本研究中利用「金屬－多層介電質」電漿波導能同時維持電磁場之高侷限性與高模態雙折射之特性，設計一以方向性耦合器為基礎，可用於奈米光路之波導極化分離器，進而能於單一耦合長度內將不同極化之基模分離。本論文除詳述設計之步驟與方法外，同時推導可用於有損介質之耦合波模理論，以做為本研究之理論基礎。
因運算資源有限，故本研究僅對二維結構進行探討。最佳化設計之結構於操作波長為1550 nm時，TE模態與TM模態之傳輸效率分別可達-0.1443 dB與-0.3777 dB，極化分離區域結構之總長度僅7.28 ，分離比與消光比亦皆超過20 dB。於最佳化結構下，TE模態之傳輸效率對於波長之變化相當敏感，波長範圍1473 nm至1606 nm間可達-0.4575 dB以上。而TM模態之傳輸效率因表面電漿模態之激發，於波長範圍1000 nm至1800 nm間皆達-0.6545 dB以上。此外，TE模態與TM模態分離比與消光比於波長範圍1502 nm至1581 nm間皆可達15 dB以上。
本研究之理論基礎，為由Maxwell方程式開始，推導可用於有損介質之修正性Lorentz互易性定理，並以此為基礎發展可用於有損介質之耦合波模理論。將此理論用於分析「金屬－多層介電質」電漿波導之TE模態耦合特性，並與有限元素分析法之數值模擬結果比較，兩者所得之耦合長度與傳輸效率大小皆相當接近；以數值模擬之結果為基準，耦合長度相差0.9652%，傳輸效率相差0.1313%，顯示此理論分析具有相當程度之可靠性。
將本論文提出之波導極化分離器與文獻資料比較顯示，以非對稱「金屬－多層介電質」組態實現之方向性耦合極化分離器可有效地縮小元件之尺寸，為縮小積體光路提供一創新之想法。

This thesis described the design and analysis of a novel directional-coupler-based polarization splitter for optical nanocircuitry in two-dimensional (2-D) asymmetric metal/multi-insulator configuration. The design and optimization of the proposed device are conducted using 2-D finite-element-based numerical simulations while modified coupled-mode theory for lossy parallel waveguides is developed as the mathematical background of this research.
The introduction of silver region in asymmetric air/silicon/silica waveguide is shown to not only enhance the field confinement but also control the dynamic range of the effective index associated with the transverse magnetic (TM) mode. A large modal birefringence of > 0.69 is estimated, enabling a clean polarization separation within 7.28 , inclusive of the input/output tapers. The proposed polarization splitter is optimized at the wavelength of 1550 nm. The transmission efficiencies of -0.1443 dB and -0.3777 dB are obtained for the respective transverse electric (TE) and TM modes while the extinction ratios and splitting ratios are larger than 20 dB at 1550 nm. Due to the excitation of the plasmonic mode, an extremely broadband operation from 1000 nm to 1800 nm is found for the TM transmission, which in turn affects directly the TM splitting ratio as well as the extinction ratio along the cross path. The TE behavior is; however, similar to that of the conventional direction coupler. The extinction ratios and extinction ratios are estimated to be larger than 15 dB for wavelengths ranging from 1502 nm to 1581 nm.
The modified coupled-mode theory is derived based on the modified Lorentz reciprocity theorem suitable for describing the field perturbations in a lossy system. The application of the theory to the TE mode coupling in the present case is in good agreement with the finite-element-based numerical simulations. Specifically, the respective differences between the coupling length and power transfer along the cross path are merely 0.9652% and 0.1313% with respect to the numerical results.

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