本研究中我們結合保角映射理論與傳輸線理論並首次應用於非對稱「金屬－多層介電質」表面電漿90度圓弧波導結構，並以此方法設計一能同時提供橫電(TE)模態與橫磁(TM)模態高傳輸效率之次波長圓弧波導。於此方法中，圓弧波導可運用保角映射理論等效成直線幾何結構，後續使用傳輸線法解析於保角映射後之折射率分佈下，導波模態之等效折射率並做後續之傳播損耗與模態轉換損耗之分析計算。
研究中發現，當操作波長為1550 nm下，TM模態與TE模態隨銀厚度增加至100 nm後，其等效折射率之實部與虛部皆會收斂。理論分析中定義有效橫向寬度為保角映射後之橫向折射率分佈對映射後之轉彎結構各區域寬度之積分。將有效橫向寬度對不同轉彎半徑分析並與以有限時域差分(Finite-Different Time-Domain, FDTD)法為基礎之數值模擬相互比較後發現有效橫向寬度能物理性地描述TM模態於此非對稱「金屬－介電質」表面電漿90度圓弧轉彎結構之傳輸行為。將「直線波導－圓弧轉折波導－直線波導」經保角映射等效後可視為有效橫向寬度為「窄－寬－窄」之直線結構。而由寬至窄結構時會有部分能量逸散至空氣中。
最佳化設計中，解析計算發現可將矽區域與二氧化矽區域寬度分別減少至150 nm與50 nm，並由功率移轉分析中發現可移去連接轉彎區域波導與輸出端模態轉換器之直線結構。最終可得在轉彎區域面積為0.2165微米平方下，TM模態與TE模態傳輸效率分別達到90.50 %與93.22 %。

This thesis describes an analytical approach to analyze subwavelength 90̊ curved waveguide bend in an asymmetric metal/multi-insulator configuration. This approach employs the conformal mapping to first transform a curved waveguide bend into an equivalent straight waveguide structure and then calculate the modal index of the guided mode under the continuously-varying index profile using the transmission line network method. The propagation loss and mode transition loss along the curved waveguide bend are quantified accordingly.
Based on the convergence of the attenuation constant at the operating wavelength of 1550 nm, the width of the silver region is set to 100 nm. We then define the effective transverse width as the integral of the transformed index profile over the transverse axis in the radial direction. When quantified as a function of the bending radius, the newly defined parameter is found to be in good agreement in tendency with the finite-difference-time-domain-method-based numerical simulations and can be used to describe physically the TM wave behavior along the curved bending. In general, the curved bending region along with the input/output straight sections can be treated conceptually as a structure composed of narrow, wide, narrow sections connected in sequence. Significant power loss occurs at the interface going from the wide section to the narrow section.
Following the analytical analysis and power interchange studies, the width of silicon and silica regions are reduced to 150 nm and 50 nm, respectively, and the respective TM and TE transmissions could be up to 90.50% and 93.22% with a curved bending area of 0.2165 /mum^2.

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