Second-order Coefficients Research Articles

Nonlinear generation of an optical bottle beam in domain-engineered ferroelectric crystals.

Nonlinear wavefront shaping in periodically poled ferroelectric crystals has received great attention because it offers a convenient way to generate a structured light beam at new frequencies. In contrast to structurally uniform beams like Laguerre-Gaussian or Hermite-Gaussian modes, here we demonstrate the possibility to generate a spatially varied optical bottle beam via a frequency doubling process in a domain-engineered Sr0.61Ba0.39Nb2O6 (SBN) crystal. The nonlinear holography method was employed to design the modulation pattern of the second-order nonlinear coefficient χ(2), and the femtosecond laser poling was used to imprint the χ(2) pattern into the SBN crystal via ferroelectric domain inversion. The second harmonic bottle beam with zero intensity in its center that is surrounded in all three dimensions by light was observed with the incidence of a fundamental Gaussian beam. These results are useful for nonlinear generation and control of structured light at new frequencies, which has important applications in nonlinear photonics and quantum optics.

Measurement of the Sensitivity of Two-Particle Correlations in pp Collisions to the Presence of Hard Scatterings.

A key open question in the study of multiparticle production in high-energy pp collisions is the relationship between the "ridge"-i.e., the observed azimuthal correlations between particles in the underlying event that extend over all rapidities-and hard or semihard scattering processes. In particular, it is not known whether jets or their soft fragments are correlated with particles in the underlying event. To address this question, two-particle correlations are measured in pp collisions at sqrt[s]=13 TeV using data collected by the ATLAS experiment at the LHC, with an integrated luminosity of 15.8 pb^{-1}, in two different configurations. In the first case, charged particles associated with jets are excluded from the correlation analysis, while in the second case, correlations are measured between particles within jets and charged particles from the underlying event. Second-order flow coefficients, v_{2}, are presented as a function of event multiplicity and transverse momentum. These measurements show that excluding particles associated with jets does not affect the measured correlations. Moreover, particles associated with jets do not exhibit any significant azimuthal correlations with the underlying event, ruling out hard processes contributing to the ridge.

The dynamical second-order transport coefficients of smeared Dp-brane

The smeared Dp-brane is constructed by having the black Dp-brane uniformly smeared over several transverse directions. After integrating the spherical directions and the smeared directions, the smeared Dp-brane turns out to be a Chamblin-Reall model with one background scalar field. Within the framework of the fluid/gravity correspondence, we not only prove the equivalence between the smeared Dp-brane and the compactified Dp-brane by explicitly calculating the 7 dynamical second-order transport coefficients of their dual relativistic fluids, but also revisit the Correlated Stability Conjecture for the smeared Dp-brane via the fluid/gravity correspondence.

A Hanbury Brown and Twiss renascence: measurement of photon correlations yields spatio-temporal coherence

Investigations of photon correlations similar to the Hanbury Brown and Twiss experiment are since the advent of quantum optics in the center of both fundamental and application-oriented research. We derive a factorial moment-generating function of the probability distribution of electromagnetic radiation emitted by a source and absorbed by a photodetector from which we calculate an analytical expression for the second-order correlation coefficient g^{(2)} which reflects spatial coherence properties of the emitted light. The measurement of g^{(2)} thus allows to retrieve the spatial coherence parameter of the light source in terms of the combination of source area, source-detector distance, wavelength and detector area. The validity of the concept is proven by investigating g^{(2)} of true thermal light from a Xenon arc lamp and from the sun for various detector areas, in excellent agreement with the theory. Finally, we suggest a novel scheme for determining light source diameters by exploiting the spatially dependent statistics and confirm its validity by exemplary calculations. These results based on radiation thermodynamics and photon statistics give fresh insight into quantum optical properties of classical light sources, photon correlations and photodetection with promising applications perspectives, more than 68 years after the original Hanbury Brown and Twiss experiment.

Measurements of azimuthal anisotropies at forward and backward rapidity with muons in high-multiplicity p–Pb collisions at [formula omitted] TeV

The study of the azimuthal anisotropy of inclusive muons produced in p–Pb collisions at sNN=8.16 TeV, using the ALICE detector at the LHC is reported. The measurement of the second-order Fourier coefficient of the particle azimuthal distribution, v2, is performed as a function of transverse momentum pT in the 0–20% high-multiplicity interval at both forward (2.03<yCMS<3.53) and backward (−4.46<yCMS<−2.96) rapidities over a wide pT range, 0.5<pT<10 GeV/c, in which a dominant contribution of muons from heavy-flavour hadron decays is expected at pT>2 GeV/c. The v2 coefficient of inclusive muons is extracted using two different techniques, namely two-particle cumulants, used for the first time for heavy-flavour measurements, and forward–central two-particle correlations. Both techniques give compatible results. A positive v2 is measured at both forward and backward rapidities with a significance larger than 4.7σ and 7.6σ, respectively, in the interval 2<pT<6 GeV/c. Comparisons with previous measurements in p–Pb collisions at sNN=5.02 TeV, and with AMPT and CGC-based theoretical calculations are discussed. The findings impose new constraints on the theoretical interpretations of the origin of the collective behaviour in small collision systems.

