Propagation of Gaussian beams through parabolic index optical waveguides with random dielectric constant gradient

Abstract

The propagation of gaussian beams through parabolic index optical waveguides having random irregularities in the dielectric constant gradient has been studied. For fundamental mode propagation, the perturbation approach has been employed and an analytic expression for the loss of power from the fundamental mode has been obtained. For an incident gaussian beam with arbitrary width, geometrical optics approximation has been used and an exact analytical expression for the average value of the beamwidth has been derived for a particular random process, namely, the dichotomic Markov process. The fluctuations in the beamwidth have also been calculated.     

Multiobjective fractional programming problems involving (p,r)?ρ?(η,θ)-invex function

In this paper we move forward in the study of multiobjective fractional programming problem and established sufficient optimality conditions under the assumption of (p,r)????(??,??)-invexity. Weak, strong and strict converse duality theorems are also derived for three type of dual models related to multiobjective fractional programming problem involving aforesaid invex function.     

Colour emission tunability in Ho3+–Tm3+–Yb3+ co-doped Y2O3 upconverted phosphor

The frequency upconversion (UC) emission throughout the visible region from the Y₂O₃:Ho³⁺?CTm³⁺?CYb³⁺ co-doped phosphors synthesized by using low temperature combustion process upon excitation with a diode laser operating at 980?nm have been presented. The colour emission tunability in co-doped phosphor has been observed on increasing the pump power and seen by the naked eyes. The tunability in colour emission has also been visualized by CIE chromaticity diagram. The variation in UC emission intensity of the ¹G₄????³H₆ (Tm³⁺) and ⁵F₃????⁵I₈ (Ho³⁺) transitions lying in the blue region has been monitored with increase in the pump power and marked that their ratio can be used to determine the temperature. The developed phosphor has been used to record fingerprints. The observed most intense visible colour emission from the developed material may be used for photodynamic therapy and as an alternative of traditional fluorescent biolabels.     

Selective Detection of Multicarboxylate Anions based on “Turn on” Electron Transfer by Self‐Assembled Molecular Rectangles

Two new large molecular rectangles ( 4 and 5 ) were obtained by the reaction of two different dinuclear arene ruthenium complexes [Ru₂(arene)₂(O O)₂Cl₂] (arene=p‐cymene; O O=2,5‐dihydroxy‐1,4‐benzoquinonato ( 2 ), 6,11‐dihydroxy‐5,12‐naphthacene dionato ( 3 )) with the unsymmetrical amide (N‐[4‐(pyridin‐4‐ylethynyl)phenyl]isonicotinamide) donor ligand 1 in methanol in the presence of AgO₃SCF₃, forming tetranuclear cations of the general formula [Ru₄(arene)₄( )₂(O O)₂]⁴⁺. Both rectangles were isolated in good yields as triflate salts and were characterized by multinuclear NMR, ESI‐MS, UV/Vis, and photoluminescence spectroscopy. The crystal structure of 5 was determined by X‐ray diffraction. Luminescent rectangle 5 was used for anion sensing with an amide ligand as a hydrogen‐bond donor and an arene–ruthenium acceptor as a signaling unit. Rectangle 5 strongly bound multicarboxylate anions, such as oxalate, tartrate, and citrate, in UV/Vis titration experiments in 1:1 ratios, in contrast to monoanions, such as F^?, Cl^?, NO₃^?, PF₆^?, CH₃COO^?, and C₆H₅COO^?. The fluorescence titration experiment showed a large fluorescence enhancement of 5 upon binding to multicarboxylate anions, which could be attributed to blocking of the photoinduced electron transfer process from the arene–ruthenium moiety to the amidic donor in 5 ; this was likely to be a result of hydrogen bonding between the ligand and the anion. On the other hand, rectangle 5 was not selective towards any other anions. To the naked eye, multicarboxylate anions in a solution of 5 in methanol appear greenish upon irradiation with UV light.     

Diphoton signals in theories with large extra dimensions to NLO QCD at hadron colliders

We present a full next-to-leading order (NLO) QCD corrections to diphoton production at the hadron colliders in both standard model and ADD model. The invariant mass and rapidity distributions of the diphotons are obtained using a semi-analytical two cut-off phase space slicing method which allows for a successful numerical implementation of various kinematical cuts used in the experiments. The fragmentation photons are systematically removed using smooth-cone-isolation cuts on the photons. The NLO QCD corrections not only stabilise the perturbative predictions but also enhance the production cross section significantly.     

