Vector Beams for Fundamental Physics and Applications

Lights salient degrees of freedom are the independent parameters that completely de- scribe an electromagnetic wave (in the paraxial approximation) and include polarization, wavelength, and time. Most recently, lights space degree of freedom has received sig- nificant attention via the sub-discipline of optics that can be referred to as complex light or structured light. The study of complex light is a veritable renaissance of optics; us- ing lights space degree of freedom many classical optics phenomena have been revisited with novel results. In this thesis, a novel form of structured light referred to as vector beams will be investigated. It will be shown that vector beams have properties very much connected to fundamental physical phenomena. In Chapters 1 and 2, it will be shown that Laguerre-Gaussian modes and cylindrical vector beams are inherently connected. The con- nection can be illustrated by their representation on what is referred to as a higher-order Poincare sphere. In analogy to the representation of linear and circular polarizations on the well-known Poincare sphere, on the higher-order Poincare sphere, radially and azimuthally polarized cylindrical vector beams are represented by points on the equator, and orthogonal circularly polarized Laguerre-Gaussian modes whose azimuthally varying phases have op- posite handedness are represented by North and South poles. In Chapter 3, it will be shown that vector beam can be generated using an optical element referred to as a q-plate inside. Using the q-plate, any state of polarization on the well-known Poincare sphere could be converted into any Laguerre-Gaussian mode or cylindrical vector beam on the higher-order Poincare sphere, effectively breaking the spatial modes degeneracy. In chapters 4 and 5, it will be shown that vector beams can be used for optical communication, i.e., they can be used to encode or carry that information. The transmitted vector beams’ spatial patterns must not change as they propagate so that the information they encode or carry can be re- ceived with minimal error. Equally important, solutions to the paraxial Helmholtz wave equation make up a complete and orthogonal set. As solutions to the paraxial Helmholtz wave equation, with regard to optical communication, the complete and orthogonal set of vector beams can be used as an ”N” dimensional state space with which to encode data, or as N channels to carry information. In chapter 6, it will be shown that vector Bessel beams can be generated by combining liquid crystal q-plates with ”Durnin’s” ring method. Similar to scalar Bessel beams, it will be shown that the spatially inhomogeneous states of polarization of vector Bessel beams can self-heal after they are obstructed. The polarization of vector Bessel beams was measured using Stokes polarimetry before and after they were obstructed. It will be experimentally verified that their spatially inhomogeneous states of polarization can self-heal

El derecho a un proceso público en la jurisprudencia del Tribunal Europeo de derechos humanos

[Resumen] El autor realiza un análisis de los aspectos más relevantes de una faceta del derecho a la tutela judicial efectiva, el derecho a un proceso público, consagrado en el Art. 6 del Convenio Europeo de Derechos Humanos (CEDH). En el estudio del contenido, del ámbito de aplicación y de los límites de dicha garantía procesal, el autor hace referencia a las resoluciones judiciales más importantes que, en materia, han sido adoptadas por el órgano encargado de velar sobre la aplicación y el respeto de las normas contenidas en el Convenio: el Tribunal Europeo de Derechos Humanos[Abstract] The author carries out an analysis of one of the most important aspect of the right to a fair trial: the right to a public hearing, established by the Article 6 of the European Convention on Human Rights (ECHR). The author dwells on the content, aim and limits of this fundamental right, making reference to the most important case law which has been adopted by the body responsible for ensuring the implementation and compliance of the Convention rules: the European Court of Human Rights

El afianzamiento de las competencias sistémicas e instrumentales en el alumno universitario a través de la enseñanza práctica del Sistema Constitucional Español de Protección de los Derechos y Libertades

La adaptación de los estudios universitarios al Espacio Europeo de Educación Superior implica, además del tradicional aprendizaje de contenidos técnicos sobre una materia, la adquisición de competencias sistémicas, instrumentales e interpersonales. La enseñanza práctica del Derecho Constitucional, y, concretamente, del sistema constitucional español de protección de los derechos fundamentales y las libertades públicas, afianza, sin duda alguna, dichas competencias en el estudiante universitario.The adaptation of university studies at the EEES involves, in addition to the traditional learning content on a technical matter, the acquisition of systemic, instrumental and interpersonal skills. The practice teaching of Constitutional Law, and specifically the Spanish constitutional system of protection of fundamental rights and public freedoms, strengthens undoubtedly those skills in the university student

