Orthogonal almost-complex structures of minimal energy

In this article we apply a Bochner type formula to show that on a compact conformally flat riemannian manifold (or half-conformally flat in dimension 4) certain types of orthogonal almost-complex structures, if they exist, give the absolute minimum for the energy functional. We give a few examples when such minimizers exist, and in particular, we prove that the standard almost-complex structure on the round S ⁶ gives the absolute minimum for the energy. We also discuss the uniqueness of this minimum and the extension of these results to other orthogonal G-structures.     

Nonlinear phase shift from photon-photon scattering in vacuum

We show that QED nonlinear effects imply a phase correction to the linear evolution of electromagnetic waves in vacuum. We provide explicit solutions of the modified Maxwell equations for the propagation of a superposition of two plane waves and calculate analytically and numerically the corresponding phase shift. This provides a new framework for the search of all-optical signatures of photon-photon scattering in vacuum. In particular, we propose an experiment for measuring the phase shift in projected high-power laser facilities.     

Single-design-parameter microstructured optical fiber for chromatic dispersion tailoring and evanescent field enhancement

A microstructured optical fiber with a single design parameter is proposed and demonstrated. In such a structure three thin, long glass webs join in the fiber center, forming its core. By changing the web thickness it is possible to tune the zero-dispersion wavelength from approximately 0.7 to >2.0 microm while keeping a tiny core area and single-mode guidance. Supercontinuum generation is shown in a silica fiber with a web thickness of 850 nm. The small core area and the massive hole area also make the structure very attractive for the sensing and study of fluids.     

Intrinsic gas-phase reactivity of ionized 6-(oxomethylene)cyclohexa-2,4-dienone: evidence pointing to its neutral alpha-oxoketene counterpart as a proper precursor of various benzopyran-4-ones and analogues

Despite its unique structure and potential use as an important building block in organic synthesis, the title alpha-oxoketene 1 has been formed mostly under very special conditions as a short-lived species. The reactivity of 1 is, therefore, nearly unexplored. In great contrast, it seemed that its ionized gaseous form 1*+ is stable and easily accessible. In this study, we used multiple-stage pentaquadrupole mass spectrometry to probe the formation of gaseous 1*+ and explore its stability and intrinsic reactivity. With water and methanol, gaseous 1*+ was found to react similarly to solvated 1, which indicates that there is a close parallel between their reactivities. Gaseous 1*+ was also found to react promptly via polar [3 + 2] cycloadditons with various dienophiles including alkenes, alkynes, isocyanates, ketones and esters, thus forming a series of benzopyran-4-ones (flavones, 4-chromanones, 4-chromenones, benzo[1,3]dioxin-4-ones, and analogues) that are common structural units in many natural products. The present availability of 1 at room temperature and the gas-phase findings reported herein for gaseous 1*+ indicate that solvated 1 should undergo many [4 + 2] cycloadditions and functions as a versatile precursor of a variety of biologically active molecules.     

Pi-pi stacking versus steric effects in stereoselectivity control: highly diastereoselective synthesis of syn-1,2-diarylpropylamines

N-Arylarylideneamines react with sulfinylbenzyl carbanions derived from 2-(p-tolylsulfinyl)toluenes (S)-1 and (S)-2, affording epimeric mixtures at C1 of 1,2-diarylethyl- and 1,2-diarylpropylamine derivatives. The sulfinyl group completely controls the configuration at C2 in the reactions of (S)-2. The configuration at C1 depends on the electron density of the ring adjacent to the iminic carbon atom which is modulated by pi-pi stacking interactions with the ring joined to the carbanionic centre. The stereoselectivity was controlled by modifying the acceptor character of the arylideneamine ring with appropriate substituents, the formation of the highly selective (R) configuration at C1 being made possible by electron-donating groups. N-(2,4,6-Trimethoxyphenyl)arylideneamines have been shown to be suitable starting materials for the preparation of (R)-1,2-diarylethyl- and (1R,2S)-1,2-diarylpropylamines (syn epimers) in a highly stereoselective manner.