Second order duality for nondifferentiable minimax programming problems with generalized convexity

In this paper, we are concerned with a class of nondifferentiable minimax programming problem and its two types of second order dual models. Weak, strong and strict converse duality theorems from a view point of generalized convexity are established. Our study naturally unifies and extends some previously known results on minimax programming.     

On Structured Surfaces with Defects: Geometry,Strain Incompatibility,Stress Field,and Natural Shapes

In this paper we study the stress and deformation fields generated by nonlinear inclusions with finite eigenstrains in anisotropic solids. In particular, we consider finite eigenstrains in transversely isotropic spherical balls and orthotropic cylindrical bars made of both compressible and incompressible solids. We show that the stress field in a spherical inclusion with uniform pure dilatational eigenstrain in a spherical ball made of an incompressible transversely isotropic solid such that the material preferred direction is radial at any point is uniform and hydrostatic. Similarly, the stress in a cylindrical inclusion contained in an incompressible orthotropic cylindrical bar is uniform hydrostatic if the radial and circumferential eigenstrains are equal and the axial stretch is equal to a value determined by the axial eigenstrain. We also prove that for a compressible isotropic spherical ball and a cylindrical bar containing a spherical and a cylindrical inclusion, respectively, with uniform eigenstrains the stress in the inclusion is uniform (and hydrostatic for the spherical inclusion) if the radial and circumferential eigenstrains are equal. For compressible transversely isotropic and orthotropic solids, we show that the stress field in an inclusion with uniform eigenstrain is not uniform, in general. Nevertheless, in some special cases the material can be designed in order to maintain a uniform stress field in the inclusion. As particular examples to investigate such special cases, we consider compressible Mooney-Rivlin and Blatz-Ko reinforced models and find analytical expressions for the stress field in the inclusion.     

Coupling of two parallel multimode parabolic index waveguides: An exact analysis in the weakly guiding approximation

A model analysis of a guiding structure consisting of two parallel multimode parabolic-index waveguides in the weakly guiding approximation has been presented. Such structures are expected to play an important role as directional couplers in data bus systems, etc. The modes thus obtained have been used to study the power exchange between the two waveguides and a simple analytical expression has been obtained for the coupling length in a case of practical importance.     

Chromatographic and electrophoretic migration parameters in capillary electrochromatography

Chromatographic retention factor, k', as defined in high-performance liquid chromatography (HPLC) in terms of the migration times of the separand and the inert tracer, has limited applicability to capillary electrochromatography (CEC) when both chromatographic and electrophoretic processes determine the magnitude of the overall migration rates of the separands. This situation is unlike that in HPLC, where k' serves as a useful peak locator for the various sample components, as well as, provides thermodynamic insights into the interactions between the components and the stationary phase. Most publications have borrowed the definition of k' from HPLC and applied it on CEC. However, due to the dual separation mechanisms that are in action in CEC, the system is significantly complicated in comparison to that of HPLC. This paper discusses the impossibility of defining with a k' which would have all the attributes that it has in regular chromatography. The interplay of the two separation mechanisms in determining the overall migration process in CEC is discussed and the various definitions of the electrochromatographic retention factor are presented.     

Migration behavior of weakly retained, charged analytes in voltage-assisted micro-high performance liquid chromatography

The application of voltage in micro-high performance liquid chromatography (micro-HPLC) creates a system where separation is governed by a hybrid differential migration process, which entails the features of both HPLC and capillary zone electrophoresis (CZE), i.e., chromatographic retention and electrophoretic migration. In this paper, we use our previously published approach to decouple these two mechanisms via analysis of the input data for estimation of electrokinetic parameters, such as conductivity, equivalent lengths, mobilities and velocities. Separation of weakly retained, charged analytes was performed via voltage-assisted micro-HPLC. Contrary to conclusions from data analysis using the conventional definitions of the retention factor, it is shown that our approach allows us to isolate the "chromatographic retention" component and thus, investigate the "modification" of the retention process upon application of voltage in micro-HPLC. It is shown that the traditional approaches of calculating retention factor would erroneously lead to conclusion that the retention behavior of these analytes changes upon application of voltage. However, the approach suggested here demonstrates that under the conditions investigated, most of the charged analytes do not show any significant retention on the columns and that all the changes in their retention times can be attributed to their electrophoretic migration.