| Summary: | 碩士 === 國立交通大學 === 電子物理系 === 90 === Materials with periodic dielectric structure have the property to suppress or allow the propagation of the electromagnetic waves in them for only some specific wavelengths. It means that light with specific wavelength can not subsist in such a material structure. Materials with this property is named as photonic crystal.
This study aims at the development of simulation technique to investigate the photonic crystal or photonic bandgap structure. We use MathCAD and C++ -Language in calculations.
We formulate the photonic crystal equations mainly with the Plane Wave Method Expansion Method. This method is efficient in investigating the behavior of transverse-electric modes and transverse—magnetic modes of electromagnetic waves in photonic crystal. However, for the analysis of 1-dimensional (1-D) photonic crystal where the material is lossy (σ≠0) and the dielectric distribution has finite periodicity, we adopt the Transfer Method for the reason that the Plane Wave Expansion Method is not appropriate in dealing with those problems. The solutions for the lossless material obtained by the Transfer Method agree basically with that of the Plane Wave Method Expansion Method. From the analysis for 1-D photonic crystal, we also propose the implementing structures of an optical filter which has a center wavelength 1500nm with a bandwidth of nearly 130nm. Taking Si and GaAs as base materials, according to the simulations, the proposed 1-D structure has period around 1μm in space. This filter possesses still wide frequency bandgap for an oblique incidence of light at angle within ±30°.
We also apply the Plane Wave Expansion Method to deal with the 2- dimensional (2-D) photonic crystal. Since at this stage of study no experimental work is conducted to verify our simulations, the numerical results of 1-D and 2-D simulations can only be compared with the published data found in the literature. The fair agreement of our results with that of the literature would suggest that the so far self-developed simulation technique is acceptable, although it needs surely further work of improvement.
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