This thesis analyzes some aspects of electromagnetic wave propagation in double negative materials. Double negative materials have negative refractive indices. They are backward-wave materials. Plane waves undergo negative refraction at interfaces between double positive and double negative media. Causality principle implies these properties. High frequency plane wave scattering from a double negative infinitely long cylinder has been analyzed by using modified Watson transform, geometrical optics and Mie series. Mie series results and the modified Watson transform results have been found to be in good agreement. Hence, the physical mechanism of the scattering has been revealed.

Dissertation (Ph. D.)--University of Akron, Dept. of Electrical and Computer Engineering, 2009. / "August, 2009." Title from electronic dissertation title page (viewed 9/23/2009) Advisor, Igor Tsukerman; Committee members, Nathan Ida, Iqbal Husain, Ernian Pan; Department Chair, Alex De Abreu Garcia, Dmitry Golovaty; Dean of the College, George K. Haritos; Dean of the Graduate School, George R. Newkome. Includes bibliographical references.

After being theorized by Veselago in 1967, recent developments in metamaterials over the last two decades have allowed scientists and researchers to physically demonstrate that artificial composite media can be engineered to exhibit exotic material properties, such as negative refractive index, by exploiting features in arrays of sub-wavelength unit inclusions. These unconventional electromagnetic properties are realized through the coupling of the microscopic unit inclusions, which govern the macroscopic properties of the structure. After demonstrating that a periodic array of capacitively-loaded loop (CLL) inclusions paired with continuous wire results in negative refraction, this study performs numerical simulations to characterize random metamaterial structures. These structures consist of CLLs that are randomized in both position and orientation. In addition, this thesis introduces an innovative antenna enhancing structure consisting of capacitively-loaded loop (CLL) metamaterial elements loaded radially around a standard dipole antenna at an electrically small distance. As a result of this innovative arrangement, the dipole antenna is easily transformed into a directive mechanically scanned antenna with high realized gain. The desired directivity and gain can be tuned based on the number of radial CLL fins placed around the dipole. Interactions between the antenna and metamaterial elements result in significant enhancement of the maximum radiated field amplitude and front-to-back ratio. This innovative CLL-loaded dipole antenna is compared to the conventional Yagi-Uda antenna. The structures presented in this thesis are modeled using full-wave simulation, and one antenna structure is experimentally verified as a proof-of-concept. / Master of Science

The Maxwell equations of electromagnetism form the foundation of classical electromagnetism, and are of interest to mathematicians, physicists, and engineers alike. The first part of this thesis concerns boundary value problems for the anisotropic Maxwell equations in Lipschitz domains. In this case, the material parameters that arise in the Maxwell system are matrix valued functions. Using methods from functional analysis, global in time solutions to initial boundary value problems with general nonzero boundary data and nonzero current density are obtained, only assuming the material parameters are bounded and measurable. This problem is motivated by an electromagnetic inverse problem, similar to the classical Calder\'on inverse problem in Electrical Impedance Tomography. The second part of this thesis deals with materials having negative refractive index. Materials which possess a negative refractive index were postulated by Veselago in 1968, and since 2001 physicists were able to construct these materials in the laboratory. The research on the behavior of these materials, called metamaterials, has been extremely active in recent years. We study here refraction problems in the setting of Negative Refractive Index Materials (NIMs). In particular, it is shown how to obtain weak solutions (defined similarly to Brenier solutions for the Monge-Amp\`ere equation) to these problems, both in the near and the far field. The far field problem can be treated using Optimal Transport techniques; as such, a fully nonlinear PDE of Monge-Amp\`ere type arises here. / Mathematics

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The dispersion property of periodic structures is a hot research topic in the last decade. By exploiting dispersion properties, one can manipulate the propagation of electromagnetic waves, and produce effects that do not exist in conventional materials. This thesis is devoted to two important dispersion effects: negative refraction and designed surface plasmons. First, we introduce negative refraction and designed surface plasmons, including a historical perspective, main areas for applications and current trends. Several numerical methods are implemented to analyze electromagnetic effects. We apply the layer-KKR method to calculate the electromagnetic wave through a slab of photonic crystals. By implementing the refraction matrix for semi-infinite photonic crystals, the layer-KKR method is modified to compute the coupling coefficient between plane waves and Bloch modes in photonic crystals. The plane wave method is applied to obtain the band structure and the equal-frequency contours in two-dimensional regular photonic crystals. The finite-difference time-domain method is widely used in our works, but we briefly discuss two calculation recipes in this thesis: how to deal with the surface termination of a perfect conductor and how to calculate the frequency response of high-Q cavities more efficiently using the Pad\`{e} approximation method. We discuss a photonic crystal that exhibits negative refraction characterized by an effective negative index, and systematically analyze the coupling coefficients between plane waves in air and Bloch waves in the photonic crystal. We find and explain that the coupling coefficients are strong-angularly dependent. We first propose an open-cavity structure formed by a negative-refraction photonic crystal. To illuminate the physical mechanism of the subwavelength imaging, we analyze both intensity and phase spectrum of the transmission through a slab of photonic crystals with all-angle negative refraction. It is shown that the focusing properties of the photonic crystal slab are mainly due to the negative refraction effect, rather than the self-collimation effect. As to designed surface plasmons, we design a structured perfectly conducting surface to achieve the negative refraction of surface waves. By the average field method, we obtain the effective permittivity and permeability of a perfectly conducting surface drilled with one-dimensional periodic rectangle holes, and propose this structure as a designed surface plasmon waveguide. By the analogy between designed surface plasmons and surface plasmon polaritons, we show that two different resonances contribute to the enhanced transmission through a metallic film with an array of subwavelength holes, and explain that the shape effect is attributed to localized waveguide resonances. / QC 20100817

