臺灣博碩士論文加值系統

為了使光在次波長的尺度下傳輸，矽混合電漿 (silicon hybrid plasmonic)結構由於其高電磁場侷限能力與較低之傳播損耗，已被視為可用於實現高密度光子積體線路 (integrated photonic circuit)整合的解決方案。本研究提出的兩個基於模態漸變(mode evolution)原理之嵌入式 (embedded)矽波導至混合電漿波導 (hybrid plasmonic waveguide)之極化模態轉換器都具有四段不同的金屬結構，且使用矽、二氧化矽與銀作材料並相容於絕緣層覆矽 (silicon on insulator)製程，可將介質波導中的準TE$_{00}$模態旋轉並耦合至混合電漿波導之HP$_{01}$基模 ，以連結矽光子 (Si photonics)與電漿 (plasmonic)線路。
設計原理是先將轉換器視為沿傳播方向的無數區域截面結構之組合，分析各截面之特徵模態後，以橫向磁場 (TM)極化分量之梯度變化描述模態之漸變過程，並同時以有效折射率 (effective index)實部描述傳播損耗，最後將兩者結合以快速取得次優化之設計以減少運用數值模擬進行參數掃描之需求。經有限元素法 (finite element method, FEM)與有限時域差分 (finite-different time-domain)法逐段進行最佳化後得到的兩個結構其元件面積分別為<7$\times$0.6 $\mu$m$^2$與<6$\times$0.43 $\mu$m$^2$。於工作波長1.55 $\mu$m下考慮模態匹配 (mode-matching)所得輸出端之模態轉換效率、極化轉換效率、極化消光比與插入損耗分別為87.58 % (90.09 %)、99.87 % (99.96 %)、27.9114 dB (34.3846 dB)與0.5899 dB (0.4592 dB)。此外，在輸出端之模態轉換效率>80 %、極化轉換效率>92 %與插入損耗<1 (dB)的條件下，帶寬分別為133 nm (176 nm)、182 nm (>200 nm)與139 nm (181 nm)。金屬之厚度與寬度容差在插入損耗<1 dB的條件下分別為80 nm與120 nm，在模態轉換效率>80 %的條件下分別為80 nm與>105 nm。各特性參數除了證明元件適用於光通訊C波段、製程要求度低與小型化，亦支持本研究對模態漸變之極化模態轉換器所提出的設計原理。

For realizing high-density photonic integrated circuits, subwavelenth waveguides are essential. Hybrid plasmonic waveguides (HPWs) have been regarded as a promising solution for its subwavelength field confinement capability and low loss characteristic compared to traditional plasmonic waveguides. In this research, two hybrid-plasmonic-mode-evolution-based polarization mode converters (PMCs) for rotating and coupling the photonic quasi-TE$_{00}$ mode in an embedded silicon waveguide to the HP$_{01}$ mode in a HPW have been presented. Both designs are silicon-on-insulator-compatible and consist of four-section asymmetric/symmetric top silver (Ag) structures.

The design principle is based on considering the whole PMC as a cascade of HPW slices, each of which having its eigenmodes along the propagation direction. The gradient ascent of the transverse magnetic polarization fraction and the minimum rate of change in the modal index (real part) of the eigenmode are used to rapidly obtain sub-optimum designs and are proved to effectively reduce heavy reliance on parameter sweeps using numerical computations. The former describes the mode evolution process, while the later deals with the propagation loss problem.

The footprints of the two numerically optimized PMCs are <6$\times$0.43 $\mu$m$^2$ and<7$\times$0.6 $\mu$m$^2$, respectively. The mode conversion efficiency (MCE), polarization conversion efficiency (PCE), polarization extinction ratio (PER), and the insertion loss (IL) of the first (second) PMC design are found to be 87.58 % (90.09 %), 99.87 % (99.96 %), 27.9114 dB (34.3846 dB), and 0.5899 dB (0.4592 dB), respectively, at the operating wavelength of 1550 nm. Under the conditions of MCE>80 %, PCE>92 % and IL>80 %, the corresponding spectral range of the first (second) design is 133 nm (176 nm), 182 nm (>200 nm) and 139 nm (181 nm), all covering the entire $C$ band of optical telecommunication. The fabrication tolerances of the top Ag structure and the silica spacer are also discussed. The PMCs presented here whose performance are rigorously evaluated are not only well-designed and ultracompact in size, but also support the novel design principle for mode-evolution-based PMCs presented in this work.

中文摘要....................................................................................................................... i
英文摘要...................................................................................................................... ii
目錄............................................................................................................................. iv
圖目錄 ........................................................................................................................ v
表目錄 ...................................................................................................................... xii
一、 緒論 .................................................................................................................. 1
1.1 背景 ……………………………………………………………………………………………………………….. 1
1.2 文獻探討 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.1 基於模態耦合原理之轉換器 . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . 4
1.2.2 基於模態漸變原理之轉換器 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.2.3 矽波導至混合電漿波導之轉換器 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.3 研究動機、流程與內容架構 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
二、 理論背景與分析方法..................................................................................... 20
2.1 在三維導波結構中傳播之模態的電磁場行為 . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2 表面電漿與混合電漿波導 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3 區域耦合模理論 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.4 元件特性分析方法 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.4.1 極化功率與模態功率 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.4.2 極化消光比與橫向電場極化分量 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.4.3 轉換效率 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.4.4 損耗 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.5 材料的選擇 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
三、 設計與分析 .................................................................................................... 37
3.1 輸入與輸出端結構尺寸 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.2 輸出端混合電漿波導表現 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.3 元件橫截面特徵模態分析 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.3.1 擾動金屬結構 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.3.2 模態漸變與TM極化分量 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.3.3 模態有效折射率與損耗 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.3.4 設計原理 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.4 初始結構的設計與表現 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.5 固定寬度金屬結構之設計 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
四、 結果與討論 .................................................................................................... 59
4.1 兩個最佳化方向 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.2 各段金屬長度最佳化 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.2.1 模型一 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.2.2 模型二 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.3 模型間比較與檢討 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.4 傳輸頻譜特性 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.5 容差分析 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.5.1 金屬寬度的容差 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.5.2 金屬高度的容差 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.5.3 二氧化矽薄膜高度的容差 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.6 研究結果分析與比較 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
五、 結論 ............................................................................................................... 95
參考文獻.................................................................................................................... 97

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