三維光子晶體的理論模擬

Theoretical Simulation of 3-D Photonic Crystal

陳航(Hang Chen)

指導教授 ： 陳郁文

國立中央大學/工學院/化學工程與材料工程學系/碩士(2006年)

摘要

在光子晶體的研究中，光子帶隙的位置和大小一直是關注的重點，多數研究
針對單一的晶體結構探討介電常數，晶格常數等對帶隙引起的變化，本研究則較
系統化的以長程有序(晶體結構)，短程有序(本地幾何形體)，物理性質(介電常數
比)三個觀點，探討如何作帶隙的優化。本研究定義一量:變異，作為最大化帶隙
時的準則: 降低此變異，則可得到較大的完全帶隙; 變異以不可約化布里淵區上
之高對稱性點作為數據來源，並以多重性加權計算得來; 本研究將反結構視為破
壞本地幾何形體之對稱性以獲得較大帶隙的光子晶體類型，並對反結構對帶隙的
影嚮加以討論; 介電常數比的提高使得帶隙變寬，但同時亦使得帶隙位置往較長
波長處移動，此一趨勢並不利於帶隙位置在可見光波長范圍的設定，因此需要一
個最適當的介電常數比，而非傳統認為的介電常比越高越好。
本研究模擬的工具是使用稱為MPB 的軟體，其計算方法是屬於平面波展開
法，另有其他分析工具如Perl, XCrySDen 等作為輔助之用，這些軟體均是自由軟
體。

關鍵字

晶格常數 ； 帶隙 ； 模擬 ； 光子晶體

並列摘要

Band gap structure is the most important information while studying
electromagnetic propagation in photonic crystals. A collection of free software is used
to set up an analysis tool system for simulation purpose. Because it is desired for
application and has been a technique challenged to fabricate a photonic crystal
possessing a complete photonic band gap operates at the optical wavelength regime,
we have studied a method to optimize the size and position of band gap from the
standpoint of long range order, short range order and material property. We have
shown in this thesis that, decreasing the variance of k points on the first Brillouin zone
by choosing an appropriate lattice type and adjusting the lattice parameters is required
to the formation of a larger complete photonic band gap, and for easy calculations we
defined the variance quantity when the coordinates of high symmetry points are
known; a local symmetry distorted along some specific directions always opens and
extends the gaps, and the effects of structure inversion are considered from this
viewpoint; dielectric contrast should have a optimum value to fulfill the requirements
of position and size of gap simultaneously rather than an as-high-as-possible value, to
prevent the wavelength shift of gap to a longer range.

並列關鍵字

lattice type ； simulation ； band gap ； band structure ； photonic crystal

參考文獻

Literature Cited

A. Kokalj, Comp. Mater. Sci. 28 (2003) 155

Code available from http://www.xcrysden.org/

Blanco, A., Chomski, E., Grabtchak, S., Ibisate, M., John, S., Leonard, S. W., Lopez, C., Meseguer, F., Migues, H., Mondia, J. P., Ozin, G. A., Toader, O., and Driel, H. M. V., “Large-Scale Synthesis of a Silicon Photonic Crystals with a Complete Three-Dimensional Band Gap Near 1.5 Micrometers”, Nature 405 (2000) 437.

Braun, P. V. and Wiltzius, P., “Microporous Materials: Electrochemically Grown Photonic Crystals”, Nature 402 (1999) 603.