THE STUDY OF NEGATIVE REFRACTION、METAMATERIALS、 TRANSFORMATION OPTICS AND INVISIBILITY CLOAKING

• Main Authors: Shih, Yau-Yuan, 石耀淵
• Other Authors: Yang,Y i
• Format: Others
• Language: zh-TW
• Published: 2014
• Online Access: http://ndltd.ncl.edu.tw/handle/99503384149952780748

碩士 === 國立交通大學 === 電子物理系所 === 102 === Abstract This thesis mainly introduces the principle and the history of negative refraction, perfect lens, transformation optics and invisibility cloaking. We explore the theoretical works of Professor John Pendry in these areas during 1999-2006, as well as the works of Professor Ulf Leonhardt during 2008-2010 about transformation optics, which include those using the language of differential geometry for manipulating the tensor form of Maxwell equations in curved spacetime. In 2006, D.Schurig, D.R.Smith and John Pendry et al proposed the concept of transformation optics, which can provide the material parameters for designing invisibility cloaks with metamaterials. Under the assumption of the validity of geometrical optics approximation, they also derived the Hamiltonian from Maxwell equations for obtaining the canonical equations of motion for generating the ray trace. This work triggers the human dreams about making invisibility cloaks. In that work, the derivation of Hamiltonian and Hamilton canonical equations are too brief and compact to understand. In 2011 four mathematicians Miles M. Crosskeya, Andrew T. Nixonb, Leland M. Schickc, Gregor Kovačičd re-investigated the principle of invisibility cloaking and provided the rigorous proof of its existence mathematically. In this thesis, especially for the spherical and cylindrical of invisibility cloaks, we provide the detailed derivations of the tensor parameters, material Hamiltonian and Hamilton E.O.M, and the physical principles are explained thoroughly. Finally, we discuss the works of Professor Molin Ge of applying the language of general relativity to interpret the anisotropic inhomogeneous media, and prove the geodesic equations of light ray thoroughly.