摘要：光學超常材料係以次波長精密元件而由人工設計製造之結構，其集體行為呈現出如負折射率、高人工磁性及異常色散關係之奇異材料特性。於過去十年中，光學超材料因其於超透鏡裝置、高度色散稜鏡、光學掩蔽、奈米級光微影術、光線陷捕與儲存坑、電漿子波導乃至於奈米光子實驗室晶片上之潛在應用，而受到熱烈的研究。對於材料中波傳播之光譜及散射特性的清楚理解，能有助於操控對於微型化光電裝置之最佳效益，進而能夠創新設計操控電磁波。早期材料的研究係採用低介電常數(e~11-14)之半導體結構而工作於微波頻率範圍，現今許多研究花費大量的工夫於降低材料尺寸的大小以配合可見光頻率。先前大部份的研究使用金屬塗布於介電結構外，例如隙環共振器，主要是因為金屬在超過十億赫茲頻率時呈現出負介電係數。然而，於高頻範圍之金屬幾乎總是會能量耗散。此外，金屬的特性主要受幾何所控制，因而非常難以主動調節超常材料之共振。為避免金屬於光學頻率範圍中與生俱來的耗散損失及飽和效應，我們提議探究全介電超常材料之光學特性，例如其帶隙結構。近來對於全介電超常材料之研究表示出極高介電係數(e~200)結構之新穎特性，但並非實際可用於真實材料上。我們初步的成果(Opt. Exp. 16, 16600, 2008)顯示對於二維柱型光子晶體而言，存有介電常數的範圍(如，陶瓷的e~20-27)，其表現出寬的全帶隙以及強烈的場侷限。不像通常的光子帶隙結構，該些帶隙開啟於高位光子帶。這些先前較少研究過的帶隙之帶隙開啟機制為成功實現此超常材料之關鍵。因此，於此計畫中，我們提議藉由將系統擴展成其他光子晶體、整齊非週期性陣列及不規則固體，進行對於全介電超常材料之高位光子帶的詳盡研究。我們意圖獲得非尋常帶隙開啟之廣泛傾向規則，且探索其於波傳播特性上之效應。我們的方法是使用區塊疊代頻率域方法及時間域有限差分法來解馬克斯威爾方程式。模擬結果將透過解析弗羅奎茲定理來分析，且與多重散射法進行比對。將計算與討論布拉格散射與米氏共振模型二者以解釋帶隙開啟的機制。另將透過勻化或有效介質理論來計算有效的光學常數。本計劃應可做為未來對於光子奈米技術之全介電超常材料之創新應用之基石。
Abstract: Optical metamaterials are artificially engineered structures with subwavelength microscopic elements whose collective behavior exhibits exotic material properties such as negative refractive index, high artificial magnetism and anomalous dispersion relation. In the past decade optical metamaterials have been intensely studied because of their potential applications on superlensing devices, highly dispersive prisms, optical cloaking, optical nanolithography, light trapping and storage cavities, plasmonic waveguides and even nanophotonic lab-on-chip. A clear understanding of the spectral and scattering properties of the wave propagation in metamaterials can help to harness the best utilities for miniaturized photoelectronic devices, leading to innovative design to manipulate the electromagnetic waves. While earlier studies of metamaterials employ semiconductor structures of low dielectric constants (e~11-14) working at the microwave frequency range, much effort is currently spent on scaling down the metamaterials size to visible frequencies. Most previous researches use metal coated dielectric structures such as split-ring resonators, mainly because metals exhibit negative permittivity beyond the gigahertz frequency. However, for high frequency range metals are almost always energy dissipative. In addition, the properties of metals are controlled mainly by the geometry so it is very difficult to actively tune the metamaterial resonances. To avoid the dissipative losses and saturation effects inherent to metals at optical frequency range, we propose to explore the optical properties of all-dielectric metamaterials such as their band gap structures. Recent studies on all-dielectric metamaterials demonstrate novel properties of these structures with very high dielectric constants (e~200), which are not practically available using realistic materials. Our preliminary results (Opt. Exp. 16, 16600, 2008) show that for two dimension rod-type photonic crystals there exists a range of dielectric constants (i.e. e~20-27 for ceramics) which exhibit wide full band gaps and strong field localizations. Unlike normal photonic band gap structures, these gaps open between high-lying photonic bands. The gap opening mechanism of these previously understudied gaps is the key to the success of realizing such metamaterials. Therefore, in this project we propose to perform detailed studies of these high-lying bands of all-dielectric metamaterials by extending the systems to other photonic crystals, orderly aperiodic arrays, and amorphous solids. We aim to obtain a general propensity rule for the opening of these unusual band gaps and explore their effects on the wave propagation properties. Our methodology is to solve the Maxwell equations using the block-iterative frequency domain method and the time domain finite difference method. The simulation results will be analyzed through analytical Floquet theory and compared with the multi-scattering approach. Both Bragg scattering and Mie resonance models to explain the band gap opening will be calculated and discussed. Effective optical constants will be calculated through the homogenization or effective medium theory. This project should serve as a cornerstone for future innovative applications of all-dielectric metamaterials to photonic nanotechnology.
time domain finite difference method
effective medium theory