本論文致力於濾波器理論分析與數值模擬，而論文中的絕緣層覆矽(SOI)雙模濾波器為非對稱方向耦合器(asymmetrical directional coupler, ADC)，並以量子系統中的perturbation theory設計參數而成。論文首先介紹波導系統之基本理論，並討論近共振電磁場其二能階系統的光學相似性與波導系統的比較。
我們利用量子系統中的perturbation theory與window functions設計出符合濾波效果的參數，並利用三維光子結構計算軟體(FIMMWAVE)模擬出雙模濾波器。其後比較雙模濾波器與傳統濾波器(conventional direction coupler filters)之頻寬特性，發現雙模與傳統濾波器其模擬結果符合我們以perturbation theory作出的預測。

This thesis is devoted to the theoretical investigation and numerical simulations of filters based on silicon-on-insulator (SOI). The designed filters in this thesis are based on asymmetrical directional couplers filter and designed with perturbation theory. First we introduce and compare the theory of coupled-waveguide system with the quantum-optical analogies between coupled waveguide structure and two-level system driven by near-resonant laser.
We then design the parameters of filters by perturbation theory and window functions and simulate the designed directional coupler filters by FIMMWAVE. Then we compare the bandwidth of designed directional coupler filters with that of conventional directional coupler filter. Finally, we find that the results of simulation agree with the theoretical predictions.

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