色散光子晶體能隙之研究

王哲安(Jer-An Wang)

指導教授 ： 欒丕綱

國立中央大學/理學院/照明與顯示科技研究所/碩士(2014年)

摘要

本論文採用平面波展開法 (plane wave expansion) 模擬電磁波在色散性介質的光子晶體的能帶結構 (band structure) 圖，我們所採用的是Drude model形式的色散性介質電係數 (permittivity)。本研究主要探討電磁波在二維色散介質柱所組成之光子晶體的能帶結構圖。從能帶結構圖中可以發現全方位光子能隙 (full photonic band gap)，也就是在任何情況下特定電磁波頻率均無法進入此介質的頻段。我們藉由更改色散介質柱子的截面形狀、填充率的變化、柱子不同排列方式、柱子的旋轉角度與交換柱子內外的介質來觀察全方位光子能隙的變化，並作比較。

關鍵字

色散 ； 光子晶體

並列摘要

In this thesis we use plane wave expansion (PWE) method to compute the band structures of two dimensional dispersive photonic crystals (DPCs) consisting of periodically arranged cylinders whose permittivity has the Drude model type dispersion. My research is mainly about computing the full photonic band gap, that is, the frequency ranges that the incident light cannot penetrate through. We compare the computation results of different DPCs consisting of cylinders with different cross sections and different positioning, and study the influences to the full band gaps by changing the filling factor, altering the rotation angle of the cylinders, and exchanging the media inside and outside the cylinders.

參考文獻

[1] S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486 (1987).

[2] E. Yablonovitch, “Inhibited Spontaneous Emission in Solid-State Physics and Electronics,” Phys. Rev. Lett. 58, 2059 (1987).

[3] J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals—Molding the Flow of Light, Princeton University Press, 1995.

[5] C. Kittel, Introduction to Solid State Physics, 8th Ed., John Wiley & Sons, USA, 2005.

[6] S.Kushwaha and P. Halevi, ”Giant acoustic stop bands in two-dimensional periodic arrays of liquid cylinders”,Appl. Phys. Lett. 69,31 (1996).