Hyperbolic reflections as fundamental building blocks for multilayer optics

We reelaborate on the basic properties of lossless multilayers by using bilinear transformations. We study some interesting properties of the multilayer transfer function in the unit disk, showing that hyperbolic geometry turns out to be an essential tool for understanding multilayer action. We use a simple trace criterion to classify multilayers into three classes that represent rotations, translations, or parallel displacements. Moreover, we show that these three actions can be decomposed as a product of two reflections in hyperbolic lines. Therefore, we conclude that hyperbolic reflections can be considered as the basic pieces for a deeper understanding of multilayer optics.Comment: 7 pages, 7 figures, accepted for publication in J. Opt. Soc. Am.

General unit-disk representation for periodic multilayers

We suggest a geometrical framework to discuss periodic layered structures in the unit disk. The band gaps appear when the point representing the system approaches the unit circle. We show that the trace of the matrix describing the basic period allows for a classification in three families of orbits with quite different properties. The laws of convergence of the iterates to the unit circle can be then considered as universal features of the reflection.Comment: 3 pages, 2 eps-figures. To be published in Optics Letter

Perfect antireflection via negative refraction

We suggest a geometrical framework to discuss the action of slabs of negatively refracting materials. We show that these slabs generate the same orbits as normal materials, but traced out in opposite directions. This property allows us to confirm that the action of any lossless multilayer can be optically cancelled by putting it together with the multilayer constructed as the inverted mirror image, with $\epsilon$ and $\mu$ reversed in sign.Comment: Some typos corrected. New references addes. Accepted for publication in Physics Letters

Relaciones en conflicto. Nuevas perspectivas sobre relaciones internacionales desde la historia

Este libro recoge las aportaciones de los investigadores del IV Encuentro de Jóvenes Investigadores en Historia Contemporánea que tuvo lugar en el Valencia en septiembre de 2013

Iwasawa Effects in Multi-layer Optics

There are many two-by-two matrices in layer optics. It is shown that they can be formulated in terms of a three-parameter group whose algebraic property is the same as the group of Lorentz transformations in a space with two space-like and one time-like dimensions, or the $Sp(2)$ group which is a standard theoretical tool in optics. Among the interesting mathematical properties of this group, the Iwasawa decomposition drastically simplifies the matrix algebra under certain conditions, and leads to a concise expression for the S-matrix for transmitted and reflected rays. It is shown that the Iwasawa effect can be observed in multi-layer optics, and a sample calculation of the S-matrix is given.Comment: RevTex 10 pages including 1 psfi

Perspectivas de la Infotecnología para la Editorial Universitaria en Cuba

The word "Infotecnología" defines the key discipline for reaching the training and the development of the technical-social relationships and the communications infrastructure of the Cuban Higher Education. The use of Information Technology for producing and publishing the graduation theses is highly important for the best use of TICs in Higher Education in Cuba, so, since the 2008-2009 course the decision was make that all the Cuban students should produce their graduation theses in digital format. The results of the application of a procedure to produce the graduation theses by using Free software and their publication in digital format are discussed in this paper. The paper proposes the use of the Editorial University's Websites to become the main tools for training professors and students in the intensive use of the Information Technology and for producing and publishing the academic documents. The creation of the Register of the Cuban Academic Publications is proposed to make possible the use of bibliographical references managers

Constructing Fresnel reflection coefficients by ruler and compass

A simple and intuitive geometical method to analyze Fresnel formulas is presented. It applies to transparent media and is valid for perpendicular and parallel polarizations. The approach gives a graphical characterization particularly simple of the critical and Brewster angles. It also provides an interpretation of the relation between the reflection coefficients for both basic polarizations as a symmetry in the plane

Rotations associated with Lorentz boosts

It is possible to associate two angles with two successive non-collinear Lorentz boosts. If one boost is applied after the initial boost, the result is the final boost preceded by a rotation called the Wigner rotation. The other rotation is associated with Wigner's O(3)-like little group. These two angles are shown to be different. However, it is shown that the sum of these two rotation angles is equal to the angle between the initial and final boosts. This relation is studied for both low-speed and high-speed limits. Furthermore, it is noted that the two-by-two matrices which are under the responsibility of other branches of physics can be interpreted in terms of the transformations of the Lorentz group, or vice versa. Classical ray optics is mentioned as a case in point.Comment: LaTeX, 16 Pages, 4 epsfigure

Optimizing omnidirectional reflection by multilayer mirrors

Periodic layered media can reflect strongly for all incident angles and polarizations in a given frequency range. Quarter-wave stacks at normal incidence are commonplace in the design of such omnidirectional reflectors. We discuss alternative design criteria to optimize these systems.Comment: 9 pages, 6 figures. To be published in J. Opt. A: Pure and Applied Optic

La enseñanza de la Ingeniería Legal: impactos y desafíos

La Ingeniería Legal se ha caracterizado por sus cambios, dados por avances importantes que proporcionan nuevos horizontes de la ciencia y de la tecnología. Hoy se espera que la enseñanza del Derecho aplicado a la Ingeniería, pueda variar al ritmo de los nuevos cambios científicos o tecnológicos, incorporándose su regulación al plexo normativo