超穎材料的重要研究為材料內的次波長結構設計與搭配，至今已發表的文獻中講述了超穎材料的異常特性以及應用，而雙曲超穎材料因為具有開方式的等頻率曲線，較大波向量的倏逝波能在其中傳遞，對於繞射極限的突破以及積體光路的實際應用能提供一良好方式。但這些文獻中對於的超穎材料的結構設計，如材料的選擇、金屬與介電質材料的體積填充比以及堆疊層數等並未詳細說明以及探討，並且對於導納的匹配也未加以考慮，導納不匹配的損耗與金屬材料的吸收會減少電磁波耦合至超穎材料中 本研究以介電質-金屬-介電質對稱膜堆為單位晶胞進行設計，討論多層結構在次波長尺度下的等效介質特性。利用等效模型計算並透過分枝的選擇以獲得準確的等效光學常數，等效光學常數決定了電磁波在介質內的傳遞行為與特性，虛數部分決定電磁波的衰減程度。此外更進一步計算並且設計符合與入射介質導納匹配的等效介質結構參數，等效導納與入射介質的匹配程度影響了等效介質與入射介質介面間的光學反射特性，計算出最佳的導納匹配參數能使反射所造成的損耗降至最低以提高耦合效能。 雙曲超穎材料因其獨特的等頻率曲線包含較高的波向量範圍可應用於許多領域，利用此方法能精準的計算並獲得所需的光學特性以及良好的導納匹配，且能快速的獲得最佳的結構參數值，包括膜層厚度、入射角度、單位晶胞的週期數以及基板的折射率。 而且此種計算與設計方法適用於各個波長、材料的選擇搭配以及各種對稱結構，對於雙曲超穎材料應用的結構參數設計提供了一大幫助，能精準有效的獲得符合雙曲超穎材料特性以及導納匹配的最佳設計結構參數。 ;One of the important works on metamaterials is the design of the subwavelength structure and the composition of the materials. There are abnormal characteristics and applications of metamaterials that have been reported in the literatures. Hyperbolic metamaterials have larger wave vectors due to the open isofrequency curves. The evanescent wave with high-k vectors can propagate in it, which can provide a method to break the diffraction limit and for the practical application of the integrated optical circuit. However, the structural design of metamaterials in those literatures, such as the selection of materials, the volume filling ratio of metal and dielectric materials, etc., was not been described and discussed in detail, and the matching of admittance was also not considered. There is loss due to admittance mis-matching and the absorption of metal materials will reduce the coupling of electromagnetic waves into the metamaterial. In this study, dielectric-metal-dielectric symmetrical film stack as a unit cell was used to design a multilayer equivalent medium with a subwavelength scale structure. The precise equivalent optical constant was calculated by the equivalent model with the current choice of branch. The propagating properties of the electromagnetic wave were depended on the optical constant. The decay of electromagnetic was affected by the imaginary part of the optical constant. Additionally, the equivalent admittance was considered and calculated to obtain the optimal parameters of a multilayer structure with the lowest reflectance. Hyperbolic metamaterials can be applied in the various field because it has unique iso-frequency curve with high-k vector propagating. This method can precisely calculate the structure parameters, including the thickness of the film, incident angle, number of period of the unit cell, and refractive index of the substrate according to the required optical properties. This method can be applied to various materials and symmetrical film stacks for various wavelengths.
