Razumikhin-type exponential stability criteria of neutral stochastic functional differential equations

The paper discusses both pth moment and almost sure exponential stability of solutions to neutral stochastic functional differential equations and neutral stochastic differential delay equations, by using the Razumikhin-type technique. The main goal is to find sufficient stability conditions that could be verified more easily then by using the usual method with Lyapunov functionals. The analysis is based on paper [X. Mao, Razumikhin-type theorems on exponential stability of neutral stochastic functional differential equations, SIAM J. Math. Anal. 28 (2) (1997) 389-401], referring to mean square and almost sure exponential stability.     

Polarization-controlled switching between diffraction orders in transverse-periodically aligned nematic liquid crystals

Transverse-periodic-oriented nematic liquid crystals (LCs) are a special type of optical axis grating that are capable of very high efficiency diffraction (theoretically, 100%) in thin layers of materials with thickness comparable to the radiation wavelength. In particular, they fully diffract linearly polarized input beam into circularly polarized +1st and -1st diffraction orders. We experimentally demonstrate switching between diffraction orders of such gratings when the polarization of the incident beam changes from right-circular to left-circular and vice versa with the aid of an electrically controlled LC phase retarder. Such a setup in which the diffraction efficiency and direction are controlled externally, without application of an electric field to the transverse-periodic grating, provides additional control opportunities and does not compromise the quality of the grating. The grating used in the experiment was 1.5 microm thick and had a period of 4 microm. The contrast ratio of switching between the +1st and -1st orders was as high as 267:1 for a He-Ne laser beam with a switching time of 6.6 ms.     

Theoretical prediction of a dramatic Q-factor enhancement and degeneracy removal of whispering gallery modes in symmetrical photonic molecules

Coupled-microdisk photonic molecules with high-symmetry geometries that support nondegenerate whispering gallery modes with high quality factors are numerically designed, based on a two-dimensional model. Dramatic enhancement of calculated Q factors of nondegenerate modes as compared with single-microdisk whispering gallery modes of the same radial order is achieved by tuning the intercavity coupling distances. Potential applications of this work to the design of single-mode coupled-microdisk structures with large spontaneous emission factors and low threshold lasing operation and to random laser simulations are discussed.     

Novel Zinc(II) Bis(Dipyrromethenate)-Doped Ethyl Cellulose Sensors for Acetone Vapor Fluorescence Detection

In this paper, we report on the results of spectrofluorimetric study of new fluorescent sensor based on [Zn₂L₂] doped in ethyl cellulose. The sensor optical signal is based on the rapid fluorescence quenching in the presence of acetone vapor. The acetone vapor detection limit in a gas mixture by means of sensor based on [Zn₂L₂] doped in ethyl cellulose is 1.68 ppb. Being highly sensitive to the acetone acetone presence, instant in response and easy to use, the sensor can find an application for the noninvasive diagnostics of diabetes as well as for the monitoring of the content of acetone acetone in the air at industrial and laboratory facilities.

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Refractive-index dispersion of glassy semiconductors in the pseudo-binary As2Se3–SbSI system

The bulk chalcogenide glasses in the pseudo-binary system (As₂Se₃)_100?x(SbSI)_x (with x = 20, 30, 50, 70 and 80 at.%) were prepared from high-purity elemental components by melt-quenching technique. It is a system with the variable ratio of classical amorphous compound As₂Se₃ and the molecule of antimony-sulphoiodide, SbSI, which in the monocrystal form is characterized as a ferroelectric. The refractive-index behaviour (magnitude and spectral dispersion) of investigated glasses was determined by the prism method and analyzed. To calculate and discuss the parameters of dispersion in the band gap region three different approaches were used (Cauchy, Sellmeier and Wemple–DiDomenico single-oscillator model). The comparison of the results shows good agreement between all applied models. It was found that the value of the refractive-index shows normal dispersion behaviour and increases with the increase of Sb (or SbSI) content in the investigated system, whereas the optical gap of these glasses E_g slightly decreases.     

