Composition law for polarizers

The polarization process when polarizers act on an optical field is studied. We give examples for two kinds of polarizers. The first kind presents an anisotropic absorption - as in a polaroid film - and the second one is based on total reflection at the interface with a birefringent medium. Using the Stokes vector representation, we determine explicitly the trajectories of the wave light polarization during the polarization process. We find that such trajectories are not always geodesics of the Poincar\'e sphere as it is usually thought. Using the analogy between light polarization and special relativity, we find that the action of successive polarizers on the light wave polarization is equivalent to the action of a single resulting polarizer followed by a rotation achieved for example by a device with optical activity. We find a composition law for polarizers similar to the composition law for noncollinear velocities in special relativity. We define an angle equivalent to the relativistic Wigner angle which can be used to quantify the quality of two composed polarizers.Comment: 23 pages, 9 figures, accepted for publication in Physical Review

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

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

Weakness of accelerator bounds on electron superluminality without a preferred frame

The reference laboratory bounds on superluminality of the electron are obtained from the absence of in-vacuo Cherenkov processes and the determinations of synchrotron radiated power for LEP electrons. It is usually assumed that these analyses establish the validity of a standard special-relativistic description of the electron with accuracy of at least a few parts in $10^{14}$, and in particular this is used to exclude electron superluminality with such an accuracy. We observe that these bounds rely crucially on the availability of a preferred frame. In-vacuo-Cherenkov processes are automatically forbidden in any theory with "deformed Lorentz symmetry", relativistic theories that, while different from Special Relativity, preserve the relativity of inertial frames. Determinations of the synchrotron radiated power can be used to constrain the possibility of Lorentz-symmetry deformation, but provide rather weak bounds, which in particular for electron superluminality we establish to afford us no more constraining power than for an accuracy of a few parts in $10^4$. We argue that this observation can have only a limited role in the ongoing effort of analysis of the anomaly tentatively reported by the OPERA collaboration, but we stress that it could provide a valuable case study for assessing the limitations of "indirect" tests of fundamental laws of physics.Comment: LaTex, 6 page

Author Correction: Metabolism of the predominant human milk oligosaccharide fucosyllactose by an infant gut commensal

The original version of this Article contained an error in Affiliation 4..

Job Strain and Late-Life Cognition: Findings From the Puerto Rican Elderly Health Conditions Study

We examined associations between job strain and cognitive aging in a sample of older Puerto Ricans. Members of the Puerto Rican Elderly: Health Conditions study, aged 60-100 years at baseline, participated. Job strain indicators were quantified from O*NET ( = 1632) and a matrix of Job Content Questionnaire scores (JCQ; = 1467). Global cognition was assessed twice across 4 years. Controlling for age, sex, depressive symptoms, financial problems, hypertension, diabetes, childhood economic hardship, low job control and high job strain were consistently associated with greater cognitive decline. Adding education attenuated these associations. High education strengthened the JCQ job control-cognitive change link. Low job control and high job strain may accelerate cognitive aging in this population. However, it may be more difficult to disentangle the intersecting roles of education and job strain in cognitive aging among older Puerto Ricans relative to older adults from contiguous United States or Europe