Novel Metamaterial Blueprints and Elements for Electromagnetic Applications Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Hayrettin Odabasi, B.S., M.S. Graduate Program in Electrical and Computer Engineering The Ohio State University 2013 Dissertation Committee: Fernando L. Teixeira, Advisor, Prabhakar Pathak Roberto Rojas-Teran c Copyright by Hayrettin Odabasi 2013 Abstract In the first part of this dissertation, we explore the metric invariance of Maxwell’s equations to design metamaterial blueprints for three novel electromagnetic devices. The metric invariance of Maxwell’s equations here means that the effects of an (hypothetical) distortion of the background spatial domain on the electromagnetic fields can be mimicked by properly chosen material constitutive tensors. The exploitation of such feature of Maxwell’s equations to derive metamaterial devices has been denoted as ‘transformation optics’ (TO). The first device proposed here consists of metamaterial blueprints of waveguide claddings for (waveguide) miniaturization. These claddings provide a precise control of mode distribution and frequency cut-off. The proposed claddings are distinct from conventional dielectric loadings as the former do not support hybrid modes and are impedance-matched to free-space. We next derive a class of metamaterial blueprints designed for low-profile antenna applications, whereby a simple spatial transformation is used to yield uniaxial metamaterial substrate with electrical height higher than its physical height and surface waves are not supported, which is an advantage for patch antenna applications. We consider the radiation from horizontal wire and patch antennas in the presence of such substrates. Fundamental characteristics such as return loss and radiation pattern of the antennas are investigated in detail. Finally, transformation optics is also applied to design cylindrical impedance-matched absorbers. In this case, we employ a complex-valued ii transformation optics approach (in the Fourier domain) as opposed to the conventional real-valued approach. A connection of such structures with perfectly matched layers and recently proposed optical pseudo black-hole devices is made. In the second part of this dissertation, we move from the derivation of metamaterial blueprints to the application of pre-defined unit-cell metamaterial structures for miniaturization purposes. We first employ electric-field-coupled (ELC) resonators and complementary electric-field-coupled (CELC) resonators to design a new class of electrically small antennas. Since electric-field coupled resonators were recently proposed in the literature to obtain negative permittivity response, we next propose ELC resonators as a new type of waveguide loadings to provide mode control and waveguide miniaturization. iii Dedicated to my family. iv Acknowledgments First and foremost, I would like to express my sincere gratitude to my advisor Prof. Fernando L. Teixeira for his continuous guidance, encouragement, patience and understanding throughout my PhD. He has been a great advisor with patience, calmness and guidance and I felt very fortunate to work with him. His perspective and approach on scientific problems was one of the many things that I learned from him that I deeply appreciate. I would also like to thank Prof. Prabhakar Pathak and Prof. Roberto Rojas for participating in my doctoral committee. I would like to thank Prof. Kubilay Sertel for supporting me in my last semester at OSU, which I am very grateful. I would like to extend my sincere appreciation to Prof. Durdu O. Guney for intro- ducing me the metamaterial concept and supporting me during my stay in Houghton, MI. During my studies here at OSU, I have had many good friends that I always felt very fortunate. I would like to thank Ahmed Fouda not only for his friendship but also fruitful discussion on many topics during our coffee breaks. I would like to thank Erdinc Irci, Mustafa Kuloglu and Ugur Olgun for their friendship and help on various aspects of my study. I would like to thank Bunyamin Koz, Yunus Zeytuncu, Yusuf Danisman, Oguz Kurt, Huseyin Acan, Fatih Olmez, Fatih Akyol, Huseyin Ayvaz, Mustafa Yesil, Erdem Ozbek, Mehmet N. Tomac for their friendship over v past five years. I would also like to thank to Seyit A. Sis, Fahri Sarac, Kamil Ciftci, Sinan Savas, Selman Sakar, Orhan Bulan, Kasim Cologlu and all my friends for their valuable friendship. I would like to thank my dear wife Zehra. Without her continuous support and love this work would have not been completed. Thank you for your endless love and support for myself and our daughter Ahsen Neva. Finally, I would like to thank my parents, Halime and Mehmet Kadir, my sister Hale for their