在本論文中我們討論如何利用介質參數為空間上特別設計的函數的特殊介質，來做為電磁波、壓力波、與純剪波的隱形斗篷。首先推導證明出三種波動在二維系統中的數學公式均可互相對應，顯示此三種波動的特性可以被統一處理。此外，再用數值模擬的方法研究其個別結果，並進而提出改良的方法來提升隱形效果。由於自然界中並無法找到介質函數如此特別的介質，因此我們也探討利用多層均勻介質經過特殊排列的層狀結構，來在長波極限下等效原本介質參數為空間連續函數的特殊連續介質。除了二維系統之外，本論文也對三維壓力波隱形斗篷的特性進行了初步的研究。此論文對隱形斗蓬之物理特性的分析與數值模擬為隱形斗蓬的具體實現提供了理論基礎。In this thesis, we discuss how to use specially designed inhomogeneous material parameters to construct the “invisibility cloaks” for use in cloaking the electromagnetic waves, acoustic pressure waves, and elastic shear waves. We first prove that by identifying the original material parameters with some abstract parameters, the wave equations for these three kinds of waves can be cast into a universal form, which reveals that their behaviors can be studied in a universal manner. We then study the behaviors of the cloaks numerically, and propose various methods to improve their invisibility efficiency. Since naturally existing materials never have such special material parameters satisfying the cloaking condition, we design the invisibility cloaks instead using layered structure consisting of successively arranged layers of homogeneous isotropic materials. And this structure can mimic the behaviors of the original cloak of continuous material in the long wavelength limit. In addition to the two dimensional wave systems, we also have studied briefly the behaviors of 3D acoustic invisibility cloak. Our analyses and numerical simulations on the cloaking systems provides the necessary theoretical foundation for realizing practical cloaking devices.
