具手徵性之三維光子晶體特性分析與應用

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姓名

張學而(Xue-Er Zhang) 查詢紙本館藏

畢業系所

光電科學與工程學系

論文名稱

具手徵性之三維光子晶體特性分析與應用

相關論文

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★ 光子晶體異常折射之研究	★ 光子晶體傳導帶與介電質柱波導之研究
★ 平面波展開法在光子晶體之應用	★ 偏平面光子晶體能帶之研究
★ 通道選擇濾波器之探討	★ 廣義光子晶體元件之研究與分析
★ 新式光子晶體波導濾波器之研究	★ 廣義非均向性介質的光傳播研究
★ 光子晶體耦合濾波器之研究	★ 聲子晶體傳導帶與週期性彈性柱波導之研究
★ 對稱與非對稱波導光柵之特性研究	★ 雙曲透鏡之研究
★ 電磁波與聲波隱形斗篷之研究	★ 一維光子晶體等效非均向介值之研究

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摘要(中)

本論文主要討論三維介電質光子晶體，並希望藉由適當的形狀設計來得到具有手徵性質的光子晶體，以介電質取代金屬來克服一般手徵超材料的缺點。在本論文中設計了三種形狀的光子晶體柱並且以兩個方面討論它們的特性，第一個方面是以平面波展開法來計算光子晶體的頻帶結構，並且檢視本徵模態的場向量是否具有圓偏振的特徵來驗證光子晶體的手徵性。我們也發展了一套方法來對模態分類，最後我們取頻帶結構中的前兩個頻帶來計算出其等效手徵參數。

第二個方面我們將光子晶體做成有限厚度平板並以線偏振平面波正向入射，以RCWA (Rigorous Coupled-Wave Analysis)方法計算此平面波通過平板後的偏振態與原先偏振態的夾角以分析光子晶體作為偏振旋轉器的效果，並且我們也發現特定頻率的光會產生leaky guided resonance，這種共振會增強光子晶體的圓二色性進而使得在該頻率的偏振旋轉角度會特別大。

摘要(英)

This thesis concerns the effective chirality of some three-dimensional dielectric photonic crystals consisting of two-dimensional-periodically arranged twisted rods. Through properly choosing the dielectric rod’s shape in a 2D unit cell, we can obtain a photonic crystal with nonzero chirality, overcoming the disadvantage of absorption of the chiral metamaterial consisting of metallic elements.

In our work we design three different types of photonic crystal and discuss their properties in two aspects. The first is calculating their band structures using the plane wave expansion method and check if their field vectors have the feature of circular polarization to confirm their chirality. We also developed a way to classify these propagating modes, and extracted the effective chirality parameters for the first two bands in the band structure.

In another aspect, we consider a photonic crystal slab with finite thickness and being illuminated by a normally incident linearly polarized plane EM wave, and use the RCWA (Rigorous Coupled-Wave Analysis) method to calculate the field distribution. We then compare the polarization states of the outgoing wave with the incident wave and analyze the effectiveness of the photonic crystal slab as a polarization rotator. We also found that at certain frequencies there occur resonances called leaky guided resonances. Such resonances enhance the circular dichroism of the photonic crystal slab, result in large polarization rotation angles.

關鍵字(中)

★ 光子晶體
★ 手徵超材料
★ 嚴格耦合波分析法
★ 向量波平面波展開法

關鍵字(英)

★ Photonic Crystal
★ Chiral Metamaterial
★ Rigorous Coupled-Wave Analysis
★ Vector-Wave Plane Wave Expansion Method

論文目次

摘要 I
誌謝 III
目次 IV
圖目錄 VI
一、緒論 1
1-1 光子晶體與超材料 1
1-2 手徵超材料 2
1-3論文章節安排 2
二、手徵波導及光子晶體 4
2-1 電磁波的波方程式 5
2-1-1 手徵介質的本構關係 5
2-1-2 光學活性 6
2-2 電磁波在波導中的行為 9
2-2-1 波導的色散關係 10
2-3 手徵波導 13
2-3-1 手徵波導中的波方程式 13
2-3-2 手徵波導的色散關係推導 15
2-4 光子晶體 20
三、電磁波數值模擬方法 24
3-1　平面波展開法 24
3-1-1　向量波平面波展開法 24
3-1-2　倒晶格空間的取樣 27
3-2　嚴格耦合波分析法 27
3-2-1　馬克斯威爾方程 24
3-2-2　單層週期結構的色散關係 27
3-2-3　單層中總場的表示法 30
3-2-4　以散射矩陣匹配邊界條件 31
3-2-5　穿透率與反射率的計算 33
四、以數值方法分析介電質光子晶體的手徵特性 36
4-1　使用結構 36
4-2　光子晶體之特性分析 37
4-2-1　頻帶結構與模態分析 37
4-2-2　模態之分類 37
4-2-3　不同結構之手徵特性性比較 43
4-3　手徵性光子晶體應用為偏振旋轉器 46
4-3-1　偏振旋轉討論 48
五、結論與未來展望 57
5-1 結論 57
5-2 未來展望 57
參考文獻 59

參考文獻

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指導教授

欒丕綱(Pi-Guan Luan)

審核日期

2015-7-1

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