臺灣博碩士論文加值系統

本論文探討新型結構之表面電漿波導布拉格光柵，將金屬與多層介電質組態取代傳統金屬與單層介電組態之電漿子波導，在高介電材料與金屬之間加入低折射率材料，可降低有效折射率之虛部，進而減少損耗。研究顯示增加低折射率材料區域之寬度可使有效折射率之實部、虛部下降；而增加高折射率材料區域寬度反而使有效折射率之實部上升、虛部下降。利用有限元素法為基礎之數值模擬設計布拉格波長為1310 nm 窄頻、1550 nm窄頻及1550 nm寬頻之波導布拉格光柵。1310 nm窄頻設計之布拉格光柵的禁帶半高全寬(full width at half maximum, FWHM)帶寬為15 nm，1550 nm窄頻及寬頻設計之布拉格光柵的禁帶半高全寬為2.9 nm及174 nm。操作波長在禁帶中，發現能量在布拉格光柵中形成渦流。操作波長在通帶中，布拉格光柵在矽與二氧化矽中能量會互相耦合交換。本論文亦分析製程誤差使布拉格光柵可能產生之傳輸特性變化。當波導結構週期長度或二氧化矽間隙寬度增加時，使布拉格波長紅移。相較於窄頻設計之布拉格光柵，寬頻設計之布拉格光柵，當其二氧化矽間隙寬度變化約±6 nm或當週期長度變化約±16 nm將使禁帶中某些波長之傳輸效率提升至10%；當變化幅度愈大，傳輸頻譜最後將分成兩個禁帶，因此寬頻設計之布拉格光柵所承受之製程容忍度遠小於窄頻設計。

A novel metal/multi-insulator/metal (MMIM) waveguide plasmonic Bragg grating is described in this thesis. The imaginary part of the mode index associated with an unperturbed MMIM waveguide can be decreased by inserting a low-index material in between the high-index core and metal region. It is shown that, as the width of the low-index region increases, the real and imaginary parts of the mode index decrease. On the other hand, as the width of the high- index region increases, the real part of the effective index increases but the imaginary part decreases. The design and analysis of the grating presented in this thesis are conducted using the finite-element-method-based numerical simulations. By optimizing the structure parameters, several design examples are obtained, including narrow-band/wide-band designs in the 1310-nm and 1550-nm communication windows. For the narrow-band cases, the full-width-at-half-maximum bandwidths are 15 nm and 2.9 nm for the 1310- and 1550-nm designs, respectively, while that of the 1550-nm wideband case is 174 nm. Time-average power vertexes are shown to occur in the stop band in particular for the narrow-band design examples. Moreover, power interchange exists between the silicon core and silica gap regions in the passband. The fabrication tolerance associated with the proposed Bragg grating is also studied. The Bragg wavelength exhibits a red shift if the period or silica gap width is larger than the designed value. For the wide-band design, fabrication errors in silica gap width of ±6 nm or in period of ±16 nm may raise the power transmission to about 10% in the stop band. An even larger error can finally cause the transmission spectrum to split into two stop bands. The fabrication tolerance associated with the wide-band design is found to be smaller than that in the narrow-band cases.

中文摘要 i
Abstract ii
誌謝 iii
目錄 iv
圖目錄 v
表目錄 ix
第一章 緒論 1
第二章 電漿波導布拉格光柵結構與材料之描述 5
2.1 結構描述 5
2.2 介電材料與金屬介面之色散關係 8
2.3 金屬的光學特性 10
2.3.1 杜德模型 10
2.3.2 真實金屬之光學性質 13
第三章 數值模擬方法概述 15
3.1 Comsol Multiphysics簡介 15
3.2 有限元素法 16
3.2.1 邊界值問題 16
3.2.2 里茨法 17
3.2.3 葛樂金法 18
3.2.4 有限元素法 19
3.3 連續性彎曲結構之步階近似 24
第四章 結果與討論 26
4.1 金屬與多層介電質組態波導之傳播特性 26
4.2 收斂性分析 32
4.3 表面電漿模態轉換器 35
4.4 電漿波導布拉格光柵之設計 37
4.4.1 金屬與多層介電質組態波導布拉格光柵之收斂性分析與設計
結果 37
4.4.2 線性漸窄結構之簡易最佳化設計 44
4.5 能量交換與製程容忍度之分析 48
4.5.1 能量交換分析 48
4.5.2 製程容忍度分析 57
第五章 結論 65
參考文獻 67

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