Poynting vector in transfer-matrix formalism for the calculation of light absorption profile in stratified isotropic optical media

In spite of the fact that solutions to Maxwell's equations in stratified isotropic optical media are well known, it appears that an explicit expression of the Poynting vector flux spatial evolution inside such a medium has not been derived so far. Based on exact electromagnetic field solutions in the transfer-matrix formalism, I derive such an expression and show that, due to the presence of counterpropagating waves in the medium, an additional contribution to the flux appears that exists only in optically absorbing layers and arises from the interference between these waves. Based on this theory, the concept of incremental absorption is introduced for the calculation of the light absorption profile along the stratification direction. As an illustration of this concept, absorption profiles in a Si-based thin-film tandem solar cell are predicted at typical wavelengths.     

Adaptive optics wide-field microscopy using direct wavefront sensing

We report a technique for measuring and correcting the wavefront aberrations introduced by a biological sample using a Shack-Hartmann wavefront sensor, a fluorescent reference source, and a deformable mirror. The reference source and sample fluorescence are at different wavelengths to separate wavefront measurement and sample imaging. The measurement and correction at one wavelength improves the resolving power at a different wavelength, enabling the structure of the sample to be resolved.     

Ultrafast and bias-free all-optical wavelength conversion using III-V-on-silicon technology

Using a 7.5 μm diameter disk fabricated with III-V-on-silicon fabrication technology, we demonstrate bias-free all-optical wavelength conversion for non-return-to-zero on-off keyed pseudorandom bit sequence (PRBS) data at the speed of 10 Gbits/s with an extinction ratio of more than 12 dB. The working principle of such a wavelength converter is based on free-carrier-induced refractive index modulation in a pump-probe configuration. We believe it to be the first bias-free on-chip demonstration of all-optical wavelength conversion using PRBS data. All-optical gating measurements in the pump-probe configuration with the same device have revealed that it is possible to achieve wavelength conversion beyond 20 Gbits/s.     

Numerical Eulerian method for linearized gas dynamics in the high frequency regime

We study the propagation of an acoustic wave in a moving fluid in the high frequency regime. We calculate the asymptotic approximation of the solution, around a mean flow, of this problem using an Eulerian method. By introducing the stretching matrix (deformation tensor for the geometrical optics rays) of the linearized Euler system, we deduce the geometrical spreading. This quantity is the key tool for computing the leading order term of the asymptotic expansion thanks to a conservation equation along the group velocity. The main contribution is to construct and implement a numerical scheme in the Eulerian framework for the eikonal equation and for the transport equation on the stretching matrix. We present numerical results for several test cases to study the convergence and validate our approach.     

Fixed Points of Compact Quantum Groups Actions on Cuntz Algebras

Given an action of a Compact Quantum Group (CQG) on a finite dimensional Hilbert space, we can construct an action on the associated Cuntz algebra. We study the fixed point algebra of this action, using Kirchberg classification results. Under certain conditions, we prove that the fixed point algebra is purely infinite and simple. We further identify it as a C ^*-algebra, compute its K-theory and prove a “stability property”: the fixed points only depend on the CQG via its fusion rules. We apply the theory to SU _q (N) and illustrate by explicit computations for SU _q (2) and SU _q (3). This construction provides examples of free actions of CQG (or “principal noncommutative bundles”).     

Racemization of secondary alcohols catalyzed by ruthenium: application to chemoenzymatic dynamic resolution

In this paper, we have shown that the [RuCl₂(p-cymene)]₂ complex associated with simple hemisalen ligands is able to racemize (S)-1-phenylethanol. The influence on the racemization process of the ligand’s structure as well as the nature of a co-catalyst have been evaluated and optimized. This [RuCl₂(p-cymene)]₂/Ligand/TEMPO racemization system was then associated with the Candida Antarctica B lipase in order to carry out dynamic kinetic resolution experiments on rac-phenylethanol. This led us to identify the best conditions for effective DKR, which was then applied to various secondary benzylic and aliphatic alcohols. It was thus possible to obtain (R)-1-cyclohexylethyl acetate from rac-1-cyclohexylethanol in quantitative conversion and with high enantioselectivity (98%).