Algebraic and analytic Dirac induction for graded affine Hecke algebras

We define the algebraic Dirac induction map \Ind_D for graded affine Hecke algebras. The map \Ind_D is a Hecke algebra analog of the explicit realization of the Baum-Connes assembly map in the $K$-theory of the reduced $C^*$-algebra of a real reductive group using Dirac operators. The definition of \Ind_D is uniform over the parameter space of the graded affine Hecke algebra. We show that the map \Ind_D defines an isometric isomorphism from the space of elliptic characters of the Weyl group (relative to its reflection representation) to the space of elliptic characters of the graded affine Hecke algebra. We also study a related analytically defined global elliptic Dirac operator between unitary representations of the graded affine Hecke algebra which are realized in the spaces of sections of vector bundles associated to certain representations of the pin cover of the Weyl group. In this way we realize all irreducible discrete series modules of the Hecke algebra in the kernels (and indices) of such analytic Dirac operators. This can be viewed as a graded Hecke algebra analogue of the construction of discrete series representations for semisimple Lie groups due to Parthasarathy and Atiyah-Schmid.Comment: 37 pages, revised introduction, updated references, minor correction

Polarization and wavelength agnostic nanophotonic beam splitter

High-performance optical beam splitters are of fundamental importance for the development of advanced silicon photonics integrated circuits. However, due to the high refractive index contrast of the silicon-on-insulator platform, state of the art Si splitters are hampered by trade-offs in bandwidth, polarization dependence and sensitivity to fabrication errors. Here, we present a new strategy that exploits modal engineering in slotted waveguides to overcome these limitations, enabling ultra-wideband polarization-insensitive optical power splitters, with relaxed fabrication tolerances. The proposed splitter relies on a single-mode slot waveguide which is transformed into two strip waveguides by a symmetric taper, yielding equal power splitting. Based on this concept, we experimentally demonstrate -3$\pm$0.5 dB polarization-independent transmission in an unprecedented 390 nm bandwidth (1260 - 1650 nm), even in the presence of waveguide width deviations as large as $\pm$25 nm

Anesthésie ambulatoire pour curetages gynécologiques (comparaison de trois protocoles anesthésiques et recherche du délai optimum d'aptitude à la rue)

TOULOUSE3-BU Santé-Centrale (315552105) / SudocPARIS-BIUM (751062103) / SudocSudocFranceF

Facteurs de contrôle de l'expansion du volume plasmatique au retour au niveau de la mer après un séjour en altitude

RENNES1-BU Santé (352382103) / SudocPARIS-BIUM (751062103) / SudocSudocFranceF

Enhancing Si3N4Waveguide Nonlinearity with Heterogeneous Integration of Few-Layer WS2

| openaire: EC/H2020/820423/EU//S2QUIP | openaire: EC/H2020/965124/EU//FEMTOCHIP | openaire: EC/H2020/834742/EU//ATOPThe heterogeneous integration of low-dimensional materials with photonic waveguides has spurred wide research interest. Here, we report on the experimental investigation and the numerical modeling of enhanced nonlinear pulse broadening in silicon nitride waveguides with the heterogeneous integration of few-layer WS2. After transferring a few-layer WS2 flake of similar to 14.8 mu m length, the pulse spectral broadening in a dispersion-engineered silicon nitride waveguide has been enhanced by similar to 48.8% in bandwidth. Through numerical modeling, an effective nonlinear coefficient higher than 600 m(-1) W-1 has been retrieved for the heterogeneous waveguide indicating an enhancement factor of larger than 300 with respect to the pristine waveguide at a wavelength of 800 nm. With further advances in two-dimensional material fabrication and integration techniques, on-chip heterostructures will offer another degree of freedom for waveguide engineering, enabling high-performance nonlinear optical devices, such asfrequency combs and quantum light sources.Peer reviewe

Supercontinuum generation in 800nm thick ultra-low loss silicon nitride waveguides

International audienceWe report SCG over 1.4 octave(from 620nm to 1.5µm) by pumping at 1060nm on a dispersion-engineered ultra low-loss SiN integrated waveguide with femtosecond pulse of 300W as peak power. We demonstrate SCG over 2.5 octaves(from 580nm to 2.05µm) when a wider and longer waveguide being pumped at 1550nm with peak power of 800W. We also experimentally observe a 4.5 octaves(from 500nm to 2.75µm) SCG by pumping at 1550nm on the 800nm thick SiN platform. We show the versatility of CEA LETI 800nm thick ultra-low loss SiN platform to SCG

Generation of multiple user-defined dispersive waves in a silicon nitride waveguide

International audienceThe quest for a wide and bright supercontinuum source has received significant attention, addressing pivotal challenges in ultra-fast spectroscopy, imaging, and frequency metrology. Among the diverse optical nonlinear mechanisms steering supercontinuum generation, dispersive waves emerge as crucial contributors, providing heightened spectral intensity, wavelength tunability, and superior temporal coherence. Nevertheless, their generation is tightly bound by waveguide geometry, limiting both their numbers and the wavelengths at which they manifest. In this paper, we demonstrate the controlled generation of multiple dispersive waves in fundamental optical transverse mode by leveraging quasi phase-matching in an integrated silicon nitride (Si 3 N 4 ) waveguide. This approach involves modulating the group velocity dispersion through varying the width of the Si 3 N 4 waveguide crossing anomalous and normal dispersion, which facilitates the creation of diverse dispersive waves in fundamental transverse electromagnetic (TE) polarization at multiple phase-matched wavelengths. A wide nonlinear optical spectral broadening surpassing conventional approaches is achieved with good temporal and spatial coherence. Remarkably, the generation of the multiple dispersive waves and the supercontinuum is achieved by a 190-fs pulse duration pump with peak power as low as 110 W (24 pJ). This work offers flexibility to manipulate dispersive waves in an integrated platform beyond current dispersion engineering. It represents a significant step forward in developing an integrated broadband source with a user-defined spectral shape, accomplished with minimal pump power requirements

Strategic exploitation of a common resource under environmental risk

10.1016/j.jedc.2012.06.010Journal of Economic Dynamics and Control371125-136JEDC