Gromov hyperbolicity of periodic planar graphs

The study of hyperbolic graphs is an interesting topic since the hyperbolicity of a geodesic metric space is equivalent to the hyperbolicity of a graph related to it. The main result in this paper is a very simple characterization of the hyperbolicity of a large class of periodic planar graphs.

A numerical study of Bi-periodic binary diffraction gratings for solar cell applications

In this paper, a numerical study is made of simple bi-periodic binary diffraction gratings for solar cell applications. The gratings consist of hexagonal arrays of elliptical towers and wells etched directly into the solar cell substrate. The gratings are applied to two distinct solar cell technologies: a quantum dot intermediate band solar cell (QD-IBSC) and a crystalline silicon solar cell (SSC). In each case, the expected photocurrent increase due to the presence of the grating is calculated assuming AM1.5D illumination. For each technology, the grating period, well/tower depth and well/tower radii are optimised to maximise the photocurrent. The optimum parameters are presented. Results are presented for QD-IBSCs with a range of quantum dot layers and for SSCs with a range of thicknesses. For the QD-IBSC, it is found that the optimised grating leads to an absorption enhancement above that calculated for an ideally Lambertian scatterer for cells with less than 70 quantum dot layers. In a QD-IBSC with 50 quantum dot layers equipped with the optimum grating, the weak intermediate band to conduction band transition absorbs roughly half the photons in the corresponding sub-range of the AM1.5D spectrum. For the SSC, it is found that the optimised grating leads to an absorption enhancement above that calculated for an ideally Lambertian scatterer for cells with thicknesses of 10 ?m or greater. A 20um thick SSC equipped with the optimised grating leads to an absorption enhancement above that of a 200um thick SSC equipped with a planar back reflector.

Directional Geodesic Active Contours

We present a non-conformal metric that generalizes the geodesic active contours approach for image segmentation. The new metric is obtained by adding to the Euclidean metric an additional term that penalizes the misalignment of the curve with the image gradient and multiplying the resulting metric by a conformal factor that depends on the edge intensity. In this way, a closer fitting to the edge direction results. The provided experimental results address the computation of the geodesics of the new metric by applying a gradient descent to externally provided curves. The good performance of the proposed techniques is demonstrated in comparison with other active contours methods.

Optimization of a label-free biosensor vertically characterized based on a periodic lattice of high aspect ratio SU-8 nano-pillars with a simplified 2D theoretical model

We have recently demonstrated a biosensor based on a lattice of SU8 pillars on a 1 μm SiO2/Si wafer by measuring vertically reflectivity as a function of wavelength. The biodetection has been proven with the combination of Bovine Serum Albumin (BSA) protein and its antibody (antiBSA). A BSA layer is attached to the pillars; the biorecognition of antiBSA involves a shift in the reflectivity curve, related with the concentration of antiBSA. A detection limit in the order of 2 ng/ml is achieved for a rhombic lattice of pillars with a lattice parameter (a) of 800 nm, a height (h) of 420 nm and a diameter(d) of 200 nm. These results correlate with calculations using 3D-finite difference time domain method. A 2D simplified model is proposed, consisting of a multilayer model where the pillars are turned into a 420 nm layer with an effective refractive index obtained by using Beam Propagation Method (BPM) algorithm. Results provided by this model are in good correlation with experimental data, reaching a reduction in time from one day to 15 minutes, giving a fast but accurate tool to optimize the design and maximizing sensitivity, and allows analyzing the influence of different variables (diameter, height and lattice parameter). Sensitivity is obtained for a variety of configurations, reaching a limit of detection under 1 ng/ml. Optimum design is not only chosen because of its sensitivity but also its feasibility, both from fabrication (limited by aspect ratio and proximity of the pillars) and fluidic point of view. (© 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Electromagnetic analysis of periodic structures under a waveguide viewpoint

