Generalized composition law from 2x2 matrices

Many results that are difficult can be found more easily by using a generalization in the complex plane of Einstein's addition law of parallel velocities. Such a generalization is a natural way to add quantities that are limited to bounded values. We show how this generalization directly provides phase factors such as the Wigner angle in special relativity and how this generalization is connected in the simplest case with the composition of 2x2 S matrices.Comment: Accepted for publication in Am. J. Phy

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

Sending femtosecond pulses in circles: highly non-paraxial accelerating beams

We use caustic beam shaping on 100 fs pulses to experimentally generate non-paraxial accelerating beams along a 60 degree circular arc, moving laterally by 14 \mum over a 28 \mum propagation length. This is the highest degree of transverse acceleration reported to our knowledge. Using diffraction integral theory and numerical beam propagation simulations, we show that circular acceleration trajectories represent a unique class of non-paraxial diffraction-free beam profile which also preserves the femtosecond temporal structure in the vicinity of the caustic

Arbitrary non-paraxial accelerating periodic beams and spherical shaping of light

We report the observation of arbitrary accelerating beams designed using a non-paraxial description of optical caustics. We use a spatial light modulator-based setup and techniques of Fourier optics to generate circular and Weber beams subtending over 95 degrees of arc. Applying a complementary binary mask also allows the generation of periodic accelerating beams taking the forms of snake-like trajectories, and the application of a rotation to the caustic allows the first experimental synthesis of optical accelerating beams upon the surface of a sphere in three dimensions.Comment: 4 pages, 4 figures articl

EFFETTO DELLA DENSITÀ SULLA CONDIZIONE DI TRE SPECIE DI DECAPODI NATANTI NELLA LAGUNA DI VENEZIA

Quantitative samples of three species of decapod crustaceans were collected across different seasons in three habitat types of the Venice lagoon, in order to evaluate how species density may affect the individual condition. The three species showed a different spatial distribution, with significant differences in density across lagoon habitats. A possible negative effect of density on individual weight was recorded for all the species considere

High speed cleaving of crystals with ultrafast Bessel beams

International audienceWe develop a novel concept for ultra-high speed cleaving of crystalline materials with femtosecond lasers. Using Bessel beams in single shot, fracture planes can be induced nearly all along the Bessel zone in sapphire. For the first time, we show that only for a pulse duration below 650 fs, a single fracture can be induced in sapphire, while above this duration, cracks appear in all crystallographic orientations. We determine the influential parameters which are polarization direction, crystallographic axes and scanning direction. This is applied to cleave sapphire with a spacing as high as 25 μm between laser impacts

Void reactivity coefficient benchmark results for a 10x10 BWR assembly in the full 0-100% void fraction range

A boiling water reactor SVEA-96+ fresh fuel lattice has been used as the basis for a benchmark study of the void reactivity coefficient at assembly level in the full voidage range. Results have been obtained using the deterministic codes CASMO-4, HELIOS, PHOENIX, BOXER and the probabilistic code MCNP4C, combined for almost all cases with different cross section libraries. A statistical analysis of the results obtained showed that the void reactivity coefficient tends to become less negative beyond 80% void and that the discrepancies between codes tend to increase from less than 15% at voidages lower than 40% to more than 25% at voidages higher than 70%. The void reactivity coefficient results and the corresponding differences between codes were isotopically decomposed to interpret discrepancies. The isotopic decomposition shows that the minimum observed in the void reactivity coefficient between 80% and 90% void is largely due to the decrease in the relative importance of the 157Gd(n, ) rate with increasing voidage, and that the fundamental discrepancies between codes or libraries are mainly governed by the different predictions of the 238U(n, ) variation with voidage. [All rights reserved Elsevier]