本論文主要在探討石墨烯特性，以及模擬石墨烯nanoribbon波導模態和共振腔模態，石墨烯的電導率分為intra-band和inter-band兩個部分，而intra-band的部分可以利用Drude model來fitting，但是inter-band由於是複數對數的形式，而不是j的多項式，因此無法直接代入FDTD，但是本實驗室發展出一套方法提供了一個有效的近似模型，可以fitting出石墨烯inter-band的部分，並使之可以代入FDTD來進行模擬，我們以此套模型為基礎去模擬出hard-boundary和soft-boundary的石墨烯nanoribbon，畫出其色散關係圖，並且分析模態和其特性，之後再模擬分析石墨烯nanoribbon下加了介電層的影響，最後為了因應量子級聯雷射(Quantum Cascaded laser)的長波段雷射，我們設置了一個石墨烯的環形共振腔，利用其波導模態的高等效折射率能將長波段有效壓縮至石墨烯nanoribbon中的特性，模擬並分析可雷射的共振腔模態。

This thesis mainly discusses the finite difference time domain method to describe graphene plasmonic properties and simulates graphene nanoribbon waveguide and resonant cavity modes. The conductivity of graphene consists of two parts: intra-band and inter-band. While the intra-band part can be fitted by Drude model, Inter-band is a form of complex logarithm, not a polynomial of (jn terms, and cannot be directly implemented in FDTD. We developed an effective approximation method to fit the inter-band of graphene over a broadband range. Based on this model, we simulate the hard-boundary and soft-boundary graphene nanoribbon to obtain the dispersion relation, and analyze these waveguide modes. We further simulated and analyzed the effect of the dielectric layer on the graphene nanoribbon. Finally, we design a ring-shaped resonant cavity of graphene nanoribbon to effectively compress the long-wavelength of the quantum cascaded laser light into a cavity with a small footprint. This is accomplished by using the high effective refractive index of graphene nanoribbon. We further simulated and analyzed the laser resonator modes of graphene nanoribbon ring cavity.

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