# 臺灣博碩士論文加值系統

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 近期，絕熱轉換的捷徑理論已開始被提出並研究。這種結構，可以有效縮短以受激拉曼絕熱轉換所設計的模態轉換器長度，而最短距離可縮短至4 mm，且此裝置對波長有很好的容忍度。除此之外，我們利用直接耦合的概念去計算折射變化率及耦合係數的關係，透過此關係，可以利用光柵的折射變化率來找到耦合理論上的耦合係數，進而利用耦合理論來預測模態轉換器的結果。
 Shortcut to adiabatic mode conversion in multimode waveguide is investigated. By using the shortcut scheme, the device length of adiabatic mode converter which is designed by stimulated Raman adiabatic passage is reduced. The shortest length of the device is 4 mm. Moreover, the device has a broad bandwidth. On the other hand, we use the condirecional coupler to calculate the relationship between the modulation of the refractive index and the coupling coefficient, so we can use the modulation of the refractive index on the gratings to find the coupling coefficient of coupled mode equation. Then we can use the result of coupled mode equation to predict the result of the mode converter.
 口試合格證書中文摘要………………………………………………………………………………………………………………………………………IAbstract…………………………………………………………………………………………………………………………………IIAcknowledgements…………………………………………………………………………………………………………IIIList of figures……………………………………………………………………………………………………………………………………VIChapter 1 Introduction………………………………………………………………………………………………11.1 Introduction……………………………………………………………………………………………………1Chapter 2 Theory of Multimode Waveguides………………………………………………32.1 Wave equation for electric field in optical waveguide …………………………………………………………………………………………………………………………………………………………32.2 Effective index method……………………………………………………………………………………72.3 Coupled Mode Theory ………………………………………………………………………………………112.4 Codirectional coupling condition………………………………………………………13Chapter 3 Analogies between Waveguide Optics and Quantum Theory………………………………………………………………………………………………………………………………………153.1 Schematic of the optical ridge waveguide used for simulation……………………………………………………………………………………………………………………………153.2 Equation for shortcut to adiabatic passage in quantum theory………………………………………………………………………………………………………………………………………173.2.1 Adiabatic passage in quantum theory…………………………………………173.2.2 General transitionless tracking algorithm…………………………183.3 Shortcut to adiabatic passage in two- and three-level atoms…………………………………………………………………………………………………………………………………………213.3.1 Rapid adiabatic passage…………………………………………………………………………213.3.2 Stimulated Raman adiabatic passage (STIRAP)……………………263.4 Similarity between the waveguide optics and quantum theory………………………………………………………………………………………………………………………………………313.4.1 Two modes converter……………………………………………………………………………………313.4.2 Three modes converter………………………………………………………………………………36Chapter4 Beam Propagation Method Simulation Results and Discussion……………………………………………………………………………………………………………………………404.1 The relationship between the coupling coefficient and the modulation of refractive index……………………………………………………………404.1.1 Equation for test the scheme……………………………………………………………404.1.2 Coupling coefficient of mode1 transferring to mode2 at the central wavelength 1.55 μm………………………………………………………………………414.1.3 Coupling coefficient of mode2 transferring to mode3 at the central wavelength 1.55 μm………………………………………………………………………444.1.4 Coupling coefficient of mode1 transferring to mode3 at the central wavelength 1.55 μm………………………………………………………………………464.2 Three modes converter………………………………………………………………………………………………………………………………494.2.1 Mode1 transfer to mode3 at the central wavelength 1.55 μm…………………………………………………………………………………………………………………………………………………494.2.2 Shortest converter length …………………………………………………………………564.2.3 Bandwidth analysis of the SHAPE scheme…………………………………57Chapter5 Conclusion……………………………………………………………………………………………………………………………60Reference………………………………………………………………………………………………………………………………62Appendix…………………………………………………………………………………………………………………………………64