The fundamental objective of this Ph. D. dissertation is to demonstrate that, under particular circumstances which cover most of the structures with practical interest, periodic structures can be understood and analyzed by means of closed waveguide theories and techniques. To that aim, in the first place a transversely periodic cylindrical structure is considered and the wave equation, under a combination of perfectly conducting and periodic boundary conditions, is studied. This theoretical study runs parallel to the classic analysis of perfectly conducting closed waveguides. Under the light shed by the aforementioned study it is clear that, under certain very common periodicity conditions, transversely periodic cylindrical structures share a lot of properties with closed waveguides. Particularly, they can be characterized by a complete set of TEM, TE and TM modes. As a result, this Ph. D. dissertation introduces the transversely periodic waveguide concept. Once the analogies between the modes of a transversely periodic waveguide and the ones of a closed waveguide have been established, a generalization of a well-known closed waveguide characterization method, the generalized Transverse Resonance Technique, is developed for the obtention of transversely periodic modes. At this point, all the necessary elements for the consideration of discontinuities between two different transversely periodic waveguides are at our disposal. The analysis of this type of discontinuities will be carried out by means of another well known closed waveguide method, the Mode Matching technique. This Ph. D. dissertation contains a sufficient number of examples, including the analysis of a wire-medium slab, a cross-shaped patches periodic surface and a parallel plate waveguide with a textured surface, that demonstrate that the Transverse Resonance Technique - Mode Matching hybrid is highly precise, efficient and versatile. Thus, the initial statement: ”periodic structures can be understood and analyzed by means of closed waveguide theories and techniques”, will be corroborated. Finally, this Ph. D. dissertation contains an adaptation of the aforementioned generalized Transverse Resonance Technique by means of which the analysis of laterally open periodic waveguides, such as the well known Substrate Integrated Waveguides, can be carried out without any approximation. The analysis of this type of structures has suscitated a lot of interest in the recent past and the previous analysis techniques proposed always resorted to some kind of fictitious wall to close the structure. vii Resumen El principal objetivo de esta tesis doctoral es demostrar que, bajo ciertas circunstancias que se cumplen para la gran mayoría de estructuras con interés práctico, las estructuras periódicas se pueden analizar y entender con conceptos y técnicas propias de las guías de onda cerradas. Para ello, en un primer lugar se considera una estructura cilíndrical transversalmente periódica y se estudia la ecuación de onda bajo una combinación de condiciones de contorno periódicas y de conductor perfecto. Este estudio teórico y de caracter general, sigue el análisis clásico de las guías de onda cerradas por conductor eléctrico perfecto. A la luz de los resultados queda claro que, bajo ciertas condiciones de periodicidad (muy comunes en la práctica) las estructuras cilíndricas transversalmente periódicas guardan multitud de analogías con las guías de onda cerradas. En particular, pueden ser descritas mediante un conjunto completo de modos TEM, TE y TM. Por ello, ésta tesis introduce el concepto de guía de onda transversalmente periódica. Una vez establecidas las similitudes entre las soluciones de la ecuación de onda, bajo una combinación de condiciones de contorno periódicas y de conductor perfecto, y los modos de guías de onda cerradas, se lleva a cabo, con éxito, la adaptación de un conocido método de caracterización de guías de onda cerradas, la técnica de la Resonancia Transversal Generalizada, para la obtención de los modos de guías transversalmente periódicas. En este punto, se tienen todos los elementos necesarios para considerar discontinuidades entre guías de onda transversalmente periódicas. El analisis de este tipo de discontinuidades se llevará a cabo mediante otro conocido método de análisis de estructuras cerradas, el Ajuste Modal. Esta tesis muestra multitud de ejemplos, como por ejemplo el análisis de un wire-medium slab, una superficie de parches con forma de cruz o una guía de placas paralelas donde una de dichas placas tiene cierta textura, en los que se demuestra que el método híbrido formado por la Resonancia Transversal Generalizada y el Ajuste Modal, es tremendamente preciso, eficiente y versátil y confirmará la validez de el enunciado inicial: ”las estructuras periódicas se pueden analizar y entender con conceptos y técnicas propias de las guías de onda cerradas” Para terminar, esta tésis doctoral incluye también una modificación de la técnica de la Resonancia Transversal Generalizada mediante la cual es posible abordar el análisis de estructuras periódica abiertas en los laterales, como por ejemplo las famosas guías de onda integradas en sustrato, sin ninguna aproximación. El análisis de este tipo de estructuras ha despertado mucho interés en los últimos años y las técnicas de análisis propuestas hasta ix el momento acostumbran a recurrir a algún tipo de pared ficticia para simular el carácter abierto de la estructura.

