Propagation of coherent waves through disordered media, whether optical, acoustic, or radio waves, results in a spatially redistributed random intensity pattern known as speckle -- a statistical phenomenon. The subject of this dissertation is the statistics of monochromatic coherent light traversing disordered photonic lattices and its dependence on the disorder class, the level of disorder and the excitation configuration at the input. Throughout the dissertation, two disorder classes are considered, namely, diagonal and off-diagonal disorders. The latter exhibits disorder-immune chiral symmetry -- the appearance of the eigenmodes in skew-symmetric pairs and the corresponding eigenvalues in opposite signs. When a disordered photonic lattice, an array of evanescently coupled waveguides, is illuminated with an extended coherent optical field, discrete speckle develops. Numerical simulations and analytical modeling reveal that discrete speckle shows a set of surprising features, that are qualitatively indistinguishable in both disorder classes. First, the fingerprint of transverse Anderson localization -- associated with disordered lattices, is exhibited in the narrowing of the spatial coherence function. Second, the transverse coherence length (or speckle grain size) freezes upon propagation. Third, the axial coherence depth is independent of the axial position, thereby resulting in a coherence voxel of fixed volume independently of position. When a single lattice site is coherently excited, I discovered that a thermalization gap emerges for light propagating in disordered lattices endowed with disorder-immune chiral symmetry. In these systems, the span of sub-thermal photon statistics is inaccessible to the input coherent light, which -- once the steady state is reached -- always emerges with super-thermal statistics no matter how small the disorder level. An independent constraint of the input field for the chiral symmetry to be activated and the gap to be observed is formulated. This unique feature enables a new form of photon-statistics interferometry: by exciting two lattice sites with a variable relative phase, as in a traditional two-path interferometer, the excitation-symmetry of the chiral mode pairs is judiciously broken and interferometric control over the photon statistics is exercised, spanning sub-thermal and super-thermal regimes. By considering an ensemble of disorder realizations, this phenomenon is demonstrated experimentally: a deterministic tuning of the intensity fluctuations while the mean intensity remains constant. Finally, I examined the statistics of the emerging light in two different lattice topologies: linear and ring lattices. I showed that the topology dictates the light statistics in the off-diagonal case: for even-sited ring and linear lattices, the electromagnetic field evolves into a single quadrature component, so that the field takes discrete phase values and is non-circular in the complex plane. As a consequence, the statistics become super-thermal. For odd-sited ring lattices, the field becomes random in both quadratures resulting in sub-thermal statistics. However, this effect is suppressed due to the transverse localization of light in lattices with high disorder. In the diagonal case, the lattice topology does not play a role and the transmitted field always acquires random components in both quadratures, hence the phase distribution is uniform in the steady state.

[pt] Este estudo apresenta um método computacional para modelar campos eletromagnéticos em guias de onda retangulares curvados com seção transversal uniforme, usando o método variacional de Rayleigh-Ritz. Potenciais aplicações desta pesquisa em engenharia incluem o projeto de alimentadores para antenas, conversores de modais na faixa de micro-ondas, filtros, entre outros. Embora vários modelos tenham sido propostos para resolver este problema, as técnicas numéricas convencionais baseadas em elementos finitos, diferenças finitas e volumes finitos requerem altos custos computacionais. Para superar esses problemas, foi desenvolvida uma formulação variacional para resolver as equações de Maxwell em um sistema de coordenadas toroidal local, por meio de um novo funcional introduzido neste trabalho. O funcional foi adaptado para domínios uniformemente curvados com seção transversal arbitrária, e investigações analíticas foram conduzidas para confirmar suas características estacionárias. O formalismo Rayleigh-Ritz foi utilizado para converter o funcional em um problema equivalente de autovalores e autovetores, usando uma expansão em harmônicas retangulares de um guia de onda reto como funções de base para modelar um guia de onda retangular curvo. Um algoritmo numérico foi desenvolvido em Matlab para validar nosso modelo, e os resultados foram comparados com soluções perturbacionais e numéricas de referência, demonstrando alta precisão e menor custo computacional. / [en] This study presents a computational method for modeling electromagnetic fields in curved rectangular waveguides with uniform cross-section, using the variational Rayleigh-Ritz method. The potential applications of this research in engineering include the design of feeders for antennas, microwave mode converter devices, filters, among others. While various models have been proposed to solve this problem, conventional numerical techniques based on finite elements, finite differences, and finite volumes require high computational costs. To overcome these issues, a variational formulation for solving Maxwell s equations in a local toroidal coordinate system was developed via a novel functional introduced in this work. The functional was adapted to handle uniformly bend domains with arbitrary cross-section, and analytical investigations were conducted to confirm its stationary characteristics. The Rayleigh-Ritz formalism was employed to convert the functional into an equivalent problem of eigenvalues and eigenvectors using an expansion in terms of rectangular harmonics of a straight waveguide as basis functions for modeling a bend rectangular waveguide. A numerical algorithm was developed in Matlab to validate our model, and the results were compared against reference perturbational and numerical solutions, demonstrating high accuracy and lower computational costs.

