Caracterización modal de sistemas guiadores inhomogéneos: análisis de superficies selectoras de frecuencia dieléctricas.

RESUMEN El primer trabajo realizado en la tesis ha sido el de desarrollar la teoría básica para el estudio riguroso del espectro modal de medios guiadores inhomogéneos (guías blindadas o guías dieléctricas abiertas), como también de medios dieléctricos periódicos infinitos, los cuales son el elemento básico de las SSFD. Para tal fin se ha adaptado el Método de las Bases Bi-Ortogonales, desarrollado inicialmente en el Departamento de Física Aplicada y Electromagnetismo y en el Departamento de Óptica de la Universitat de València al estudio de un amplio espectro de guías ópticas y de microondas. En segundo lugar se ha llevado a cabo el análisis de la dispersión de ondas planas en Superficies Selectoras de Frecuencia Dieléctricas (SSFD), que son estructuras planares multicapa formadas por láminas dieléctricas homogéneas o periódicas en una dimensión. Dentro del análisis de las SSFD, las principales aportaciones y conclusiones de este estudio se resumen a continuación: En primer lugar se ha desarrollado la teoría básica para el estudio del campo electromagnético en regiones dieléctricas con periodicidad en una dirección, empleando para ello el Método de las Bases Bi-Ortogonales en el caso de dieléctricos sin pérdidas, mientras que para el caso de medios con pérdidas se ha empleado el Método de los Momentos. Dada la geometría del problema, se ha planteado una descomposición modal en los modos de Floquet o de Bloch Tipo-E y Tipo-H. Se ha desarrollado un algoritmo eficiente y rápido que se basa en la transformación de las ecuaciones diferenciales que describen la evolución de los campos en el plano transversal, en un problema matricial de autovalores. La resolución del mismo permite obtener las constantes de propagación y los campos eléctrico y magnético modales. Las pérdidas óhmicas en los materiales se pueden incluir de una forma natural en la formulación. Con el fin de analizar la bondad del método propuesto, se han comparado nuestros resultados con los obtenidos en la bibliografía, obteniendo buena concordancia entre ambos, tanto para incidencia 2D como para incidencia 3D. Para el análisis de la dispersión de ondas planas bajo incidencia 3D en SSFD se ha empleado la Técnica de Adaptación Modal, formulada con Matrices de Dispersión Generalizadas. Dicho análisis de dispersión se ha llevado a cabo suponiendo que sobre las SSFD incide una onda plana linealmente polarizada con polarización arbitraria, cuyos campos se han descompuesto en modos de Floquet de orden n=0 tipo-E, tipo-H. Esta descomposición se ha particularizado para los dos casos más habituales, que corresponden a la incidencia de una onda plana con polarización perpendicular y paralela al plano de incidencia, respectivamente, comúnmente conocidas como polarización TE y TM. Se ha desarrollado un programa en FORTRAN que calcula los parámetros de dispersión y los coeficientes de reflexión y transmisión en potencia de estas estructuras a partir de la obtención de la MDG de las mismas. El programa es muy eficiente, con tiempos de computación por punto en frecuencia muy reducidos. Tras ello se han comparado los resultados obtenidos para una serie de estructuras con los proporcionados en la bibliografía, resultando para todos los casos un excelente acuerdo entre ambos. Por último, se ha realizado el diseño de una serie de filtros en reflexión basados en SSFD, que han resultado tener buenas prestaciones. Finalmente, podemos concluir que el modelo desarrollado permite tratar con eficacia tanto el estudio del espectro modal en sistemas guiadores inhomogéneos, como el análisis de la dispersión de ondas planas en SSFD. Una parte de los resultados obtenidos en este trabajo ha dado lugar a una serie de publicaciones científicas en revistas de ámbito internacional y en congresos, tanto nacionales como internacionales. ____________________________________________________________________________________________________In first place it has been developed the basic theory for the rigorous study of the modal spectrum in inhomogeneous guiding media (shielded waveguides and open dielectric waveguides), and also in infinite periodic dielectric media, which are the basic element of dielectric frequency selective surfaces (DFSS). To this end the Bi-Orthogonal Basis Method developed in the Departamento de Física Aplicada y Electromagnetismo and in the Departamento de Óptica de la Universitat de València has been adapted to the study of a wide variety of optical and microwave waveguides, based on the transformation of the differential equations describing the evolution of the transverse fields in a matrix eigenvalue problem, whose solution yields the propagation constants and the transverse magnetic and electric field distributions of the modes. Secondly, it has been analyzed the dispersion of plane waves in DFSS, which are multilayer planar structures formed by homogeneous and periodic dielectric layers with periodicity in one dimension. To this end, the modes in a periodic dielectric medium have been obtained with the Bi-Orthogonal Basis method in the case of lossless dielectrics, while for the case of lossy dielectric media it has been used the Method of Moments. These modes are expressed as a superposition of E-Type and H-Type Floquet modes. The reflection and transmission coefficients of the structures have been obtained by imposing the boundary conditions between adjacent layers, under a linearly polarized plane wave excitation with arbitrary polarization, whose fields have been decomposed in E-Type and H-Type Floquet modes of zero order. This decomposition has been particularized to the two most usual cases of incidence with polarization perpendicular (TE) or parallel (TM) to the plane of incidence, respectively. Study of the scattering parameters of the whole multilayered structure is accomplished by the cascade connection of components as characterized by their scattering parameters. Results for the scattering of 2D and 3D plane waves in DFSS are compared with both theoretical and experimental results presented in the literature, finding a very good agreement. Finally, several spectral and angular reflection filters have been designed based on DFSS for optical and microwave frequencies

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