計算分析高介電質材料光子晶體的最大完全帶隙特性及應用

Calculation of the high dielectric contrast photonic crystals with maximal full band gaps

王俊傑(Jyun-Jie Wang)

指導教授 ： 趙聖德

國立臺灣大學/工學院/應用力學研究所/碩士(2010年)

https://doi.org/10.6342/NTU.2010.03470

摘要

為了快速尋找最大完全帶隙，我們希望可以正確判斷尋找的方向。所以本論文主要使用平面波展開法的理論模擬方法來研究不同的介電質材料圓柱經過週期排列後而形成不同結構的二維光子晶體。對由低到極高的材料參數與幾何參數做進一步分析，探討其最大完全帶隙與各參數間的關係。我們將完全帶隙、TM模態與TE模態帶隙頻率對各可變參數做分析後，發現TM與TE帶隙邊緣頻率值相同時會有最大完全帶隙，亦即最佳結構會出現在TM與TE模態帶隙邊緣頻率相同的情況。且根據最大完全帶隙與TE、TM帶隙的關係，我們可發現完全帶隙是由TE模態來決定。
觀察由低到極高的材料參數以及幾何參數之頻帶圖，可發現幾何填充率與材料參數增加則帶隙邊緣頻率會有紅移現象，所有頻帶的紅藍移有一致性，且帶隙大小是取決於頻帶的紅藍移速度。而最大完全帶隙都落在高頻帶區域，且在高頻帶區的特性與之前研究低頻帶的帶隙特性有很大不同。另外，完全帶隙附近的頻帶隨著參數改變有很明顯的重光子現象，我們發現重光子現象在高介電質材料時會趨於飽和，而幾何結構造成的重光子現象則取決於完全帶隙的大小。

關鍵字

光子晶體 ； 高介電質 ； 完全帶隙 ； 米氏共振 ； 重光子態

並列摘要

In this paper, we employ a plane wave expansion method to calculate the band structures of two-dimensional photonic crystals. For the types of photonic crystal, we have studied square lattice, triangular lattice, honeycomb lattice of circular columns, each connected to its nearest neighbors by rectangular rods.
We explore the relation of the radius r/a and the dielectric constant ε of rods, the width d/a of connecting rods to determine full band gaps. The dispersion curves for the TM and TE modes of the propagating electromagnetic waves have been analyzed separately. We found some characteristics of full band gaps :
(1)When TM and TE mode band gaps have approaching the same band edges, maximum full band gaps occur.
(2) Unlike the fundamental band gap which usually opens larger in low-lying bands, we obtain the maximum full band gap to open with high-lying bands. When changing the parameter, the dispersion curves around the full band gap are dense and flat. Material and geometry parameters can affect heavy photon state, but material parameter affect more than geometry parameters. The band structure exhibits a red shift phenomenon in frequency as the geometrical fill factor and material parameter increase. The width of band gaps have depends on the velocity of frequency shift.
(4)For honeycomb lattice, we added the connecting rods and obtain the full band gaps which are smaller than the full band gaps of no connecting rods.
(5) Band gaps of TE mode is very much more variation than band gaps of TM mode.

並列關鍵字

Photonic crystals ； full band gap ； high dielectric ； Mie resonance,heavy photon state

參考文獻

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