On the geometry of master-slave synchronization

In 1990, Pecora and Carroll reported the observation that one can synchronize the orbits of two identical dynamical systems, which may be chaotic, by feeding state variables of one of them to the other one with no feedback, a phenomenon often called master-slave synchronization. We report here some results on the theory of master-slave synchronization for maps and flows, which are all inspired by a similar geometric and coordinate independent point of view to the one introduced in master-slave synchronization by Tresser, Worfolk, and Bass. Our results are variations on the theme that projection often can compensate for expansion.(c) 2002 American Institute of Physics.     

Self-induced generation of an off-axis frequency shifted radiation from atoms

The transient resonant linear response at wavelength λ_a of an N two-level atom vapor driven by a strong pulse with wavelength λ_f = λ_a - |Δλ| is shown to promote an emission of radiation peaked at wavelength λ_c = λ_a + |Δλ| in a conical shell around the propagation axis of the incident beam. In the limit of weak excitation, i.e. for an incident Rabi frequency much smaller than the detuning, the cone angle is found to be equal to 2λμ(2N/ch|Δλ|)^{$\text{1}\text{2}$} where μ is the transition dipole moment.     

Solid-supported reagents and catalysts for the preparation of large ring compounds

Parallel combinatorial synthesis in solution using immobilized reagents, catalysts, and scavengers has emerged as a powerful technique for the preparation of diverse libraries of compounds. This technique has only recently been applied to the synthesis of large-ring compounds. In this comprehensive review several strategies are presented and discussed, including Pd-catalyzed allylic alkylation, Stille-coupling, macrolactonization and macrolactamization using solid supported reagents and catalysts. In several cases site isolation has allowed operation of these macrocyclization reactions in concentrated solution (pseudo-dilution effect).     

Design and synthesis of two pyrazole libraries based on o-hydroxyacetophenones

Two new solid-phase syntheses of substituted pyrazoles are described. The first includes supporting an o-hydroxyacetophenone on Merrifield resin, Vilsmeier-Haack formylation on the methyl group and cyclization with a substituted hydrazine to afford a pyrazole ring with two diversity centers. The second starts from o-hydroxyacetophenone supported on Wang resin, which undergoes a Claisen condensation with a carboxylic acid ester to yield a 1,3-dicarbonyl compound that cyclizes to a pyrazole using a hydrazine. Both methods have been used to synthesize two small pyrazole libraries.     

Parametric generation of twin photons in vertical triple microcavities

We report the realization of a monolithic vertical-cavity, surface emitting micro-optical parametric conversion nanostructure, triply resonant with the parametric frequencies, allowing parametric oscillation with ultra-low pump power threshold. The photonic phase-space naturally provides triple resonance for the parametric frequencies, together with built-in cavity phase-matching for the pump wave at normal incidence. Parametric oscillation is observed in both the strong and weak exciton–photon coupling regime, allowing a high operating temperature. Signal and idler beams can be collected at 0° or at finite angles. The OPO threshold is low enough to envisage the realization of an all-semiconductor electrically-pumped micro-parametric oscillator. To cite this article: C. Diederichs et al., C. R. Physique 8 (2007).