超常材料在不同組成律下之負折射和後退波之研究

Abstract

人工超常材料雍有自然界天然材料所沒有之電磁行為。這些特殊現象導致了新的物理機制與工程應用。以物理角度而言，我們可用一等效材料參數來表示。 一旦等效參數確立，即可代入組成率方程式並研究其波傳行為。 本論文即已組成率為基礎下探討不一樣之波傳行為。由馬克斯威方程式，我們解析推導出色散關係、共振模態、阻抗與波因廷向量。之後考慮單一介面之波傳問題並利用模態解出反射與穿透係數。其中，針對其中一種非等效性材料:假對掌性材料做波傳研究。本研究發現到在假對掌性材料中波傳模態為兩個橢圓偏振且這兩個不同橢圓模態可分別導致負折射與後退波。最後並用數值高斯光束模擬來驗證此現象。

Meta-materials are man-made structures which exhibit unusual electromagnetic response. Such extraordinary responses give rise to new physical insights and engineered applications. The most common way to describe this kind of material is by defining effective material parameters connected to constitutive relations. Once constitutive relations are obtained, the wave propagating properties could be explored through basic electromagnetic theory. In this thesis we investigate wave propagation based on different sets of constitutive relations. Dispersion relation, eigenwaves, impedance together with Poynting vector are derived. Also we derive reflection and transmission coefficients through a single planer interface. In particular, we study plane wave propagation in a special kind of bi-anisotropic medium: pseudochiral medium. It is found that two elliptic eigenwaves appear in pseudochiral material and allow us to realize negative refraction or backward wave. Finally, Gaussian beam propagation is conducted to verify our results.