Kilohertz laser frequency sensing with Brillouin mutually modulated cross-gain modulation

Using mutually modulated cross-gain modulation, Stokes optical frequency changes are converted into modulation phase changes with high sensitivity. In the slow-light transition regime, we demonstrate kilohertz sensitivity to the Stokes optical carrier frequency. The sensitivity is inversely proportional to the modulation frequency of the pump and Stokes beams.     

Near-field measurement of amplitude and phase in silicon waveguides with liquid cladding

Heterodyne near-field scanning optical microscopy (H-NSOM) has proven useful as a tool for characterization of both amplitude and phase of on-chip photonic devices in air, but it has previously been unable to characterize devices with a dielectric overcladding, which is commonly used in practice for such devices. Here we demonstrate H-NSOM of a silicon waveguide with a liquid cladding emulating the solid dielectric. This technique allows characterization of practical devices with realistic refractive index profiles. Fourier analysis is used to estimate the effective refractive index of the mode from the measured data, showing an index shift of 0.08 from air to water cladding, which is seen to correspond well to simulations.     

γ-Active Constraints in Convex Semi-Infinite Programming

In this article, we extend the definition of γ-active constraints for linear semi-infinite programming to a definition applicable to convex semi-infinite programming, by two approaches. The first approach entails the use of the subdifferentials of the convex constraints at a point, while the second approach is based on the linearization of the convex inequality system by means of the convex conjugates of the defining functions. By both these methods, we manage to extend the results on γ-active constraints from the linear case to the convex case.     

1,3‐Dipolar cycloaddition of unstabilized N‐methyl azomethine ylide to nitrobenzene annelated with azoles

The 1,3‐dipolar cycloaddition of unstabilized N‐methyl azomethine ylide to mononitro benzazoles was studied. Depending on the nature of substituents and annelated azoles, the reaction affords previously unknown isoindole fused heterocyclic systems. The reactivity of the cycloadducts was examined. J. Heterocyclic Chem., (2011).     

In response to the article by Maxim Kontsevich: Rozansky–Witten Invariants Via Formal Geometry

We show that recently constructed invariants of 3-dimensional manifolds and of hyperkähler manifolds (L. Rozansky and E. witten) come from characteristic classes of foliations and from Gelfand-fuks cohomology.     

Low-temperature Na4Ti5O12 from X-ray and neutron powder diffraction data

The crystal structure of the low-temperature Na₄Ti₅O₁₂ (tetra­sodium penta­titanium dodeca­oxide) phase has been solved and refined from X-ray and neutron powder diffraction data at 295 K. The structure is trigonal, space group P3, with Z = 1, although it is pseudo-centrosymmetric. The O and Na atoms form a distorted close-packed structure, where Ti atoms occupy octahedral sites.     

Capelli identities for classical Lie algebras

We extend the Capelli identity from the Lie algebra to the other classical Lie algebras and . We employ the theory of reductive dual pairs due to Howe. Received: 12 February 1997 / in revised form: 24 July 1998     

New Proof of the Cheeger–Müller Theorem

We present a short analytic proof of the equality between the analytic and combinatorialtorsion. We use the same approach as in the proof given by Burghelea, Friedlander andKappeler, but avoid using the difficult Mayer-Vietoris type formula for the determinantsof elliptic operators. Instead, we provide a direct way of analyzing the behaviour of thedeterminant of the Witten deformation of the Laplacian. In particular, we show that thisdeterminant can be written as a sum of two terms, one of which has an asymptoticexpansion with computable coefficients and the other is very simple (no zeta-functionregularization is involved in its definition).