Particle and energy transport in quantum disordered and quasi-periodic chains connected to mesoscopic Fermi reservoirs

We study a model of nonequilibrium quantum transport of particles and energy in a many-body system connected to mesoscopic Fermi reservoirs (the so-called meso-reservoirs). We discuss the conservation laws of particles and energy within our setup as well as the transport properties of quasi-periodic and disordered chains.

Circuital model for the spherical geodesic waveguide perfect drain

The perfect drain for the Maxwell fish eye (MFE) is a non-magnetic dissipative region placed in the focal point to absorb all the incident radiation without reflection or scattering.

Periodic time-domain modulation for the electrically tunable control of optical pulse train envelope and repetition rate multiplication

An electrically tunable system for the control of optical pulse sequences is proposed and demonstrated. It is based on the use of an electrooptic modulator for periodic phase modulation followed by a dispersive device to obtain the temporal Talbot effect. The proposed configuration allows for repetition rate multiplication with different multiplication factors and with the simultaneous control of the pulse train envelope by simply changing the electrical signal driving the modulator. Simulated and experimental results for an input optical pulse train of 10 GHz are shown for different multiplication factors and envelope shapes.

Analysis of Super Imaging Properties of Spherical Geodesic Waveguide Using COMSOL Multyphisics

Negative Refractive Lens (NRL) has shown that an optical system can produce images with details below the classic Abbe diffraction limit using materials of negative dielectric and magnetic constants. Recently, two devices with positive refraction, the Maxwell Fish Eye lens (MFE) (Leonhardt et al 2000) and the Spherical Geodesic Waveguide (SGW)(Minano et all 2011) have been claimed to break the diffraction limit using positive refraction with a different meaning. In these cases, it has been considered the power transmission from a point source to a point receptor, which falls drastically when the receptor is displaced from the focus by a distance much smaller than the wavelength. Moreover, recent analysis of the SGW with defined object and image surfaces, which are both conical sections of the sphere, has shown that the system transmits images bellow diffraction limit. The key assumption is the use of a perfectly absorbing receptor called perfect drain. This receptor is capable to absorb all the radiation without reflection or scattering. Here, it is presented the COMSOL analysis of the SGW using a perfect drain that absorbs perfectly two modes. The design procedure for PD capable to absorb k modes is proposed, as well.

COMSOL Multyphisics Super Resolution Analysis of a Spherical Geodesic Waveguide Suitable for Manufacturing

Recently it has been proved theoretically (Miñano et al, 2011) that the super-resolution up to ?/500 can be achieved using an ideal metallic Spherical Geodesic Waveguide (SGW). This SGW is a theoretical design, in which the conductive walls are considered to be lossless conductors with zero thickness. In this paper, we study some key parameters that might influence the super resolution properties reported in (Miñano et al, 2011), such as losses, metal type, the thickness of conductive walls and the deformation from perfect sphere. We implement a realistic SGW in COMSOL multiphysics and analyze its super-resolution properties. The realistic model is designed in accordance with the manufacturing requirements and technological limitations.

Super resolution using a modified Spherical Geodesic Waveguide suitable for manufacturing

The previous publications (Miñano et al, 2011) have shown that using a Spherical Geodesic Waveguide (SGW), it can be achieved the super-resolution up to ? /500 close to a set of discrete frequencies. These frequencies are directly connected with the well-known Schumann resonance frequencies of spherical symmetric systems. However, the Spherical Geodesic Waveguide (SGW) has been presented as an ideal system, in which the technological obstacles or manufacturing feasibility and their influence on final results were not taken into account. In order to prove the concept of superresolution experimentally, the Spherical Geodesic Waveguide is modified according to the manufacturing requirements and technological limitations. Each manufacturing process imposes some imperfections which can affect the experimental results. Here, we analyze the influence of the manufacturing limitations on the super-resolution properties of the SGW. Beside the theoretical work, herein, there has been presented the experimental results, as well.

