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Microwave Metamaterials James A Advances In MICROWAVE METAMATERIALS By James A. Wigle B.S.E.E, University of Maryland, 1991 M.S.E.E, Johns Hopkins University, 1996 A dissertation submitted to the Graduate Faculty of the University of Colorado at Colorado Springs in partial fulfillment of the requirements for the degree of Doctor of Philosophy College of Engineering & Applied Science Department of Electrical and Computer Engineering 2011 P a g e | ii Copyright Notice © Copyright by James A. Wigle 2011, all rights reserved. The author, James A. Wigle, copyrights all text, ideas, figures and photographs of this document. Any form of copying, reprinting, or publishing of this document, in any portion, is not permitted without the author‟s explicit, written, and prior permission in any form or medium. Contact the author for this written permission. Advances in Microwave Metamaterials James A. Wigle This dissertation for Doctor of Philosophy degree by James A. Wigle has been approved for the Department of Electrical and Computer Engineering by ___________________________________ John Norgard, Chair ___________________________________ Hoyoung Song, Co-Chair ___________________________________ Thottam S. Kalkur, Chair ECE ___________________________________ Tolya Pinchuk, Dept. of Physics ___________________________________ Zbigniew Celinski, Dept. of Physics ____________________ Date P a g e | iv Abstract Metamaterials are a new area of research showing significant promise for an entirely new set of materials, and material properties. Only recently has three-fourths of the entire electromagnetic material space been made available for discoveries, research, and applications. This thesis is a culmination of microwave metamaterial research that has transpired over numerous years at the University of Colorado. New work is presented; some is complete while other work has yet to be finished. Given the significant work efforts, and potential for new and interesting results, I have included some of my partial work to be completed in the future. This thesis begins with background theory to assist readers in fully understanding the mechanisms that drove my research and results obtained. I illustrate the design and manufacture of a metamaterial that can operate within quadrants I and II of the electromagnetic material space (Ɛr > 0 and µr > 0 or Ɛr < 0 and µr > 0, respectively). Another metamaterial design is presented for operation within quadrant III of the electromagnetic material space (Ɛr < 0 and µr < 0). Lorentz reciprocity is empirically demonstrated for a quadrant I and II metamaterial, as well as a metamaterial enhanced antenna, or meta-antenna. Using this meta-antenna I demonstrate improved gain and directivity, and illuminate how the two are not necessarily coincident in frequency. I demonstrate a meta-lens which provides a double beam pattern for a normally hemispherical antenna, which also provides a null where the antenna alone would provide a peak on boresight. The thesis also presents two related, but different, novel tests intended to be used to definitively illustrate the negative angle of refraction for indices of refraction less than zero. It will be shown how these tests can be used to determine most bulk electromagnetic material properties of the material under test, for both right handed and left handed materials, such as Ɛr , µr , δloss, and n. Advances in Microwave Metamaterials James A. Wigle P a g e | v The work concluding this thesis is an attempt to derive modified Fresnel Coefficients, for which I actually believe to be incorrect. Though, in transposing I have corrected a few mistakes, and now I can no longer find the conundrum. I have included this work to illuminate the need for modified Fresnel coefficients for cases of negative indices of refraction, identifying all disparate cases requiring a new set of equations, as well as to assist others in their efforts through illumination of the potential erroneous path chosen. Advances in Microwave Metamaterials James A. Wigle P a g e | vi Acknowledgements This work would not be complete, if not for the help of others. My mentor Dr. John Norgard, and my in situ mentor Dr. Hoyoung Song, provided wonderful advice and guidance in my University of Colorado efforts. Indispensible, and much appreciated, technical assistance and theory were provided by Dr. Tolya Pinchuk of The University of Colorado Physics Department and Dr. Victor Gozhenko of The National Aviation University, Ukraine (Віктор Гоженко, Національний Aвіаційний Університет, Україна). I sincerely aspire to continue our relationships and expanding our knowledge of physics and electromagnetics. Mr. James Vedral significantly helped with modeling and technical discussions. It is with sincere appreciation that I thank all of you, my wife and family, and many others for the support required to complete this work. In the modified words of Sir Isaac Newton, my personal hero, efforts such as this are easy while standing on the shoulders of giants. Advances in Microwave Metamaterials James A. Wigle P a g e | vii Table of Contents Copyright Notice ............................................................................................................................................ ii Abstract ..........................................................................................................................................................iv Acknowledgements ........................................................................................................................................vi Table of Contents ......................................................................................................................................... vii List of Tables ................................................................................................................................................ xiv List of Figures ............................................................................................................................................... xv Chapter 1. Introduction................................................................................................................................... 1 1.1 Purpose and Chapter Descriptions ....................................................................................................... 1 1.2 What is a Metamaterial? ...................................................................................................................... 2 1.3 Some Metamaterial History ................................................................................................................. 2 1.4 General Metamaterials Information ..................................................................................................... 3 Chapter 2. Metamaterial Artifacts and Curiosities ......................................................................................... 7 2.1 Proposed and Theorized Metamaterial Uses........................................................................................ 7 2.2 The Perfect Lens .................................................................................................................................. 9 2.3 Cloaking Success ............................................................................................................................... 10 2.4 Directive Emission Using Metamaterials .......................................................................................... 12 2.5 The Cherenkov Detector .................................................................................................................... 13 2.6 Negative Radiation Pressure .............................................................................................................. 13 Advances in Microwave Metamaterials James A. Wigle P a g e | viii Chapter 3. Metamaterial Theory ................................................................................................................... 15 3.1 Introduction to Metamaterial Theory .................................................................................................. 15 3.2 Law of Refraction (Snell‟s Law) and Refractive Index ..................................................................... 15 3.3 Index of Refraction‟s Forced Radical Sign ........................................................................................ 16 3.4 Snell‟s Law with a Metamaterial Twist ............................................................................................. 18 3.5 Permittivity ........................................................................................................................................ 20 3.6 Split Ring Resonators ........................................................................................................................ 21 3.7 Narrow Frequency Bandwidths ......................................................................................................... 22 3.8 Plasma Frequency .............................................................................................................................. 23 3.9 Physical Description of Right vs. Left Handed Materials ................................................................. 24 3.10 Proof of Snell‟s Law Radical Sign Result ....................................................................................... 26 3.11 Bulk Plasma Frequency ................................................................................................................... 32 3.12
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