The absorptance in vertical nanowire (nw) arrays is typically dominated by three optical phenomena: radial mode resonances, near-field evanescent wave coupling, and Fabry–Perot (F-P) mode resonances. The contribution of these optical phenomena to GaAs, InP and InAs nw absorptance was simulated using the finite element method. The study compared the absorptance between finite and semi-infinite nws with varying geometrical parameters, including the nw diameter (D), array period (P), and nw length (L). Simulation results showed that the resonance peak wavelength of the HE1n radial modes linearly red-shifted with increasing D. The absorptance and spectral width of the resonance peaks increased as L increased, with an absorptance plateau for very long nws that depended on D and P. Near-field coupling between neighbouring nanowires (nws) was observed to increase with increasing diameter to period ratio (D/P). The effect of F-P modes was more pronounced for shorter nws and weakly coupled light. Based on the collective observation of the correlation between nw geometry and optical phenomena in GaAs, InP, and InAs nw arrays, a periodic array of vertical InSb nws was designed for photodetectors in the low-atmospheric absorption window (λ = 3-5 μm) within the mid-wavelength infrared (MWIR) spectrum (λ = 3-8 μm). Simulations, using the finite element method, were implemented to optimize the nw array geometrical parameters (D, P, and L) for high optical absorptance (~0.8), which exceeded that of a thin film of equal thickness. The results further showed that the HE1n resonance wavelengths in InSb nw arrays can be tuned by adjusting D and P, thus enabling multispectral absorption throughout the near infrared (NIR) to MWIR region. Optical absorptance was investigated for a practical photodetector consisting of a vertical InSb nw array embedded in bisbenzocyclobutene (BCB) as a support layer for an ultrathin Ni contact layer. Polarization sensitivity of the photodetector was examined. Lastly, how light flux enters the nw top and sidewalls on HE11 resonance was investigated. / Dissertation / Doctor of Philosophy (PhD)

I denna avhandling studeras elektromagnetisk vågutbredning i graderade materialkompositer med extraordinära egenskaper. Två sådana materialkompositsystem studeras särskilt, med hjälp av både analytiska och beräkningstekniska elektromagnetiska metoder. Det första systemet används för utvecklingen av en lovande icke-invasiv metod för cancerbehandling, som bygger på att tumören med insatta guldnanopartiklar värms upp med hjälp av mikrovågsstrålning. En vågledarstruktur föreslås bestående av ett tunt dielektriskt skikt med en kontinuerlig graderad materialövergång till dess omgivande material till vardera sidan av skiktet. Det tunna lagret består av cancervävnad med insatta guldnanopartiklar som drivs in i elektroforetisk svängning med hjälp av elektromagnetisk strålning. Analytiska lösningar för det givna vågledarproblemet erhålls, vilket möjliggör beräkning av absorptionskoefficienterna endast inom det tunna skiktet, vilket är viktigt för bedömning av genomförbarheten av den tänkta medicinska tillämpningen. De dispersiva dielektriska modellerna som beskriver de elektromagnetiska egenskaperna hos de relevanta biologiska vävnaderna föreslås och diskuteras. Numeriska simuleringar gjorda i COMSOL Multiphysics är i utmärkt överensstämmelse med och validerar de analytiska resultaten. Det andra systemet involverar vågutbredning från ett högerhänt material till ett vänsterhänt metamaterial i fri rymd. De två materialen är impedansmatchade, vilket säkerställer ingen reflektion, och det graderade gränssnittet mellan dem beskrivs av en kontinuerlig funktion. Metamaterialkompositer med rumsligt varierande materialparametrar har fått ett ökande teoretiskt och experimentellt intresse de senaste två decennierna. De är användbara för ett antal tillämpningar, såsom transformationsoptik. I denna uppsats diskuteras egenskaperna hos vänsterhänta material. Fältlösningarna till det impedansmatchade graderade gränssnittet härleds, och en numerisk modell utvecklas i COMSOL. Resultaten bekräftar de extraordinära egenskaperna hos vänsterhänta material. / In this thesis, electromagnetic wave propagation in graded material composites with extraordinary properties are studied. Two such material composite systems are studied in particular, using both analytical and computational electromagnetic methods. The first system is used for the development of a promising non-invasive method of cancer treatment based on heating the tumors with inserted gold nanoparticles by means of microwave radiation. A waveguide structure is proposed consisting of a thin dielectric layer with a continuous graded material transition to its surrounding materials to either side of the layer. The thin layer consists of cancer tissue with inserted gold nanoparticles that are driven into electrophoretic oscillation by means of electromagnetic