Phase stability of terawatt-class ultrabroadband parametric amplification

The phase stability of broadband (280 nm bandwidth) terawatt-class parametric amplification was measured, for the first time to our knowledge, with a combination of spatial and spectral interferometry. Measurements at four different wavelengths from 750 to 900 nm were performed in combination with numerical modeling. The phase stability is better than 1/23 rms of an optical cycle for all the measured wavelengths, depending on the phase-matching conditions in the amplifier.     

Narrow-line phase-locked quantum cascade laser in the 9.2 microm range

We report the operation of a 50 mW continuous-wave quantum cascade laser (QCL) in the 9.2 microm range, phase locked to a single-mode CO(2) laser with a tunable frequency offset. The wide free-running emission spectrum of the QCL (3-5 MHz) is strongly narrowed down to the kilohertz range, making it suitable for high-resolution molecular spectroscopy.     

Simultaneous Detection of Single Attoliter Droplet Collisions by Electrochemical and Electrogenerated Chemiluminescent Responses

We provide evidence of single attoliter oil droplet collisions at the surface of an ultra‐microelectrode (UME) by the observation of simultaneous electrochemical current transients (i–t curves) and electrogenerated chemiluminescent (ECL) transients in an oil/water emulsion. An emulsion system based on droplets of toluene and tri‐n‐propylamine (2:1 v/v) emulsified with an ionic liquid and suspended in an aqueous continuous phase was formed by ultrasonification. When an ECL luminophore, such as rubrene, is added to the emulsion droplet, stochastic events can be tracked by observing both the current blips from oxidation at the electrode surface and the ECL blips from the follow‐up ECL reaction, which produces light. This report provides a means of studying fundamental aspects of electrochemistry using the attoliter oil droplet and offers complementary analytical techniques for analyzing discrete collision events, size distribution of emulsion systems, and individual droplet electroactivity.     

A two-mass expanding exact space-time solution

In order to understand how locally static configurations around gravitationally bound bodies can be embedded in an expanding universe, we investigate the solutions of general relativity describing a space–time whose spatial sections have the topology of a 3-sphere with two identical masses at the poles. We show that Israel junction conditions imply that two spherically symmetric static regions around the masses cannot be glued together. If one is interested in an exterior solution, this prevents the geometry around the masses to be of the Schwarzschild type and leads to the introduction of a cosmological constant. The study of the extension of the Kottler space–time shows that there exists a non-static solution consisting of two static regions surrounding the masses that match a Kantowski–Sachs expanding region on the cosmological horizon. The comparison with a Swiss-Cheese construction is also discussed.     

Ruthenium-catalyzed enyne cycloisomerizations. Effect of allylic silyl ether on regioselectivity

The ruthenium-catalyzed cycloisomerization of 1,6- and 1,7-enynes substituted in the terminal allylic position with a tert-butyldimethylsilyl ether group emerges as an effective reaction to form unprecedented five- or six-membered rings possessing a geometrically defined enol silane. Straightforward synthetic access to a variety of achiral 1,6- and 1,7-enynes, as well as chiral ones, is presented. Ruthenium catalysts effect efficiently such single-step cycloisomerization at room temperature in acetone under neutral conditions. The cycloisomerization functions with (E) or (Z) 1,2-disubstituted alkenes. Parameters influencing the enol silane geometry are discussed. The level of selectivity depends on the alkyne substitution, the geometry of the double bond, and the nature of the catalyst. Furthermore, examples of stereoinduction are shown and lead to highly substituted carbo- and heterocycles with excellent diastereocontrol.     

Testing Gravity on Astrophysical Scales

We summarize a series of observational tests of the law of gravity on large astrophysical scales. These tests account for testing both the Poisson equation (inverse square law) using weak lensing and the Einstein equivalence principle through the test of the constancy of the constants of Nature. We emphasize the need to test general relativity on cosmological scales in light of the cosmological constant problem and of recent observational claims concerning the variation of fine structure constant.     

Beta zeolite supported on silicon carbide for Friedel-Crafts fixed-bed reactions

Beta zeolite supported on silicon carbide, with high thermal conductivity and high mechanical strength, was successfully used as an active and stable catalyst for Friedel-Crafts reactions in a fixed bed configuration.     

Interchange of infimum and integral

We prove a new interchange theorem of infimum and integral. Its distinguishing feature is, on the one hand, to establish a general framework to deal with interchange problems for nonconvex integrands and nondecomposable sets, and, on the other hand, to link the theorems of Rockafellar and Hiai-Umegaki with the one of Bouchitté-Valadier. We give an application to relaxation of nonconvex geometric integrals of Calculus of Variations.Received: 20 March 2002, Accepted: 12 March 2003, Published online: 16 May 2003