Perfect imaging analysis of the spherical geodesic waveguide

Negative Refractive Lens (NRL) has shown that an optical system can produce images with details below the classic Abbe diffraction limit. This optical system transmits the electromagnetic fields, emitted by an object plane, towards an image plane producing the same field distribution in both planes. In particular, a Dirac delta electric field in the object plane is focused without diffraction limit to the Dirac delta electric field in the image plane. Two devices with positive refraction, the Maxwell Fish Eye lens (MFE) and the Spherical Geodesic Waveguide (SGW) have been claimed to break the diffraction limit using positive refraction with a different meaning. In these cases, it has been considered the power transmission from a point source to a point receptor, which falls drastically when the receptor is displaced from the focus by a distance much smaller than the wavelength. Although these systems can detect displacements up to ?/3000, they cannot be compared to the NRL, since the concept of image is different. The SGW deals only with point source and drain, while in the case of the NRL, there is an object and an image surface. Here, it is presented an analysis of the SGW with defined object and image surfaces (both are conical surfaces), similarly as in the case of the NRL. The results show that a Dirac delta electric field on the object surface produces an image below the diffraction limit on the image surface.

Super-resolution properties of the Spherical Geodesic Waveguides using the perfect drain

Perfect drain for the Maxwell Fish Eye (MFE) is a nonmagnetic dissipative region placed in the focal point to absorb all the incident radiation without reflection or scattering. The perfect drain was recently designed as a material with complex permittivity ? that depends on frequency. However, this material is only a theoretical material, so it can not be used in practical devices. Recently, the perfect drain has been claimed as necessary to achieve super-resolution [Leonhard 2009, New J. Phys. 11 093040], which has increased the interest for practical perfect drains suitable for manufacturing. Here, we analyze the superresolution properties of a device equivalent to the MFE, known as Spherical Geodesic Waveguide (SGW), loaded with the perfect drain. In the SGW the source and drain are implemented with coaxial probes. The perfect drain is realized using a circuit (made of a resistance and a capacitor) connected to the drain coaxial probes. Superresolution analysis for this device is done in Comsol Multiphysics. The results of simulations predict the superresolution up to ? /3000 and optimum power transmission from the source to the drain.

Extreme super-resolution using the spherical geodesic waveguide

Leonhardt demonstrated (2009) that the 2D Maxwell Fish Eye lens (MFE) can focus perfectly 2D Helmholtz waves of arbitrary frequency, i.e., it can transport perfectly an outward (monopole) 2D Helmholtz wave field, generated by a point source, towards a "perfect point drain" located at the corresponding image point. Moreover, a prototype with λ/5 superresolution (SR) property for one microwave frequency has been manufactured and tested (Ma et al, 2010). Although this prototype has been loaded with an impedance different from the "perfect point drain", it has shown super-resolution property. However, neither software simulations nor experimental measurements for a broad band of frequencies have yet been reported. Here we present steady state simulations for two cases, using perfect drain as suggested by Leonhardt and without perfect drain as in the prototype. All the simulations have been done using a device equivalent to the MFE, called the Spherical Geodesic Waveguide (SGW). The results show the super-resolution up to λ/3000, for the system loaded with the perfect drain, and up to λ/500 for a not perfect load. In both cases super-resolution only happens for discrete number of frequencies. Out of these frequencies, the SGW does not show super-resolution in the analysis carried out.

Dynamic stabilization of L2 periodic orbits using attitude-orbit coupling effects

Numerical explorations show how the known periodic solutions of the Hill problem are modified in the case of the attitude-orbit coupling that may occur for large satellite structures. We focus on the case in which the elongation is the dominant satellite’s characteristic and find that a rotating structure may remain with its largest dimension in a plane parallel to the plane of the primaries. In this case, the effect produced by the non-negligible physical length is dynamically equivalent to the perturbation produced by an oblate central body on a mass-point satellite. Based on this, it is demonstrated that the attitude-orbital coupling of a long enough body may change the dynamical characteristics of a periodic orbit about the collinear Lagrangian points.