Selective creation of maximum coherence in multi-level Λ system

We consider the creation of the maximum Raman coherence in the six-level Λ system using optimal control theory. Optimal fields are designed for different initial conditions, resonant, and off-resonant, using the Krotov method including a reference field into the cost functional. Suppression of the population transfer to the intermediate level is achieved via an additional functional constraint which depends on the system dynamics. We demonstrate that the spectrum of the optimised fields has major contribution from the corresponding resonant frequencies independently of the choice of carrier frequency of the initial guess field. We also indicate that the pulse train emerges as a solution of the control problem of coherence optimisation in multi-level quantum systems.     

Some optical specificity of ultrathin crystalline films

The changes of optical properties under boundary presence in molecular crystal nanofilm were theoretically investigated in this work. The dispersion law and states of excitons as well as their space distribution along boundary direction have been determined using adjusted Green's function method and also by combined analytical and numerical calculations. On the basis of real and imaginary part of relative permittivity, both absorption and refraction indices were determined, and the influences of boundary parameters on occurrence of a very selective and strictly discrete absorption were analyzed.     

Differential SERS activity of gold and silver nanostructures enabled by adsorbed poly(vinylpyrrolidone)

We report that poly(vinylpyrrolidone) (PVP), a common stabilizer of colloidal dispersions of noble metal nanostructures, has a dramatic effect on their surface-enhanced Raman scattering (SERS) activity and enables highly selective SERS detection of analytes of various type and charge. Nanostructures studied include PVP-stabilized Au-Ag nanoshells synthesized by galvanic exchange reaction of citrate-reduced Ag nanoparticles (NPs), as well as solid citrate-reduced Ag and Au NPs, both before and after stabilization with PVP. All nanostructures were characterized in terms of their size, surface plasmon resonance wavelength, surface charge, and chemical composition. While the SERS activities of the parent citrate-reduced Ag and Au NPs are similar for rhodamine 6G (R6G) and 1,2-bis(4-pyridyl)ethylene (BPE) at various pH values, PVP-stabilized nanostructures demonstrate large differences in SERS enhancement factors (EFs) between these analytes depending on their chemical nature and protonation state. At pH values higher than BPE's pK(a2) of 5.65, where the analyte is largely unprotonated, the PVP-coated Au-Ag nanoshells showed a high SERS EF of >10(8). In contrast, SERS EFs were 10(3)- to 10(5)-fold lower for the protonated form of BPE at lower pH values, or for the usually highly SERS-active cationic R6G. The differential SERS activity of PVP-stabilized nanostructures is a result of discriminatory binding of analytes within-adsorbed PVP monolayer and a subsequent increase of analyte concentration at the nanostructure surface. Our experimental and theoretical quantum chemical calculations show that BPE binding with PVP-stabilized Au-Ag nanoshells is stronger when the analyte is in its unprotonated form as compared to its cationic, protonated form at a lower pH.     

Unusual conformational preferences of 1,3‐dimethyl‐3‐isopropoxy‐3‐silapiperidine

The conformational analysis of the first representative of the Si‐alkoxy substituted six‐membered Si,N‐heterocycles, 1,3‐dimethyl‐3‐isopropoxy‐3‐silapiperidine, was performed by low‐temperature ¹H and ¹³C NMR spectroscopy and DFT theoretical calculations. In contrast to the expectations from the conformational energies of methyl and alkoxy substituents, the Me_axi‐PrO_eq conformer was found to predominate in the conformational equilibrium in the ratio Me_axi‐PrO_eq : Me_eqi‐PrO_ax of ca. 2 : 1 as from the ¹H and ¹³C NMR study. The thermodynamic parameters obtained by the complete line shape analysis showed that the main contribution to the barrier to ring inversion originates from the entropy term of the free energy of activation. Copyright © 2012 John Wiley & Sons, Ltd.