雙折射薄膜索爾克濾波器研究

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姓名

黃泓彰(Hong-Chang Huang) 查詢紙本館藏

畢業系所

光電科學與工程學系

論文名稱

雙折射薄膜索爾克濾波器研究
(Birefringent Thin Film Šolc Filters)

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摘要(中)

光在介面傳遞時，會被分成穿透與反射兩個傳播方向，可根據界面兩側的折射率來計算這兩道光的強度。當光在多層膜的晶體結構傳遞時，這之中包含了無數介面，使其不斷地在結構穿透與反射。因此產生出無限多種光的傳遞路徑，而每一條路徑便是一種結果，將所有結果計算得出後總和，便是此多層結構的光學特性結果。
本研究透過矩陣理論(Matrix Theory)，來計算多層膜晶體的光學特性。首先由單層結構開始，根據它的折射率以及厚度兩項參數，列出波傳遞矩陣(Wave-transfer matrix)，將數個單層結構組合成多層膜結構。因為矩陣理論所具有的累乘性，將所有矩陣乘積後，便可得出多層膜結構的波傳遞矩陣。
透過上述方法，我們可計算出任何複雜結構的波傳遞矩陣，或是將不同的波傳遞矩陣組合起來，設計出寬頻抗反射膜、全向反射膜、寬頻濾波器等，具備特殊光學特性的結構。
本研究最終證實波傳遞矩陣，可應用於雙折射多層結構的光學計算上。並且設計出具有濾波和慢光效果的”玻璃夾層式索爾克結構”，該結構的群折射率和慢光程度，和總層數呈正相關。意味著不受限於材料，使用任意折射率的材料，皆可藉由結構設計來控制上述特性。

摘要(英)

When light is transmitted through the interface, it will be divided into two lights, “transmitted light” and “reflected light” respectively. The intensities of these two lights is based on the refractive index on the both sides of interface. When light is transmitted through the multilayer structure which contains countless interfaces. It makes continuously transmission and reflection in the structure. Ultimately, an infinite variety of light propagation paths are generated, and each path is one of a result. After summing all the results, the optical properties of the multilayer structure can be known.
In this study, the optical properties of the multilayer structure were calculated by Matrix Theory. First calculate the single-layer structure, and list the Wave-transfer matrix base on the refractive index and thickness of the structure. Combining several single-layer structures into multilayer structure. Because of the “multiplicative” property of the Matrix Theory, after multiplying all the single-layer matrices, the Wave-transfer matrix of the multilayer structure can be obtained.
According to the above method, the Wave-transfer matrix of any complex structure can be calculated. Combining different kind of Wave-transfer matrix to design the structure which has specific optical characteristics. Such as wideband anti-reflection film, omnidirectional reflector film, wideband filter, etc.
Finally, this research confirms that the Wave-transfer matrix can be applied to optical calculation of birefringent multilayer structure. Furthermore, the “Glass-lining folded Šolc filter” with filtering and slow light effects is designed. The positive correlation between group index, the extent of slow light and the total number of layers. It means that the above characteristics can controlled by structural design, without being limited by material.

關鍵字(中)

★ 光學偏振
★ 雙折射晶體
★ 薄膜光學
★ 波傳遞矩陣
★ 索爾克濾波器

關鍵字(英)

★ polarization
★ birefringent crystals
★ thin films
★ wave-transfer matrix
★ Šolc filter

論文目次

摘要 i
ABSTRACT ii
致謝 iv
目錄 v
第一章緒論 1
1.1 研究動機 1
1.2 研究方法 3
1.3 結論 5
第二章4x4矩陣法 6
2.1 2x2矩陣法 6
2.2 法布立-培若干涉儀 (Fabry-Pérot Interferometer) 10
2.3 4x4矩陣法 12
2.4 結論 22
第三章索爾克濾波器 23
3.1 Folded Šolc Filter 與 Fan Šolc Filter 23
3.2 玻璃夾層式索爾克結構 32
3.3 加入厚度漸增多層膜之Folded Šolc Filter 43
3.4 結論 47
第四章總結與未來展望 49
4.1 總結 49
4.2 未來展望 50
參考文獻 51

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指導教授

陳啟昌(Chii-Chang Chen)

審核日期

2022-9-16

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