On the maslov index

In this paper we give four definitions of Maslov index and show that they all satisfy the same system of axioms and hence are equivalent to each other. Moreover, relationships of several symplectic and differential geometric, analytic, and topological invariants (including triple Maslov indices, eta invariants, spectral flow and signatures of quadratic forms) to the Maslov index are developed and formulae relating them are given. The broad presentation is designed with a view to applications both in geometry and in analysis. © 1994 John Wiley & Sons, Inc.     

Thermodynamics of a continuous medium with electric and magnetic dipoles

The thermodynamics of an electrically charged, multicomponent fluid with spontaneous electric and magnetic dipoles is analysed in the presence of electromagnetic fields. Taking into account the chemical composition of the current densities and stress tensors leads to three types of irreversible terms: scalars, vectors and pseudo-vectors. The scalar terms account for chemical reactivities, the vectorial terms account for transport and the pseudo-vectorial terms account for relaxation. The linear phenomenological relations, derived from the irreversible evolution, describe notably the Lehmann and electric Lehmann effects, the Debye relaxation of polar molecules and the Landau-Lifshitz relaxation of the magnetisation. This formalism accounts for the thermal and electric magnetisation accumulations and magnetisation waves. It also predicts that a temperature gradient affects the dynamics of magnetic vortices and drives magnetisation waves.     

β-Phosphorus Hyperfine Coupling Constant in Nitroxides: Conformational Effects in 6-Membered Ring Nitroxides

Recently, we reported a significant solvent effect on the phosphorus hyperfine coupling constant a _P in β-phosphorylated 6-membered ring nitroxides (?a _P = 24 G in Org. Biomol. Chem. 2015). Thus, it led us to investigate the effect of solvent for several 6-membered ring nitroxides. Although smaller than mentioned above, a change of 5–7 G in a _P with the polarity of solvent was still observed for these nitroxides. As for other β-phosphorylated nitroxides, a _N increases with the polarity/polarizability π* and the Hydrogen Bond Donating α properties of the solvent whereas a _P exhibits the reverse trends. The change of a _P with the solvent depends a lot on a subtle interplay between the destabilizing steric hindrance due to the bulkiness of the substituents and the stabilizing hyperconjugation interactions SOMO → σ*_C–P between the anti-bonding orbitals of the C–P bond and the SOMO.     

Quantum cloning with an optical fiber amplifier

It has been shown theoretically that a light amplifier working on the physical principle of stimulated emission should achieve optimal quantum cloning of the polarization state of light. We demonstrate close-to-optimal universal quantum cloning of polarization in a standard fiber amplifier for telecom wavelengths. For cloning 1-->2 we find a fidelity of 0.82, the optimal value being 5 / 6=0.83.     

Properties of a three-dimensional photonic jet

By focusing light with a sphere several wavelengths in diameter, we can obtain a photonic nanojet [Opt. Express 13, 526 (2005)]: if light is focused on the surface of the sphere, the width of the beam stays smaller than the wavelength along a distance of propagation of approximately two wavelengths and reaches a high intensity. We use the rigorous Mie theory to analyze the basic properties of the photonic jet in the general three-dimensional polarized case. This fast algorithm allows us to determine the influence of the radius and the refractive index of the sphere on the photonic jet. The polarization response is also studied. We observe that high-intensity concentrations and subwavelength focusing are two different effects. Their basic properties are analyzed, and explanations are proposed.     

Measurement of acoustic particle velocities in enclosed sound field: Assessment of two Laser Doppler Velocimetry measuring systems

The performances of two Laser Doppler Velocimetry (LDV) systems adapted for measuring the acoustic particle velocities are assessed in enclosed sound field. This assessment is performed by comparing the acoustic velocities measured by means of LDV to reference acoustic velocities estimated from sound pressure measurements. The two LDV systems are based on a single optical bench which delivers an optical signal called Doppler signal. The Doppler signal, which is frequency modulated, is analyzed by means of two signal processing systems, the BSA (Burst Spectrum Analyser from Dantec) on the one hand, and a system specifically developed for the estimation of the acoustic velocity on the other hand. Once the experimental setup has been optimized for minimizing the errors made on the reference velocities, the assessment is performed and shows that both systems can measure the acoustic velocity in enclosed field in two the frequency ranges [0-4 kHz] and [0-2 kHz] respectively for acoustic velocity amplitudes of 10 mm/s and 1 mm/s.     

Two-dimensional vectorial photonic crystals formed in azo-dye-doped liquid crystals

A 2D, square lattice, vectorial photonic crystal is formed by vectorial holography using an azo-dye-doped liquid-crystal material. Four coherent beams are interfered to generate a highly stable, switchable polarization holography structure. The formation of the vectorial lattice by the liquid-crystal molecular orientation is confirmed by diffraction pattern and polarization microscopy analysis. Simulations of the alignment and diffraction pattern are in good agreement with the experimental results. Polarization sensitive diffraction behavior is also consistent with the Kakichashvili model.     

Simultaneous detection of ultraviolet and infrared radiation in a single GaN/GaAlN heterojunction

Results are presented for a dual-band detector that simultaneously detects UV radiation in the 250-360 nm and IR radiation in the 5-14 microm regions with near zero spectral cross talk. In this detector having separate UV- and IR-active regions with three contacts (one common contact for both regions) allows the separation of the UV and IR generated photocurrent components, identifying the relative strength of each component. This will be an important development in UV-IR dual-band applications such as fire-flame detection, solar astronomy, and military sensing, eliminating the difficulties of employing several individual detectors with separate electronics-cooling mechanisms.