本論文致力於研究絕緣層覆矽(silicon-on-insulator, SOI)多模分(多)工器之理論分析與數值模擬。本論文之多模分(多)工器，是以非對稱方向耦合器(asymmetrical directional coupler, ADC)為基底，並結合量子系統中之絕熱轉換捷徑理論(shortcuts to adiabaticity, STA)設計而成。首先，我們會介紹耦合波導系統之基本理論，並比較弱耦合波導系統與近共振電磁場下之二能階系統的光學相似性，藉此將量子系統中之絕熱轉換捷徑協定應用到耦合波導系統中。由於絕熱轉換捷徑協定的引入，進而設計了波導間的耦合係數及不匹配參數，使得元件更加穩定。接下來，我們著重於利用絕緣層覆矽材料以具體實現多模分(多)工器之設計，絕緣層覆矽材料所具有的高折射率對比特性，因此多模分(多)工器的長度可望更為縮減。模擬結果與理論預測相符合，並證明了該設計確實具有良好的頻寬特性以及製程容忍度。

This thesis is devoted to the theoretical investigation and numerical simulations of mode (de)multiplexers based on silicon-on-insulator (SOI). The mode (de)multiplexers in this thesis are based on asymmetrical directional couplers (ADCs) and designed using shortcuts to adiabaticity (STA). First, we will introduce the theory of coupled-waveguide system and the quantum‐optical analogies between weakly-coupled waveguide structure and two-level system driven by near-resonant laser light. By means of the analogies, the STA protocol is introduced into coupled-waveguide system. In this way, the coupling coefficient and propagation constants mismatch can be engineered to optimize the device robustness. Then, we emphasize the applicability of the STA protocol to the SOI material system, the high index contrast of SOI also allows devices to be more compact. The simulation results agree with the theoretical predictions, and show that the mode (de)multiplexers using STA are broadband and have large fabrication tolerance.

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