石墨烯導電率可以分為intra-band與inter-band兩部份，後者由於在低頻影響較小以及形式難以帶入時域數值模擬方法而常常被忽略，在本文中我們為石墨烯導電率中的inter-band提供了一個近似的模型，它可以輕易地經由auxiliary differential equations(ADE)代入FDTD，接著我們推導了石墨烯的穿透吸收反射率、表面電漿，驗證本模型的正確性，同時也展示了inter-band的重要性，之後以此為基礎模擬了石墨烯nanoribbon，並分析其模態，分類出了edge mode與無窮延伸mode之特性，之後考慮更實際的情形而模擬分析了inhomogeneous doping、soft-boundary，然後模擬分析了雙層石墨烯nanoribbon與外加電極的影響，對石墨烯表面電漿做全面的分析整理，之後再延伸到模擬奈米碳管的情形，而後用這些概念設計了齒形結構可以調控表面電漿，並分析它的機制。

Graphene conductivity consists of intra-band and inter-band contribution, and the latter is usually neglected due to its small effect in long wavelength regime and its difficulty to incorporate into time domain method. In this work, we provide an analytical rational form to treat the inter-band conductivity, which can easily incorporate into FDTD using the auxiliary differential equations (ADE).
Then we calculated the transmission, absorption, reflection and surface plasmon mode of single layer graphene to verify our model and also demonstrated the importance of inter-band conductivity. In the second part, we used this model combined with FDTD to simulate graphene nanoribbon. We also analyzed and classified its modes into edge mode and infinite width mode. Considering of more realistic situation, we simulated and analyzed inhomogeneous doping and soft-boundary cases. Then we simulated and analyzed double-layers graphene nanoribbons and graphene nanoribbon with PEC gate, afterwards compared their similarity and difference. Furthermore, we simulate carbon nanotubes and analyzed its surface plasmon waveguide dispersion property which is similar to graphene nanoribbons. Finally, we designed a tooth-shape structure to control surface plasmons and analyzed its Fabry-Perot like transmission mechanism.

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