在這篇論文中，我們介紹了幾個模態耦合理論，包括耦合模態理論(CMT)，光束傳播法(BPM)，有限差分時域法(FDTD)等，應用它們模擬了兩平行光波導間模態耦合的現象，比較三個方法所得模擬結果之異同，從中了解三個方法的基本差異和優缺點之所在。我們發現雖然FDTD計算的資料量龐大，耗費時間長，對硬體規格需求高，但卻遠比BPM，CMT方便而且更為精確。藉以一極短脈衝的輸入光場，即可測得一分波多工器的全頻譜響應，由此可直接設計出分離任意波長的分波多工器。
因此我們應用FDTD來研究以光纖光柵為基礎之光塞取多工器(FBG assisted OADM)，利用光柵的反射特性和光波導的耦合特性使得三個不同的頻道可在各自的輸出埠得到理想的輸出特性。由這篇論文的研究，我們希望了解反射光柵作為一個OADM設計的可行性和設計概念。

In this thesis, the theories of Coupled-Mode Theory(CMT), Beam Propagation Method(BPM), Finite-Difference-Time-Domain Method(FDTD) are introduced, studied and compared. They are employed to simulate the mode-coupling phenomenon between two parallel waveguides. FDTD is more convenient and reliable compared to BPM and CMT, in spite of tremendous computation memory and CPU processing time inevitably involved in FDTD calculation. A full-frequency spectrum of the designed optical add-drop multiplexer(OADM) could be easily obtained using a single shot of an ultra-short optical pulse input followed by Fast Fourier transform on the time variation of EM wave. In this paper, a FBG-assisted add-drop multiplexer was 2-dimensionally designed and investigated using FDTD method. It was demonstrated that an OADM can be easily designed using FDTD to divide three arbitrary chosen wavelengths into three individual output waveguides.

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