method with the uniaxial perfectly matched layer boundaries is employed to model several types of channel drop filters in two dimensions. The signal switching mechanisms of different kinds of filters are expressed. Microcavity resonator based filters including micro-ring and micro-disk for both transverse electric (TE) and transverse magnetic (TM) modes are analyzed. Various ring-waveguide widths are considered and the two-stage ring filter is also studied. Photonic crystal based filters involving the monopole cavity and the doubly degenerate hexapole cavity are then investigated. We first analyze the photonic band gap materials using the plane wave expansion method. The electromagnetic wave behavior in photonic crystal is also discussed, including negative refraction, waveguide bending and splitters. The essential properties for the channel drop filters, such as resonant frequencies, linewidth, and quality factor, are determined by the FDTD simulation. In order to obtain reliable results of these quantities, the curved dielectric interfaces are treated by the index average scheme. With the index average scheme, the resonant frequencies given by the the FDTD simulation are stabilized. Since the properties of photonic devices obtained by the FDTD method with the index average scheme are different from those with the staircase approximation, several published photonic crystal based resonators are redesigned to achieve high performance for the channel drop filters.

並列關鍵字

Finite-Difference Time-Domain ； Channel Drop Filters

參考文獻

[1] Abarbanel, S., and D. Gottlieb, “A Mathematical Analysis of the PML

Method,” J. Comput. Phys., vol. 134, pp. 357–363, 1997.

331–340, 1998.

of the perfectly matched layer equations in computational electromagnetics,”

unpublished manuscript.

國際替代計量

以有限差分時域法分析以微共振腔及光子晶體為基礎之光濾波器

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