Photonic crystals (PhCs) are periodic dielectric structures that exhibit a photonic bandgap, i.e., a range of wavelength for which light propagation is forbidden. The special band structure related dispersion properties offer a realm of novel functionalities and interesting physical phenomena. PhCs have been manufactured using semiconductors and other material technologies. However, InP-based materials are the main choice for active devices at optical communication wavelengths. This thesis focuses on two-dimensional PhCs in the InP/GaInAsP/InP material system and addresses their fabrication technology and their physical properties covering both material issues and light propagation aspects. Ar/Cl2 chemically assisted ion beam etching was used to etch the photonic crystals. The etching characteristics including feature size dependent etching phenomena were experimentally determined and the underlying etching mechanisms are explained. For the etched PhC holes, aspect ratios around 20 were achieved, with a maximum etch depth of 5 microns for a hole diameter of 300 nm. Optical losses in photonic crystal devices were addressed both in terms of vertical confinement and hole shape and depth. The work also demonstrated that dry etching has a major impact on the properties of the photonic crystal material. The surface Fermi level at the etched hole sidewalls was found to be pinned at 0.12 eV below the conduction band minimum. This is shown to have important consequences on carrier transport. It is also found that, for an InGaAsP quantum well, the surface recombination velocity increases (non-linearly) by more than one order of magnitude as the etch duration is increased, providing evidence for accumulation of sidewall damage. A model based on sputtering theory is developed to qualitatively explain the development of damage. The physics of dispersive phenomena in PhC structures is investigated experimentally and theoretically. Negative refraction was experimentally demonstrated at optical wavelengths, and applied for light focusing. Fourier optics was used to experimentally explore the issue of coupling to Bloch modes inside the PhC slab and to experimentally determine the curvature of the band structure. Finally, dispersive phenomena were used in coupled-cavity waveguides to achieve a slow light regime with a group index of more than 180 and a group velocity dispersion up to 10^7 times that of a conventional fiber. / QC 20100712

In this thesis devices for controlling the flow of surface plasmon polaritons are described. Dielectric and metallic nanostructures were designed for this purpose, and characterized by leakage radiation microscopy in real and in reciprocal spaces. Manipulation of surface plasmons by dielectric lenses and gradient index elements is presented, and negative refraction, steering and self-collimation of surface plasmons in one- and two-dimensional plasmonic crystals is demonstrated. The achieved degree of control was applied for routing of nanoparticles by optical forces, as well as for two methods of enhancing the figures of merit of plasmonic refractive index sensors, based on the one hand on Fano resonances natural to leakage radiation microscopy, and on the other hand on anisotropie plasmonic bandstructures.

