二維光子晶體帶隙分析及其波傳特性研究

Abstract

本文第一部份之主要目的是探討二維光子晶體的能帶分佈情形。利用平面波展開法(Plane Wave method)，我們計算二維光子晶體圓柱正方排列的光子能帶結構，在TM mode中，隨著圓柱半徑的改變以及介電常數的不同，能帶的大小以及位置都會有所改變﹔而在TE mode中則沒有光子能帶的產生。另外在光子晶體中製造點缺陷，可以在缺陷中產生共振頻率，不同的缺陷大小及介電常數都會對共振的頻率及其模態有影響，利用時域有限差分法(Finite Difference Time- Domain method, FDTD)搭配PML吸收邊界條件，我們可以得到不同的共振頻率所對應的共振模態。而在光子晶體結構中製造線缺陷，我們可以得到一個具有單一傳播模態光子晶體光波導。從模擬結果得知，在頻隙內的光波能被侷限在缺陷製成的通道，如果是具有90度轉彎的光波導結構，光波能沿著通道行進，而能量不會有很大的損失。 第二部分則應用光子晶體設計一多頻道的分波多工系統以及方向耦合器。利用線缺陷製成的波導結構及具有頻率選擇效果的共振腔，我們可以得到一個具有濾波效用的分波多工系統。在本文中，我們將一脈衝波分波至四個不同的通道，通道的頻寬0.003 (ωa/2πc)。另外，藉由製造鄰近的兩條光子晶體光波導，我們可以得到一方向耦合器。經由適當的設計方向耦合器的耦合長度，我們可以控制特定頻率的光波，使得能量耦合到另一波導中。

The purposes of this thesis are two fold. First, the band structure of two-dimensional photonic crystals is investigated. By using plane-wave method, we calculate the band structure of two-dimensional photonic crystals in a square array with dielectric rods. The bandwidth and the central frequency of the photonic band gap can be controlled by changing the size and the dielectric constant of the inclusions for the TM mode, but no band gap occurs for the TE mode. We also investigate the properties of resonant modes which arise from introducing local defects in photonic crystals. The resonant frequencies and resonant modes can be controlled by changing the dielectric constant and the size of the defects. The field distributions of the resonant modes are determined by using a finite-difference time-domain method with perfectly matched layer absorbing boundary condition. By removing one row of rods, the photonic crystal waveguide with a single guided mode inside the gap can be created. The light wave at frequencies in the gap is confined inside the guide, and travels with low loss energy around 90∘bends. A multichannel wavelength division multiplexing system and a direct-ional coupler with two-dimensional photonic crystals are proposed in the second part of the thesis. The WDM filter can be created by consisting of a line defect waveguide and frequency selective microcavities. In our simulation, we show the ability to filter an incident pulse to four channels with bandwidth 0.003(ωa/2πc). And by constructing two nearby line defects, a directional coupler can be created. With properly designed coupling length, we can transfer the power from one waveguide to another.