Sliderule-like property of Wigner's little groups and cyclic S-matrices for multilayer optics

It is noted that two-by-two S-matrices in multilayer optics can be represented by the Sp(2) group whose algebraic property is the same as the group of Lorentz transformations applicable to two space-like and one time-like dimensions. It is noted also that Wigner's little groups have a sliderule-like property which allows us to perform multiplications by additions. It is shown that these two mathematical properties lead to a cyclic representation of the S-matrix for multilayer optics, as in the case of ABCD matrices for laser cavities. It is therefore possible to write the N-layer S-matrix as a multiplication of the N single-layer S-matrices resulting in the same mathematical expression with one of the parameters multiplied by N. In addition, it is noted, as in the case of lens optics, multilayer optics can serve as an analogue computer for the contraction of Wigner's little groups for internal space-time symmetries of relativistic particles.Comment: RevTex 13 pages, Secs. IV and V revised and expande

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

Fresnel coefficients as hyperbolic rotations

We describe the action of a plane interface between two semi-infinite media in terms of a transfer matrix. We find a remarkably simple factorization of this matrix, which enables us to express the Fresnel coefficients as a hyperbolic rotation.Comment: 6 pages, 3 figure

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

The language of Einstein spoken by optical instruments

Einstein had to learn the mathematics of Lorentz transformations in order to complete his covariant formulation of Maxwell's equations. The mathematics of Lorentz transformations, called the Lorentz group, continues playing its important role in optical sciences. It is the basic mathematical language for coherent and squeezed states. It is noted that the six-parameter Lorentz group can be represented by two-by-two matrices. Since the beam transfer matrices in ray optics is largely based on two-by-two matrices or $ABCD$ matrices, the Lorentz group is bound to be the basic language for ray optics, including polarization optics, interferometers, lens optics, multilayer optics, and the Poincar\'e sphere. Because the group of Lorentz transformations and ray optics are based on the same two-by-two matrix formalism, ray optics can perform mathematical operations which correspond to transformations in special relativity. It is shown, in particular, that one-lens optics provides a mathematical basis for unifying the internal space-time symmetries of massive and massless particles in the Lorentz-covariant world.Comment: LaTex 8 pages, presented at the 10th International Conference on Quantum Optics (Minsk, Belarus, May-June 2004), to be published in the proceeding

Evaluation of the influence of toll systems on energy consumption and CO2 emissions: A case study of a Spanish highway

This paper studies the energy consumption and subsequent CO2 emissions of road highway transportation under three toll systems in Spain for four categories of vehicles: cars, vans, buses and articulated trucks. The influence of toll systems is tested for a section of AP-41 highway between Toledo and Madrid. One system is free flow, other is traditional stop and go and the last toll system operates with an electronic toll collection (ETC) technology. Energy consumption and CO2 emissions were found to be closely related to vehicle mass, wind exposure, engine efficiency and acceleration rate. These parameters affect, directly or indirectly, the external forces which determine the energy consumption. Reducing the magnitude of these forces through an appropriate toll management is an important way of improving the energy performance of vehicles. The type of toll system used can have a major influence on the energy efficiency of highway transportation and therefore it is necessary to consider free flow

Pulmonary but not subcutaneous vaccination confers protection to TB susceptible mice by an IL17-dependent mechanism.

Some of the most promising novel tuberculosis vaccine strategies currently under development are based on respiratory vaccination, mimicking the natural route of infection. In this work, we have compared pulmonary and subcutaneous delivery of BCG vaccine in the tuberculosis-susceptible DBA/2 mouse strain, a model in which parenterally administered BCG vaccine does not protect against tuberculosis. Our data show that intranasally but not subcutaneously administered BCG confers robust protection against pulmonary tuberculosis challenge. In addition, our results indicate that pulmonary vaccination triggers a Mycobacterium tuberculosis–specific mucosal immune response orchestrated by interleukin 17A (IL-17A). Thus, IL-17A neutralization in vivo reduces protection and abrogates M. tuberculosis–specific immunoglobulin A (IgA) secretion to respiratory airways and lung expression of polymeric immunoglobulin receptor induced following intranasal vaccination. Together, our results demonstrate that pulmonary delivery of BCG can overcome the lack of protection observed when BCG is given parenterally, suggesting that respiratory tuberculosis vaccines could have an advantage in tuberculosis-endemic countries, where intradermally administered BCG has inefficient effectiveness against pulmonary tuberculosis