邱奕鵬臺灣大學：光電工程學研究所葉文嵐Yeh, Wen-LanWen-LanYeh2007-11-252018-07-052007-11-252018-07-052006http://ntur.lib.ntu.edu.tw//handle/246246/50688在這篇論文，我們使用了平面波展開法模擬各種光子晶體波導結構的頻帶變化。 光子晶體波導中的電磁波群速跟色散變化曲線息息相關，改變波導結構將會改變導波頻寬跟導波的頻帶曲線，藉由不同的結構觀察電磁波群速變化。另外一方面在二維光子晶體的例子中，使用 tight-binding model 來近似 direct coupled resonant photonic crystal waveguide 的導波曲線，只要能求出 TB parameter，就能用簡單的公式來估計群速。 最後用平面波展開法模擬光子晶體平板波導的導波情形。In the thesis, a plane-wave expansion method for alculating the band structure of the photonic crystal is presented. As we known, photonic crystal structures provide a promising tool to control of the flow electromagnetic(EM) waves in the integrated optical devices. Therefore, there is a growing interest in developing photonic crystal-based waveguide components which can guide EM waves either along a line defect (a row of missing rods) or through coupled cavities. In the latter case, which we called coupled-cavity waveguides (CCW), the EM waves were tightly confined at each defect site, and photons can propagate by hopping, due to interactions between the neighboring evanescent cavity modes. It is observed that photon lifetime increases drastically and group velocity of photons tends towards zero at the waveguiding band edges of the periodic coupled cavities. In the photonic crystal CCW, low group velocity of light can result from localized modes in the defect. An analogy between Schrodinger's equation and Maxwell's equations allows us to use tight-binding (TB) approximation which was originally developed for electronic systems.目錄 1 導論5 1.1 光子晶體簡介. . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 光子晶體的基本原理. . . . . . . . . . . . . . . . . . . . . . 7 1.3 介紹Slow light . . . . . . . . . . . . . . . . . . . . . . . . 9 1.4 本論文的貢獻. . . . . . . . . . . . . . . . . . . . . . . . . 11 2 數值分析方法介紹14 2.1 平面波展開法理論. . . . . . . . . . . . . . . . . . . . . . . 14 2.2 利用平面波展開法的模擬實例. . . . . . . . . . . . . . . . . 18 2.3 任意週期的平面波展開法. . . . . . . . . . . . . . . . . . . 21 3 降低電磁波群速29 3.1 減低群速的原理(Slow light) . . . . . . . . . . . . . . . . . 29 3.2 Tight-BindingMethod . . . . . . . . . . . . . . . . . . . 31 3.3 共振腔耦合波導結構(Coupled cavity waveguide) . . . . . 34 4 三維的光子晶體 47 4.1 三維光子晶體的原理. . . . . . . . . . . . . . . . . . . . . 47 4.2 三維光子晶體的模擬. . . . . . . . . . . . . . . . . . . . . 49 5 結論60 參考文獻61en-US光子晶體慢光平面波展開法photonic crystalsband structureplane wave expansion methodtight-binding methodthesis