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1 METAMATERIAL LENS DESIGN by Ralph Hamilton Shepard III Metamaterial Lens Design Item Type text; Electronic Dissertation Authors Shepard III, Ralph Hamilton Publisher The University of Arizona. Rights Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. Download date 30/09/2021 22:36:57 Link to Item http://hdl.handle.net/10150/194734 1 METAMATERIAL LENS DESIGN by Ralph Hamilton Shepard III ____________________________ Copyright © Ralph Hamilton Shepard III 2009 A Dissertation Submitted to the Faculty of the COLLEGE OF OPTICAL SCIENCES In Partial Fulfillment of the Requirements For the Degree of DOCTOR OF PHILOSOPHY In the Graduate College THE UNIVERSITY OF ARIZONA 2009 2 THE UNIVERSITY OF ARIZONA GRADUATE COLLEGE As members of the Dissertation Committee, we certify that we have read the dissertation prepared by Ralph Hamilton Shepard III entitled Metamaterial Lens Design and recommend that it be accepted as fulfilling the dissertation requirement for the Degree of Doctor of Philosophy ____________________________________________________________Date: 04/23/09 Jose Sasian ____________________________________________________________Date: 04/23/09 John Greivenkamp ____________________________________________________________Date: 04/23/09 Stanley Pau Final approval and acceptance of this dissertation is contingent upon the candidate’s submission of the final copies of the dissertation to the Graduate College. I hereby certify that I have read this dissertation prepared under my direction and recommend that it be accepted as fulfilling the dissertation requirement. ____________________________________________________________Date: 04/23/09 Dissertation Director: Jose Sasian 3 STATEMENT BY AUTHOR This dissertation has been submitted in partial fulfillment of requirements for an advanced degree at the University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library. Brief quotations from this dissertation are allowable without special permission, provided that accurate acknowledgement of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the copyright holder. SIGNED: Ralph Hamilton Shepard III 4 ACKNOWLEDGEMENTS I would like to thank the dissertation committee, Jose Sasian, John Greivenkamp and Stanley Pau, for their guidance throughout the dissertation process. A special thanks to David Knapp for inspiring the topic. Appreciation goes out to Michael Schaub and Delmar Barker for their support of the topic and technical advice. Also to my friends and family whose encouragement gave me the motivation to endure through the long weeks and months (years, actually). And finally, I’d like to thank Raytheon Missile Systems and FLIR Systems for their support of my ongoing education. 5 To our forefathers, whose labor grants us the luxury of intellectual pursuit 6 TABLE OF CONTENTS LIST OF FIGURES .......................................................................................................... 10 ABSTRACT ...................................................................................................................... 14 1 INTRODUCTION ......................................................................................................... 16 1.1 Explanation of the Problem and its Context ............................................................... 16 1.2 Literature Review........................................................................................................ 18 1.3 Explanation of the Dissertation Format ...................................................................... 26 2 PRESENT STUDY ........................................................................................................ 28 2.1 Research methodology ................................................................................................ 28 3 FIRST-ORDER OPTICS ............................................................................................... 33 3.1 Introduction ................................................................................................................. 33 3.2 Fermat’s Principle ....................................................................................................... 36 3.3 Derivation of Snell’s Law ........................................................................................... 38 3.4 Sign Conventions ........................................................................................................ 40 3.5 Paraxial Ray Tracing ................................................................................................... 41 3.6 Gaussian Imaging ........................................................................................................ 46 3.7 Reduced Distance and Optical Angle ......................................................................... 49 3.8 Cardinal Points of a Metamaterial Singlet .................................................................. 52 7 TABLE OF CONTENTS - CONTINUED 3.9 Multiple Powered Surfaces – Gaussian Reduction ..................................................... 58 3.10 The Optical Invariant ................................................................................................ 62 3.11 The Collinear Transformation ................................................................................... 66 3.12 Comments on Ray Tracing ....................................................................................... 72 3.13 Chapter Summary ..................................................................................................... 75 4 MONOCHROMATIC NIM ABERRATION THEORY ............................................... 77 4.1 Introduction ................................................................................................................. 77 4.2 Definition of Wavefront Error .................................................................................... 80 4.3 Derivation of the Seidel coefficients ........................................................................... 83 4.3.1 Spherical Aberration, Coma, and Astigmatism ....................................................... 89 4.3.2 Field Curvature ........................................................................................................ 95 4.3.3 Distortion ............................................................................................................... 113 4.3.4 Seidel Aberration Summary ................................................................................... 116 4.4 Effects of Stop Shift .................................................................................................. 119 4.5 Aberrations of the Thin Lens .................................................................................... 122 4.6 Chapter Summary ..................................................................................................... 129 5 THE NIM SINGLET ................................................................................................... 131 5.1 Introduction ............................................................................................................... 131 8 TABLE OF CONTENTS - CONTINUED 5.2 Aberrations as a Function of Shape Factor ............................................................... 134 5.3 Aberrations as a Function of Conjugate Factor ........................................................ 137 5.4 Aberrations as a Function of Refractive Index ......................................................... 140 5.5 Thin Lens as a Function of Stop Location ................................................................ 153 5.6 Astigmatism and Field Curvature ............................................................................. 155 5.7 The NIM Landscape Lens ......................................................................................... 157 5.8 Chapter Summary ..................................................................................................... 169 6 MULTIPLE LENS SYSTEMS .................................................................................... 171 6.1 Introduction ............................................................................................................... 171 6.2 Positive-Index Lenses ............................................................................................... 182 6.2.1 Positive-Index Doublet .......................................................................................... 183 6.2.2 Positive-Index Triplets ........................................................................................... 185 6.3 Negative-Index Doublets and Triplets ...................................................................... 193 6.3.1 Negative-index Doublet Lenses ............................................................................. 193 6.3.2 Negative-Index Triplet Lenses ............................................................................... 197 6.4 Ambirefractive Doublets and Triplets ...................................................................... 203 6.4.1 Ambirefractive Doublets ........................................................................................ 204 6.4.2 Ambirefractive Triplets .........................................................................................
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