# 臺灣博碩士論文加值系統

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 我們以Lewis–Riesenfeld不變量算符逆向操縱法，成功地利用電腦模擬生成的平面全息圖在多模波導上達成模態轉換，此結構有完美的模態轉換效率。我們設計多組模態轉換路徑並加以分析比較，大幅地改善了傳統使用受激拉曼絕熱通道法的模態轉換裝置長度。除此之外，亦可改變裝置出口端的模態數目，做為光學模態分離之用途。
 We use computer-generated planar holograms based on Lewis–Riesenfeld invariant-based inverse engineering to realize mode conversion in multimode waveguides, and this structure has excellent mode conversion properties. We not only mathematically design different convertible pathes but also numerically analyze them. They improve the device length of traditional stimulated Raman adiabatic passage remarkably. Moreover, they can also change the number of modes at the outlet of the device to split the optical mode.
 摘要..................................IABSTRACT..................................II致謝..................................III目錄..................................IV圖目錄..................................VI第一章 序論..................................1第二章 波導基本原理..................................22.1　光波導的基本方程式..................................22.2　有效折射率法..................................62.3　模態耦合理論..................................92.3.1　同向耦合..................................13第三章 量子系統的三能階總體轉移............................163.1　受激拉曼絕熱通道法..................................163.2　不變量算符逆向操縱法..................................213.3　波導光學和量子力學的相似性...............................30第四章 模擬結果與討論 334.1　受激拉曼絕熱通道法的模態轉換..................................344.2　不變量算符逆向操縱法的模態轉換..................................384.2.1　路徑A..................................384.2.2　路徑B..................................424.2.3　路徑C..................................454.2.4　頻寬分析..................................484.2.4.1　不同路徑..................................484.2.4.2　不同裝置長度..................................494.3　模態轉換最短長度比較..................................504.4　不變量算符逆向操縱法的模態分離.............................524.4.1　模態一分為二..................................534.4.1.1　路徑A..................................544.4.1.2　路徑B..................................574.4.1.3　路徑C..................................604.4.2　模態一分為三..................................634.4.2.1　路徑A..................................634.4.2.2　路徑B..................................664.4.2.3　路徑C..................................69第五章 結論..................................72參考文獻..................................73附錄..................................76附錄 A..................................76附錄 B..................................78附錄 C..................................80附錄 D..................................82
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