radiation. Analytical solutions for the given waveguide problem are obtained, allowing the calculation of the absorption coefficients within the thin layer only, which is important for assessment of the feasibility of the envisioned medical application. The dispersive dielectric models describing the electromagnetic properties of the relevant biological tissues are proposed and discussed. Numerical simulations done in COMSOL Multiphysics are in excellent agreement with and validate the analytical results. The second system involves wave propagation from a right-handed material to a left-handed metamaterial in an open boundary system. The two materials are impedance-matched, thus ensuring no reflection, and the graded interface between them is described by a continuous function. Metamaterial composites with spatially varying material parameters have been given an increasing theoretical and experimental interest the last two decades. They are useful for a number of applications, such as transformation optics. In this thesis, the properties of left-handed media are discussed. The field solutions to the impedance-matched graded interface are derived, and a numerical model is developed in COMSOL. The results confirm the extraordinary properties of left-handed media. / <p>QC 20221129</p>

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[ES] La Teoría de Modos Característicos (TCM), desarrollada por R.F. Harrington a mediados de los años 60, se ha convertido desde los inicios del siglo XXI, en una herramienta fundamental para el diseño sistemático de antenas, gracias a la visión física que aporta de los fenómenos de radiación. Actualmente, numerosos grupos de investigación a nivel mundial han adoptado esta teoría dentro de su metodología de diseño. No obstante, la teoría de modos característicos ha sido utilizada mayormente para el análisis de estructuras planas, existiendo pocos ejemplos de aplicación de la teoría a estructuras 3D, dada la dificultad que implica su análisis. Esta tesis tiene como objetivo diseñar antenas multi-alimentadas con un gran ancho de banda usando la TMC. La principal novedad que aporta, es la aplicación de la teoría de modos característicos al análisis de estructuras 3D y el empleo de multi alimentación para excitar de forma selectiva modos concretos de radiación. Inicialmente se presenta un análisis de estructuras planas que interactúan entre sí, y se utiliza una combinación de puertos para forzar la excitación de ciertos modos con buen comportamiento radiante. Además, se demuestra que las resonancias de una antena, no solamente son causadas por un modo en resonancia, sino que también aparecen como resultado de la combinación de modos magnéticos y eléctricos. En la tesis se proponen diseños de antenas con muy bajo perfil, obtenidas a partir del plegado progresivo de las estructuras planas previamente estudiadas. Con las técnicas de plegado se consiguen antenas compactas y de bajo perfil, fácilmente integrables, que presentan muy buenas características de radiación y una forma de excitación sencilla. Se realiza un estudio sistemático de estructuras canónicas en 3 dimensiones, como las guías de onda rectangular y circular. En primer lugar, las guías de onda y cavidades equivalentes se analizan con un enfoque clásico, obteniendo los modos de campo transversal eléctrico TE y transversal magnético TM. A continuación, se analizan las mismas guías y cavidades aplicando la teoría de modos característicos, unificando y comparando por primera vez los dos tipos de analisis. Las conclusiones extraídas del análisis de las guías de onda rectangular y circular, se han aplicado para diseñar dos tipos de antenas, que proporcionan buen ancho de banda y características de radiación óptimas para aplicaciones 5G. La tesis incluye un capítulo en el que se proponen distintos prototipos de antenas, diseñados a partir de la aplicación de la teoría de modos característicos. Se aprovechan las conclusiones obtenidas en cada uno de los capítulos de la tesis y se aplican a diseños específicos, demostrando que empleando la TCM, es posible diseñar antenas que tengan buenas características de radiación y que pueden integrarse fácilmente en dispositivos que operen con nuevas tecnologías, como 5G o IoT. / [CA] La Teoria de Modes Característics (TCM), desenvolupada per R.F. Harrington a mitjans dels anys 60, s'ha convertit des dels inicis de segle XXI, en una eina fonamental per al disseny sistemàtic d'antenes, gràcies a la visió física que aporta dels fenòmens de radiació. Actualment, nombrosos grups d'investigació a nivell mundial han adoptat aquesta teoria dins de la seva metodologia de disseny. No obstant això, la teoria de modes característics ha estat utilitzada majorment per l'anàlisi d'estructures planes, i hi ha pocs exemples d'aplicació de la teoria a estructures 3D, donada la dificultat que implica el su anàlisi. Aquesta tesi té com a objectiu dissenyar antenes multi-alimentades