Training Metaphor Interpretation in RHD Patients: Preliminary Results

Five stroke patients with right hemisphere brain damage (RHD) participated in a single subject experimental design intervention study to train metaphor comprehension. The theory motivating the program posits roles for coarse-grained semantic knowledge and working memory. Four patients showed clear improvement in metaphor interpretation associated with the start of training. Results indicate the potential of an evidence-based approach for treating deficits associated with RHD. The paper will describe the training program and discuss individual performances on metaphor, line orientation, working memory and other background measures

La interpretación del art. 47 CDFUE como expresión de la labor hermenéutica del Tribunal de Luxemburgo en la construcción de un estándar europeo de protección de los derechos

Desde la entrada en vigor del Tratado de Lisboa, la Carta de los Derechos Fundamentales de la Unión Europea (CDFUE) ha adquirido una relevancia incuestionable en su ámbito material. El Tribunal de Luxemburgo, en calidad de supremo intérprete de la Carta, interviene para definir el alcance de sus preceptos, construyendo con sus sentencias un verdadero estándar de protección de los derechos en seno a la Unión. Este estudio pone de manifiesto esta evolución a partir del análisis las resoluciones más relevantes del Tribunal de Luxemburgo en relación al art. 47 (CDFUE) por el que se consagra el derecho a la tutela judicial efectiva y a un juez imparcial.Since the entry into force of the Treaty of Lisbon, the Charter of Fundamental Rights of the European Union (CFREU) has acquired an unquestionable relevance in its material scope. The Luxembourg Court, as ultimate interpreter of the Charter, intervenes to define the extent of its precepts, establishing a European standard of protection of fundamental rights. This paper describes this evolution, taking into consideration the most relevant resolutions from the Luxembourg Court on the art. 47 CFREU, which establishes the right to an effective remedy and to a fair trial

Estado de Derecho y derecho a la independencia judicial: un binomio insoslayable

El Estado de Derecho implica la sujeción del poder estatal al Derecho y a una Constitución con fuerza normativa y primacía, incluyendo la separación, limitación y legitimación democrática de los poderes estatales, la distribución territorial del poder, la seguridad jurídica y el reconocimiento de los derechos fundamentales. Para ello, se requieren sistemas de justicia basados en las garantías de un “proceso justo”. Entre estas destaca el derecho a la independencia judicial en aspectos como la designación del tribunal, la duración del mandato y la separación de influencias políticas externas. Este estudio aborda estas cuestiones, centrándose en el caso español y en la crisis sistémica del Consejo General del Poder Judicial. Recibido: 09.02.2024  Aceptado: 04.03.202

Shimura curves and their p-adic uniformization = Corbes de Shimura i les seves uniformitzacions p-àdiques

[eng] The main purpose of this dissertation is to introduce Shimura curves from the non-Archimedean point of view, paying special attention to those aspects that can make this theory amenable for computations. Despite the fact that the theory of p-adic uniformization of Shimura curves goes back to the 1960s with the results of Cerednik and Drinfeld, only in the last years explicit examples related to these uniformizations have been computed. The structure of this dissertation is as follows. In Chapter 1 we introduce Shimura curves starting from an indefinite quaternion algebra H over a totally real field F. This is done mostly following the fundamental paper of Shimura [Shi67]. We also give the definitions using the adelic approach of [Shi70b] and [Shi70c]. The point of view we adopt is the arithmetical one, since we try to make clear the link connecting Shimura curves to the arithmetic of quaternion algebras. In this sense, we give evidence of why Shimura curves have to be considered a geometric interpretation of most arithmetical phenomena in quaternion orders. Chapter 2 has the aim of introducing those non-Archimedean objects which appear later in the statements of the theorems of Cerednik and Drinfeld. In Chapter 3 we start the study of fundamental domains in Hp for the action of discrete and cocompact subgroups of PGL2(Qp) arising in the p-adic uniformization of Shimura curves. In Chapter 4 we associate to the p-adic uniformization of the Shimura curve X(DH;N) certain parameters in Hp(Cp) analogous to the complex multiplication parameters in H: we refer to them by p-imaginary multiplication paramters, since they are defined over the unramified quadratic extension of Qp. In the study of these parameters, we follow the p-adic analog of the line adopted in [AB04]. Specifically, we are able to recover these parameters as zeros of certain binary quadratic forms with p-adic coefficients