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Microwave Metamaterials for Compact Filters and Antennas

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Microwave Metamaterials for Compact Filters and Antennas Microwave Metamaterials for Compact Filters and Antennas vorgelegt von M.Sc Merih Palandöken aus Kahramanmaras Von der Fakultät IV-Elektrotechnik und Informatik der Technischen Universität Berlin zur Erlangung des akademischen Grades Doktor der Ingenieurwissenschaften Dr.-Ing genehmigte Dissertation Promotionsausschuss: Vorsitzender: Prof. Dr.-Ing. Klaus Petermann Berichter: Prof. Dr.-Ing. Heino Henke Berichter: Prof. Dr. Sergey I. Bozhevolnyi Tag der wissenschaftliche Aussprache: 06. September 2012 Berlin 2012 D83 i Acknowledgements It is my pleasure to express my deepest gratitude and respect to Prof. Dr.-Ing Heino Henke for his invaluable guidance, helpful suggestions, endless support and patience. His personal and academic virtue shaped my academic personality and changed my approach to scientific study. I am very lucky to have the opportunity to study under his supervision. I would like to thank to the members of my thesis committee, Prof. Dr. Sergey I. Bozhevolnyi and Prof. Dr.-Ing. Klaus Petermann for reading the manuscript and commenting on the thesis. I am very fortunate to have been a member of TET family, where I had a chance to work together and benefit from intelligent and excited people. I am very thankful to Dr.-Ing Manfred Filtz for motivating scientific discussions about the electromagnetic field theory, continuous support, patience and nice chance to be an evidence for his brilliant thinking approaches. Special and deep thanks to Dr. –Ing Heinrich Büssing for his incredible help, understanding and irreplaceable friend- and brothership during my research life. I would like to thank all members of TET family for their help in my doctorate period. I thank also very much to Dr.-Ing Tolga Tekin in the Department of Nano Interconnect Technology due to his help during and after my doctorate research. I am also very thankful to Prof. Dr. Siddik Yarman, the Department Chair of Electrical and Electronics Engineering at Istanbul University for his continuous motivating advices and support during my doctorate research. I would like to express my endless thanks to my mother and father for their love, encouragement and care. ii Zusammenfassung Werkstoffe mit gleichzeitig negativer Permittivität und Permeabilität in einem bestimmten Frequenzband wurden zuerst von Veselago im Jahr 1968 theoretisch untersucht. Er bezeichnet solche Medien als linkshändige Materie (LHM), weil die Vektoren des elektrischen Feldes, des Magnetfeldes und der Wellenausbreitungsrichtung ein linkshändiges System aufspannen. Weil solche Materialien in der Natur nicht vorkommen, konnten die vorhergesagten optischen und elektromagnetischen Konsequenzen aus Veselago‘s Arbeit erst ca. 30 Jahre nach deren Veröffentlichung beobachtet werden. Im Jahr 2000 wurde an einem künstlich zusammengesetzten Material, das auch als ein Metamaterial bekannt ist, und aus periodisch angeordneten negativen Permittivitäts- und Permeabilitätszellen in der Form von metallischen Drähten und Spaltringen aufgebaut ist, linkshändige Eigenschaft gezeigt. Weil die Abmessung der Drähte und Ringe klein im Vergleich zu der Wellenlänge sind, ist es möglich, die elektromagnetischen Eigenschaften dieser Strukturen durch eine effektive Permittivität und Permeabilität zu approximieren. In dieser Arbeit werden die grundlegenden Eigenschaften negativer Permeabilität, Permittivität und linkshändiger Materialien beim Entwurf von Antennen und Filtern als potenzielle Anwendungen in der Mikrowellentechnik erforscht. Bei der Untersuchung grundlegender Eigenschaften und alternativer Design-Methoden von Metamaterialien, widmet sich diese Arbeit zunächst den künstlichen magnetischen Materialien. Diese künstlichen magnetischen Materialien liegen in Form von metallischen Zylindern mit oder ohne Spalten oder Spaltringresonatoren vor. Approximierte Formulierungen für die effektive Permeabilität werden abgeleitet. Die Berechnungen der Transmissions- und Reflexionsparameter von konzentrischen Zylindern mit Spalten werden auf analytischem Wege und auch numerisch durchgeführt. Die gute Übereinstimmung zwischen analytischen und numerischen Berechnungen wird bestätigt. Die Resonanzfrequenz der Spaltringresonatoren ist zusätzlich nach einem quasistationären Ansatz berechnet worden. Es wird gezeigt, dass die Ergebnisse der numerischen Berechnungen besser mit den Ergebnissen aus dem quasistationären Ansatz übereinstimmen. Das 1D-Dispersionsdiagramm der Spaltringresonatoren wird numerisch untersucht. Effektive Materialparameter werden extrahiert, um die Frequenzabhängigkeit der effektiven Permeabilität nach dem Lorentz-Modell zu bestätigen. Zur Untersuchung eines homogeneren Materialdesigns, wird ein fraktaler Spiralresonator