amb un gran ample de banda usant la TMC. La principal novetat que aporta és l'aplicació de la teoria de modes característics a l'anàlisi d'estructures 3D i l'us de multi alimentació per excitar de forma selectiva modes concrets de radiació. Inicialment es presenta un anàlisi d'estructures planes que interactuen entre si, i s'utilitza una combinació de ports per forçar l'excitació de determinats modes amb bon comportament radiant. A més, es demostra que les ressonàncies d'una antena, no solament són causades per un mode en ressonància, sinó que també apareixen com a resultat de la combinació de modes magnètics i elèctrics. A la tesi es proposen dissenys d'antenes amb molt baix perfil, obtingudes a partir del plegat progressiu de les estructures planes prèviament estudiades. Amb les tècniques de plegat s'aconsegueixen antenes compactes i de baix perfil, fàcilment integrables, que presenten molt bones característiques de radiació i una forma d'excitació senzilla. Es realitza un estudi sistemàtic d'estructures canòniques en 3 dimensions, com les guies d'ona rectangular i circular. En primer lloc, les guies d'ona i cavitats equivalents s'analitzen amb un enfocament clàssic, obtenint els modes de camp transversal elèctric ET i transversal magnètic TM. A continuació, s'analitzen les mateixes guies i cavitats aplicant la teoria de modes característics, unificant i comparant per primera vegada els dos tipus d'anàlisi. Les conclusions extretes de l'anàlisi de les guies d'ona rectangular i circular, s'han aplicat per dissenyar dos tipus d'antenes, que proporcionen bon ample de banda i característiques de radiació òptimes per a aplicacions 5G. La tesi inclou un capítol en el qual es proposen diferents prototips d'antenes, dissenyats a partir de l'aplicació de la teoria de modes característics. S'aprofiten les conclusions obtingudes en cada un dels capítols de la tesi i s'apliquen a dissenys específics, demostrant que emprant la TCM, és possible dissenyar antenes que tinguen bones característiques de radiació i que poden integrar-se fàcilment en dispositius que operen amb noves tecnologies, com 5G o IoT. / [EN] The Theory of Characteristic Modes (TCM), developed by R.F. Harrington in the mid 1960's, has become, since the beginning of the 21st century, a fundamental tool for systematic antenna design, thanks to the physical vision it provides of radiation phenomena. Currently, many research groups worldwide have adopted this theory as part of their design methodology. However, the theory of characteristic modes has been used mainly for the analysis of planar structures, and there are few examples of application of the theory to 3D structures, given the difficulty involved in its analysis. This thesis aims to design multi-fed antennas with high bandwidth using TCM. The main novelty contribution is providing the application of characteristic modes theory to the analysis of 3D structures and the use of multi-feed to selectively excite specific radiation modes. Initially, an analysis of plane structures that interact with each other is presented, and a combination of ports is used to force the excitation of certain modes with good radiant behavior. Furthermore, it is shown that the resonances of an antenna are not only caused by a resonance mode, but also appear as a result of the combination of magnetic and electrical modes. The thesis proposes antenna designs with very low profile, obtained from the progressive folding of the previously studied planar structures. With the folding techniques, compact and low-profile antennas are designed, easily integrated, with very good radiation characteristics and a simple form of excitation. A systematic study of 3-dimensional canonical structures, such as rectangular and circular waveguides, is carried out. First, the waveguides and equivalent cavities with a classical approach are analyzed, obtaining the transverse electric TE and transverse magnetic TM field modes. Then, the same waveguides and cavities are analyzed applying the theory of characteristic modes, unifying and comparing for the first time the two types of analysis. The conclusions drawn from the analysis of the rectangular and circular waveguides have been applied to design two types of antennas, which provide good bandwidth and optimal radiation characteristics for 5G applications. The thesis includes a chapter in which different antenna prototypes are proposed, designed from the application of the characteristic modes theory. The conclusions obtained in each chapters of the thesis are taken advantage of and applied to specific designs, showing that using TCM, it is possible to design antennas that have good radiation characteristics and that can be easily integrated into devices that operate with new technologies. like 5G or IoT. / Peñafiel Ojeda, CR. (2021). Design of Multi-feed UWB Antennas using the Theory of Characteristic Modes [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/175186