假對掌性超常材料之電磁參數反算

Abstract

人工超常材料為次波長週期結構，擁有自然界所沒有的物理特性，例如負的折射率以及負的磁導係數，而次波長結構是指單位元小於入射波波長之結構且其可以用等效介質理論來分析，將整個複雜的結構視同一塊簡單的等向性或非等向性塊材用一等效參數表示。 本論文以組成率為基礎透過馬克斯威方程式推導超常材料之色散關係、共振模態、阻抗，考慮波傳問題並且解析出反射以及穿透係數，再由阻抗、折射率、反射以及穿透係數反算電磁參數。 其中針對一雙非等向性材料，假對掌性超常材料，推導其解析解，但是由於特殊的結構關係，材料之組成率比一般等向性或異向性材料複雜，並且未知數較多。 因此我們藉由三種方向入射解析出假對掌性超常材料各方向之色散關係、阻抗、折射率，並且由數值模擬的方式得到反射以及穿透係數，接著再透過三種方向之反射及穿透係數反算其組成率之電磁參數，而三種方向入射分別會產生兩種模態，TE Mode(電場垂直入射面)和TM Mode(磁場垂直入射面)，利用兩種不同的模態可以推導出不同的電磁參數反算公式，並由兩種模態所推導反算公式並互相驗證，最後做參數分析，改變假對掌性材料結構的參數，寬度，厚度，以及最大半徑，並分析改變結構參數之影響，找出最佳設計參數。

Artificial meta-materials is subwavelength periodic structures which exhibit unusual electromagnetic response such as negative refractive index and negative permeability. Subwavelength structure, a structure unit which is smaller than wavelength and it can be analyzed by the effective medium theory which the structure can be regarded as an isotropic or anisotropic effective medium and be described by retrieval of the effective parameters of meta-materials. In this thesis we derive dispersion relation, eigenwaves and impedance based on different sets of constitutive relations through Maxwell equation. Also we derive reflection and transmission coefficients through multiple planer interfaces. Then we use impedance, index of refraction, reflection and transmission coefficients to retrieve the effective parameter of meta-materials. In particular, we study plane wave propagation in a special kind of bi-anisotropic medium: pseudo chiral medium. Because of its special structure, constitutive relations of pseudo chiral medium is more complex than isotropy or anisotropy medium and is more difficult to retrieve due to a lot of unknown effective parameter. So the scattering parameters in three propagation direction are used and we derive dispersion relation, impedance and index of refraction. Then we use impedance, index of refraction, reflection and transmission coefficients from numerical simulation to retrieve the effective parameter of pseudo chiral meta-material. There are two eigenmode in each direction, TE mode and TM mode. Analytical inversion equations are derived in order to retrieve the effective parameter are different in two modes in which we can use two to verify the retrieval of effective parameter. Finally, we change the size of pseudo chiral meta-material like width, thickness, and the radius to analyze the effect of chiral meta-material and find the best parameter to design the material.