Arrays of free-standing metallic nanorods are promising candidates for sensors, switches and spectroscopy. They have structure sizes much smaller than the wavelength of visible light, feature a long-axis surface plasmonic resonance (LSPR) and show metamaterial-like properties. This thesis provides a detailed investigation of their linear optical properties and highlights some nonlinear optical aspects. By means of graded structures having a tunable LSPR and three different theoretical models -- a numerical multiple-multipole method (MMP) model, a semi-analytic collective surface plasmon (CSP) model and an analytic dipolar interaction model (DIM) -- the optical properties were analyzed. Using the DIM, the experimentally observed blueshift of the LSPR in comparison to a single nanorod is confirmed and a physical explanation is provided. The LSPR strongly depends on the angle of incidence and the rod diameter. However, for a varying length the changes are small with the long-axis mode showing a lower energy limit. The detailed arrangement of the nanorods and the azimuthal angle of the incoming light plays only a minor role for small nanorod separations. Similarly, the dependence on the metal is the same as for single particles, whereas the sensitivity to the surrounding dielectric is much stronger than in the single-particle case. For longer nanorods made of silver, angle-dependent higher-order modes are observed and reproduced using MMP. The CSP model is applied and Fabry-Pérot-like oscillations of the CSPs are found. The propagating nature of these modes leads to the discovery that the p component of the transmitted light experiences a phase jump and to the observation of polarization conversion inside the structures. Negative refraction is found in nanorod arrays; it is revealed that a negative energy flux occurs only within a bandwidth given by the LSPR of a single nanorod and the array resonance. For smaller wavelengths, the in-plane component of the Poynting vector reverses, leading to an (extraordinary) positive flux. At the LSPR itself, the flux parallel to the surface is found to be zero. The negative refraction is also exploited to mimic a nanolens with structure parameters that are infact technical realizable. In the visible regime the nanolens shows a NA of 1.06 and superlens-like features such as identical rotation and linear translation of image and object. The nonlinear measurements on graded structures are conducted using femtosecond pump-probe spectroscopy resulting in kinetics showing either an increased transmission or absorption with signal changes of up to 40%. By converting them to transient spectra and by comparison with the literature, electron distribution changes at the Fermi edge and hot electrons/phonons are identified as the main reasons for the changes. Probing at the inflection points of the LSPR reveals ultrafast signals. Using transient spectra they are traced back to a short blueshift of the LSPR. / Strukturen aus frei stehenden metallischen Nanostäbchen versprechen interessante An­wendungen als Sensoren, Schalter und in der Spektroskopie. Da ihre Strukturgrößen kleiner als die Wellenlänge des sichtbaren Lichtes sind, besitzen sie eine langachsige Oberflächen­plasmonenresonanz (LSPR) und weisen metamaterialartige Eigenschaften auf. In dieser Dissertation werden die linearen und nichtlinearen optischen Eigenschaften solcher Struk­turen im Detail untersucht. Mit Hilfe von Gradientenstrukturen, die eine durchstimmbare LSPR besitzen, und dreier theoretischer Modelle – eines numerischen Modells basierend auf der Methode der mul­tiplen Multipole (MMP), eines semianalytischen Modells kollektiver Oberflächenplasmonen (CSP) sowie eines analytischen dipolaren Interaktionsmodells (DIMs) – werden die op­tischen Eigenschaften analysiert. Unter Verwendung des DIMs wird die experimentell beobachtete Blauverschiebung der LSPR im Vergleich zur Resonanz eines Einzelstäbchens bestätigt und eine physikalische Erklärung dafür geliefert. Die LSPR ist stark vom Einfallswinkel und vom Stäbchendurch­messer abhängig. Im Unterschied dazu sind die Änderungen bei einer Längenvariation klein, wobei die langachsige Mode ein unteres Energielimit aufweist. Weiterhin haben die genaue Anordnung der Stäbchen und der azimutale Winkel des einfallenden Lichtes nur einen untergeordneten Einfluss. Die Abhängigkeit vom verwendeten Metall ist analog zu einem Einzelstäbchen, während die Empfindlichkeit in Bezug auf das Umgebungsmedium wesentlich stärker ist. Längere Nanostäbchen aus Silber zeigen winkelabhängige Moden höherer Ordnung, welche mittels MMP reproduziert werden können. Das CSP-Modell wird ebenfalls darauf ange­wendet, wobei Fabry-Pérot-artige Oszillationen der CSPs entdeckt werden. Die propa­gierende Natur der CSPs führt zur Entdeckung eines Phasensprungs der p‑Komponente des transmittierten Lichtes sowie zur Beobachtung von Polarisationskonversion in den Strukturen. Nanostäbchen-Arrays weisen außerdem negative Brechung auf. Es wird gezeigt, dass ein negativer Energiefluss nur in dem Wellenlängenbereich zwischen der LSPR der Einzelstäb­chen und der Arrayresonanz auftritt. Für kleinere Wellenlängen kehrt sich die in der Ebene befindende Poynting-Vektor-Komponente um, was zu einer (außerordentlichen) positiven Brechung führt. An der LSPR selbst ist der zur Strukturebene parallele Fluss Null. Die negative Brechung wird ferner ausgenutzt, um eine Nanolinse mit realistischen Struktur­parametern zu simulieren. Im sichtbaren Bereich zeigt sie eine NA von 1,06 und super­linsenartige Eigenschaften, wie eine identische Rotation und eine lineare Translation von Bild und Objekt. Die nichtlinearen Messungen an Gradientenstrukturen werden mittels Femtosekunden-Pump-Probe-Spektroskopie durchgeführt und liefern Kinetiken, welche entweder eine ver­stärkte Transmission oder eine verstärkte Absorption mit Signalstärken von bis zu 40% aufweisen. Durch Konvertierung in transiente Spektren und Vergleich mit der Literatur werden eine veränderte Elektronverteilung an der Fermi-Kante und heiße Elektronen/Pho­nonen als Ursache für die Änderungen gefunden. Das Abtasten mit dem Probe-Puls an den Wendepunkten der Resonanz offenbart ultraschnelle Signale. Mit Hilfe der transienten Spektren wird dies auf eine kurzzeitige Blauverschiebung der LSPR zurückgeführt.