超導與超穎材料週期多層結構之光學性質探討

Abstract

週期性多層膜結構的光學理論已發展了一段時間，過去採用的材料主要偏向於介電體，半導體以及金屬。近年來，許多不同於這些早期傳統的材料，例如超導體以及超穎材料，已被陸續開發出來。我們的研究工作重點，是將超導體材料(superconductors)及超穎材料(metamaterials)置於多層膜的結構中，探討電磁波在此週期性排列結構中的傳播特性以及光學能帶分佈，企圖尋求其特殊性質以及可應用功能的開發。對於一維的超導體的光子晶體，我們採用超導體的二流體模型理論來進行研究。從計算出的穿透頻譜和光子能帶圖，發現兩者幾乎完全的吻合。我們進一步對於二維的週期性多層膜的環型結構進行探討，採用克利提夫斯基(Kaliteevski)的計算理論，以圓柱波的轉移矩陣計算方式分別針對超導體材料及超穎材料來進行數值分析。計算會隨著頻率改變的介電係數(permittivity)和磁感係數(permeability)進而繪出反射頻譜，經過研究探討後，我們發現在材料的電漿頻率處附近圓柱波與平面波有截然不同的反應，此種特殊現象對於未來在通訊上設計濾波器或者共振器將有很大的助益。

It has been developed for periods of time to research the optical properties of periodic multilayer structures. In the past years, the photonic band gap structure were mainly fabricated by using the usual dielectrics, semiconductor and metal as well. Recently, the new materials like superconductors and the metamaterials have been developed very soon. The main purpose of our research work is to study the optical properties of the periodic multilayer structures with superconductors and metamaterials. The discussions of photonic band structure have been made and we attempt to seek some unusual phenomena and the special property for application. The photonic band structure in the transversal electric mode for a one-dimensional superconductor-dielectric superlattice is theoretically calculated. By using the two-fluid model of superconductors, the band structure is shown be strongly consistent with the transmittance spectrum. Next, we investigate the optical properties of the annular Bragg reflectors containing superconductors and metamaterials. By using the transfer matrix method for the cylindrical waves developed by Kaliteevski et al., we calculate the reflectance spectra for the annular Bragg reflectors. Numerical results show that the optical properties of the annular Bragg reflectors are fundamentally different from those of the planar Bragg reflector with azimuthal mode number . The special results suggest that the annular Bragg reflectors could be used to design a narrowband transmission filter or an annular resonator without introducing any physical defect layer in the structure.