波導通訊從18世紀以來一直都是電磁波傳遞最重要的方式，隨著奈米技術的發展 ，奈米尺寸的波導管也廣泛的在各式晶片、中央處理器中被應用。但隨著波導尺寸的縮小，奈米尺度波導的截止頻率也隨之增加至 Hz左右，在此情況下如何克服高頻互相耦合的行為成為科學家有興趣的問題。本文中使用表面電漿波(Surface Plasmon)的特殊物理特性，以牛頓法求解金屬圓柱波導之色散關係式，找到在兩種不同結構MIM(Metal-Insulator-Metal )與IMI(Insulator-Metal- Insulator) 之圓柱波導中，低於PEC材質之截止頻率之仍可傳遞的表面電漿模態。接著以有限差頻域法(FDFD, Finite Difference Frequency-Domain)驗證此種表面電漿波的各種方向分量分佈。
在整篇研究中我們得到幾個重要的結論：第一，入射頻率在金屬波導的表面電漿頻率 以下，在介面上會產生表面電漿波的共振模態，具有非常好的介面性質。相較於同尺寸的PEC圓柱波導，金屬圓柱波導在傳播頻率低於前者的截止頻率之下仍可傳遞表面電漿波。第二，以FDFD法模擬金屬圓柱波導的場形分佈，結構所對應的邊界條件必須確實考慮才能模擬出正確的模態分佈以及電磁場圖形。但在不規則形狀的結構模擬時，則必需引入介電常數平均分配法增加模擬的精確性。

Waveguide communication has been the most important method for electormagnetic wave propagation since the 18th century . While the growing of nano technology,nano-scale waveguide is widely used in cpu and chips . Nevertheless , company with the more and more smaller size of waveguide structure,the cutoff frequency of nano waveguide is reaching about Hz . How to overcome the high frequency coulping noise in nano waveguide become a interesting problem sicentists concern about . In this thesis , I discuss the special physical behavior of Surface Plasmon wave , using Netwon method to solve the metal cylindrical waveguide’s dispersion relation , finding Surface Plasmon mode can propagate even below PEC structure’s cutoff frequency in two kind of metallic structrue (Metal-Insulator-Metal & nsulator-Metal- Insulator) cylindrical waveguide . And continually I use FDFD(Finite Difference Frequency-Domain) method to verify Sufrace Plasmon wave’s validity .
In this thesis , I make some conclusions：First, below the metal surface plasmon frequency at metal waveguide , surface plasmon oscillation mode propagate at metllic interface . Compared PEC structure with same size , surface wave propagate at frequency lower than PEC waveguide’s cutoff frequency . Second ,
when simulate metllic cylindrical waveguide’s electromangetic wave pattern , boundary condition must be applied . While engaged in non-uniform structure simulation , otherwise I used dielectric constant index averaging skill to improve the accuracy of simulating .

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