三維光子晶體帶隙分析及波傳特性研究

Abstract

本文第一部分主要目的是探討三維三角排列平板光子晶體的能帶結構圖，我們利用平面波展開法(Plane Wave Expansion Method)來探討光子晶體在TE Mode和TE Mode的能帶關係，並嘗試藉由改變平板厚度、背景介電質係數、介電質圓柱半徑或空氣圓柱半徑大小來探討不同參數對於帶隙大小的影響跟其物理性質。

第二部分我們在平板光子晶體中製造出一線缺陷，則可以得到光子晶體光波導。我們先利用平面波展開法計算光波導之能帶結構圖，而由計算模擬結果我們可以得知在原本平板的帶隙範圍內，本來並沒有傳導模態的存在但因為線缺陷的關係，使得帶隙範圍內因而產生了傳導模態，此一結果和二維相同結構相同，證明了三維光波導一樣也能傳導光波。再來我們利用有限時域差分法(Finite Difference Time Domain)軟體來分析三維波導之頻譜分布圖及場形傳播圖，由計算結果可以得知光波在三維結構中和在二維結構中傳播最大的不同是在能量損失的差別，三維結構對光的侷限性不若二維結構來得好，但是光波在在三維結構中依然能順利導通。

The purposes of this thesis are two fold. First, the band structure of three-dimensional photonic crystal slab is investigated. By using plane wave expansion method, we calculate the band structure of the three-dimensional photonic crystal slab in a triangular array with the dielectric or air rods. Changing the thickness of the slab, the background material and the radius of the dielectric or air rods control the bandwidth at the central frequency of the photonic band gap.

Second, removing one row of rods can create a photonic crystal waveguide. The light wave at frequencies in the band gap can be confined inside the waveguide. We calculate the band structure of the photonic crystal waveguide by using the plane wave expansion method. We can find that removing the row of the rods can create the photonic crystal waveguide with guided modes inside the gap. Then, we use the finite difference time domain method to calculate the spectrum and field distribution of the waveguide. In our simulation, the results show that the energy loss in 3D waveguide is more than that in 2D waveguide.