超導光子晶體光學性質研究

Abstract

本篇論文採用數值模擬方法研究含超導材料層的一維光子晶體結構其光學特性。藉由轉移矩陣法計算由超導層A、介電層B交替排列形成一維週期組合，再以組合為單位進行一維的正向與反向串聯堆疊，並求得其透射頻譜，並由模擬結果可以對不同的排列歸納出其特性規律。再藉由加入磁場變因，研究超導光子晶體於外加磁場下與臨界磁場之間的關係，並觀察頻譜所產生的變化，並嘗試藉由調整各種變因達到控制頻譜狀態的目的，藉由研究得知在環境溫度小於臨界溫度，且外磁場小於臨界磁場時，禁帶帶寬會隨溫度上升、外磁場增強而變窄。最後將前兩項研究的結果進行結合，驗證高溫超導與低溫超導特性相近，在變更超導層與介電層厚度後觀察狹窄頻段內所產生的峰在外磁場影響下的變化。 關鍵字：光子晶體、超導、透射光譜。In this thesis, we study the optical properties in one-dimensional superconducting photonic crystals using numerical simulation. First, let A be the superconductor layer and B be the dielectric layer, then put layer and alternately arranged to the form air/(AB)^N/air. Define the form (AB)^N as the Positive, and the form (BA)^N as the Negative, then connect the Positive and the Negative in series that we can use the Transfer Matrix Method (TMM) to plot the transmission spectrum. By analyzing the transmission spectrum, we can generalize that the relation between period N, multiples of total thickness R, orders of combination structure Positive and Negative α, and the number of peaks P as P=R(N-1)+α. Second, we add external magnetic field to study how the magnetic field effect the transmission spectrum. After change the variables, we know that when the crystal is in the environment which temperature T is under the critical temperature Tc and external magnetic field B is under critical magnetic field Hc2(T), the bandwidth will decrease along the temperature and external magnetic field increase. In the third part, we combine the results in the Chapters aforementioned. As we change the thickness of the dielectric layer and the superconductor layer, we can see the features in narrow bands. Then add external magnetic field to study how the transmission spectrum will change while the magnetic field increased. Keyword: photonic crystals, superconductor, transmittance spectrum.