als Einheitszelle mit negativer Permeabilität zum Einsatz gebracht. Es wird bestätigt, dass die effektive Permeabilität im gesamten Bereich zwischen der magnetischen Plasmafrequenz und der Resonanzfrequenz negativ ist und einen kapazitiven Wellenwiderstand aufweist. Eine zweite Art künstliche Materie, bestehend aus periodisch angeordneten metallischen Drähten, wird durch analytische und numerische Berechnungen untersucht. Es wird gezeigt, dass die effektive Permittivität einer solchen Drahtanordnung eine Frequenzabhängigkeit nach dem Drude-Modell aufweist und bei Frequenzen unterhalb der Plasmafrequenz negativ ist. Auch hier sind die Ergebnisse der numerischen und analytischen Rechnungen in guter Übereinstimmung. Um stärker homogenisierte Metamaterialien zu entwickeln, wird ein fraktaler Antispiralresonator (fractal anti-spiral-resonator) als Einheitszelle eines Materials mit negativer Permittivität untersucht. Es wird gezeigt, dass das Material zwischen der elektrischen Plasma- und Resonanzfrequenz negative Permittivität bei induktivem Wellenwiderstand aufweist. iii Als letzte Untersuchung der Grundlagen von Metamaterialien, wird das Design linkshändiger Materialien erforscht. Die Eigenmodegleichung eines rechteckigen Hohlleiters, der periodisch mit Zellen negativer Permittivität und Permeabilität bestückt wird, wird analytisch und numerisch berechnet. Es wird gezeigt dass die Ergebnisse der analytischen und numerischen Rechnungen gut übereinstimmen. Darüber hinaus wird eine herkömmliche LHM Einheitszelle numerisch untersucht. Es wird bestätigt, dass das linkshändige Transmissionsband der Überlappungsbereich des negativen Permittivitäts- und Permeabilitätsbands ist.Eine kompakte Zellgeometrie, die auf Spiralresonatoren basiert, welche mit Drähten belastet werden, wird als Alternative zu den herkömmlichen Zelldesigns untersucht. Es wird aus numerischen Berechnungen abgeleitet, dass solche belasteten Resonatoren bei der Gestaltung von homogener LHM verwendet werden können. Als nächstes werden zwei mögliche Anwendungsbereiche in der Mikrowellentechnik untersucht. Der erste Bereich ist Antennendesign. Zwei Meta-Antennen werden untersucht. Die erste Antenne ist eine breitbandige Dipolantenne, bei der die Dipolelemente durch LHM Einheitszellen in Form eines Arrays belastet werden. Die Breitbandigkeit dieser Antenne wird experimentell durch Messung und durch die Ergebnisse der numerischen Rechnung bestätigt. Es wird mit Hilfe der Oberflächenstromverteilung und Richtcharakteristik gezeigt, dass LHM Einheitszellen mit einem geringeren Strahlungsgewinn im Vergleich zu der Dipolantenne abstrahlen. Darüber hinaus ist aus den numerischen Ergebnissen abgeleitet, dass durch Anpassung der Phasendifferenz von Zelle zu Zelle die Abstrahlungseffizienz erhöht werden kann. Mögliche Methoden zur Verbesserung des Antennengewinns werden aufgezeigt, von denen eine im Design der zweiten Antenne verwendet ist. Die zweite Antenne ist eine Schlitzantenne, welche mit elektrischen und magnetischen Dipolen in Form von geschlitzten Metamaterialzellen im Abstrahlelement gestaltet wird. Es wird numerisch bestätigt, dass die Antenne schmalbandig mit hoher Abstrahlungseffizienz und Gewinn ist. Die zweite Anwendung ist der Filterentwurf. Zwei Meta-Filter sind untersucht. Der erste Filter ist ein kompakter Bandsperrfilter, welcher durch galvanische Kopplung von vier LHM Zellen in der Form von λ/4-Resonatoren mit Speiseleitung gestaltet wird. Die Wirkung der Bandsperre wird durch experimentelle und numerische Ergebnisse bestätigt. Das zweite Design ist ein kompakter Bandpassfilter, der durch Kopplung von zwei Elementarzellen, die direkt mit der Speiseleitung verbunden sind, entworfen ist. Es ist numerisch gezeigt, dass eine niedrige Einfügedämpfung und hohe Selektivität durch die Optimierung der Feld- Kopplung zwischen den Resonatoren erreicht werden kann. Ein Vorteil der beiden Filter ist, dass es keine Notwendigkeit für eine Anpassungsschaltung gibt, wodurch die Filtergröße deutlich reduziert wird. iv Abstract Materials with simultaneous negative permittivity and permeability in a certain frequency band were first studied by Veselago in 1968. He termed such media left-handed media due to the left-handed triad formed by the electric field, magnetic field and the phase propagation vector. Because of the inexistence of such materials in nature, the optical and electromagnetic consequences examined in Veselago’s work could only be observed after nearly 30 years. In 2000, a composite material, also known as a metamaterial, consisting of periodic negative permittivity and permeability cells in the form of metallic wires and split rings was shown to exhibit left-handed properties. Because the dimension of the rods and rings are small compared to the operation wavelength, it is possible to approximately describe their bulk electromagnetic
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