unconditional love and support throughout my life. vi Vita March 03, 1983 .............................Born - Canakkale, Turkey 2005 ........................................B.S. Electronics Eng. Gebze Institute of Technology, Turkey 2008 ........................................M.S. Electrical Eng. and Computer Sci. Syracuse University, USA 2005-2007 ..................................Grad. Research & Teaching Assistant Electronics Eng., Gebze Institute of Technology, Turkey 2007-2008 ..................................Graduate Research Associate Electrical Eng. and Computer Sci., Syracuse University, USA 2008-present ................................Graduate Research Associate ElectroScience Laboratory, Electrical and Computer Eng., The Ohio State University, USA Publications Research Publications H. Odabasi, F. L. Teixeira and D. O. Guney, “Electrically small, complementary electric-field-coupled resonator antennas,” Journal of Applied Physics, 113, 084903 (2013), DOI:10.1063/1.4793090. H. Odabasi and F. L. Teixeira, “Analysis of Canonical Low-Profile Radiators on Isoimpedance Metamaterial Substrates,” Radio Science, 47, RS1002, 2012. vii H. Odabasi and F. L. Teixeira, “Impedance-Matched Absorbers and Pseudo Black Holes,” J. Opt. Soc. Am. B., vol. 28, no. 5, pp. 1317–1323, 2011. F. L. Teixeira, H. Odabasi and K. F. Warnick, “Anisotropic Metamaterial Blueprints for Cladding Control of Waveguide Modes,” J. Opt. Soc. Am. B., vol. 27, no. 8, pp. 1603–1609, 2010. Conference Publications H. Odabasi and F. L. Teixeira, “Metamaterial Claddings for Waveguide Miniatur- ization,” IIEEE International Symposium on Antennas and Propagation and USNC- URSI Natinal Radio Science Meeting, Orlando, 2013. H. Odabasi and F. L. Teixeira, “Complementary Electric-Field-Coupled (CELC) Based Resonator Antennas,” IEEE International Symposium on Antennas and Prop- agation and USNC-URSI Natinal Radio Science Meeting, Orlando, 2013. H. Odabasi and F. L. Teixeira, “Low-profile Antennas with Anisotropic Dispersive Metamaterial Substrate,” IEEE International Symposium on Antennas and Propaga- tion and USNC-URSI Natinal Radio Science Meeting, Chicago, 2012. H. Odabasi and F. L. Teixeira, “Analysis of Electromagnetic Pseudo Black-Hole Devices Using FDTD in Cylindrical Grids,” 28th Annual Review of Progress in Applied Computational Electromagnetics, Columbus, 2012. H. Odabasi and F. L. Teixeira, “Isoimpedance Anisotropic Substrates for Planar Antenna Profile Reduction,” USNC-URSI National Radio Science Meeting, Boulder, 2012. H. Odabasi and F. L. Teixeira, “Analysis of Cylindrically Conformal Patch Antennas on Isoimpedance Anisotropic Substrates,” URSI General Assembly and Scientific Symposium, Istanbul, 2011. H. Odabasi, F. L. Teixeira and W. C. Chew, “Analysis of Metamaterial Absorber Blueprints for Optical ‘Black Holes’,” URSI General Assembly and Scientific Sympo- sium, Istanbul, 2011. H. Odabasi and F. L. Teixeira, “Impedance Analysis of Extremely Low-Profile Anten- nas Using Metamaterial Substrates,” IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, Istanbul, 2010. viii Fields of Study Major Field: Electrical and Computer Engineering Studies in: Transformation Optics Prof. F. L. Teixeira Metamaterials Prof. F. L. Teixeira, Prof. Durdu O. Guney Finite Difference Time Domain Prof. F. L. Teixeira Antenna Miniaturization Prof. F. L. Teixeira ix Table of Contents Page Abstract....................................... ii Dedication...................................... iv Acknowledgments.................................. v Vita ......................................... vii ListofTables.................................... xiii ListofFigures ................................... xiv 1. Introduction.................................. 1 1.1 IntroductionandBackground . 1 1.2 Contributions and Organizations of the Dissertation . .... 4 2. A Brief on Metamaterials and Transformation Optics . ..... 8 2.1 OverviewofMetamaterials . 8 2.1.1 Introduction .......................... 8 2.1.2 EffectiveMediumTheory . 10 2.1.3 Retrieval of Effective Parameters . 11 2.2 Overview of Transformation Optics . 15 3. Anisotropic Metamaterial Blueprints for Cladding Control of Waveguide Modes..................................... 20 3.1 Introduction .............................. 20 3.2 Metamaterial Claddings for Waveguide Mode Control . 21 3.2.1 Circular Waveguide . 21 x 3.2.2 Rectangular Waveguide . 25 3.3 Examples ................................ 27 3.4 ConclusionsandFurtherRemarks. 30 4. Analysis of Canonical Low-profile Radiators on Isoimpedance Metamate- rialSubstrates................................. 35 4.1 Introduction .............................. 35 4.2 IsoimpedanceSubstrates. 38 4.3 NumericalResults..........................