Chiral Hybrid Germanium(II) Halide with Strong Nonlinear Chiroptical Properties.

Due to the pronounced anisotropic response to circularly polarized light, chiral hybrid organic-inorganic metal halides have been regarded as promising candidates for the application in nonlinear chiroptics, especially for the second-harmonic generation circular dichroism (SHG-CD) effect. However, designing novel lead-free chiral hybrid metal halides with large anisotropy factors and high laser-induced damage thresholds (LDT) of SHG-CD remains challenging. Herein, we develop the first chiral hybrid germanium halide, (R/S-NEA)3 Ge2 I7 ⋅H2 O (R/S-NGI), and systematically investigated its linear and nonlinear chiroptical properties. S-NGI and R-NGI exhibit large anisotropy factors (gSHG-CD ) of 0.45 and 0.48, respectively, along with a high LDT of 38.46 GW/cm2 ; these anisotropy factors were the highest values among the reported lead-free chiral hybrid metal halides. Moreover, the effective second-order nonlinear optical coefficient of S-NGI could reach up to 0.86 pm/V, which was 2.9 times higher than that of commercial Y-cut quartz. Our findings facilitate a new avenue toward lead-free chiral hybrid metal halides, and their implementation in nonlinear chiroptical applications.

Research on the calculation method of sensitivity coefficients of reactor power to material density based on Monte Carlo perturbation theory

The ability to calculate the material density sensitivity coefficients of power with respect to the material density has broad application prospects for accelerating Monte Carlo-Thermal Hydraulics iterations. The second-order material density sensitivity coefficients for the general Monte Carlo score have been derived based on the differential operator sampling method in this paper, and the calculation of the sensitivity coefficients of cell power scores with respect to the material density has been realized in continuous-energy Monte Carlo code RMC. Based on the power-density sensitivity coefficients, the sensitivity coefficients of power scores to some other physical quantities, such as power-boron concentration coefficients and power-temperature coefficients considering only the thermal expansion, were subsequently calculated. The effectiveness of the proposed method is demonstrated in the power-density coefficients problems of the pressurized water reactor (PWR) moderator and the heat pipe reactor (HPR) reflectors. The calculations were carried out using RMC and the ENDF/B-VII.1 neutron nuclear data. It is shown that the calculated sensitivity coefficients can be used to predict the power scores accurately over a wide range of boron concentration of the PWR moderator and a wide range of temperature of HPR reflectors.

A simple approach for the protection of EHV transmission lines

Due to the geographically widespread nature of the transmission lines, the chances of fault occurrence are more due to outdoor erection. This makes it inevitable to detect and isolate the faulty section of the system as quickly as possible. The existing fault detection and classification algorithms are limited to a specific configuration of transmission lines. This work has proposed a novel and simple methodology to recognize and classify faults on transmission lines by using single-end current data. A Harmonic Phasor Measurement Unit (HPMU) based on a non-recursive DFT algorithm is used to extract the fundamental and second-order harmonic components from current samples. The Equivalent Fundamental Component (EFC) and ΔEFC are estimated from the extracted data. Subsequently, an Index Matrix (P) is derived to recognize the fault. The non-zero value of the determinant of the index matrix detects the occurrence of a fault in the system. Second-order harmonic fault current coefficients are proposed for fault classification based on the second-order harmonic component extracted from HPMU. The proposed method accurately detects and classifies all types of conventional faults and cross-country faults (CCF) for any configuration of transmission network. The proposed method has also been validated under various abnormal conditions in PSCAD/EMTDC to ensure its efficacy.

Size of living space as a moderator for central and peripheral refractions in children

Undesirable living environment may impose risk on myopia development. Furthermore, peripheral refractive error was suggested to contribute to juvenile eye growth modulation. This study aimed to investigate the interaction between peripheral refractive error and living environment in relation to central refractive status in Hong Kong schoolchildren. Central and peripheral refractive errors, axial length (AL), and corneal radius of curvature (CR) were measured in 573 schoolchildren (age 9.5 ± 0.9 years). The AL/CR ratio was used to represent the central refractive status, accounting for non-cycloplegic refraction. The relative peripheral refractive errors (RPRE) up to ± 20° eccentricities were converted into power vectors: spherical-equivalent error (SER) and J0 astigmatic components and fitted with quadratic equations. The second-order coefficients of SER (aSER) and J0 astigmatism (aJ0) and home size reported by parental questionnaires were analyzed to indicate their relationships with AL/CR. Our results showed that children with higher AL/CR lived in smaller homes (p = 0.01) and had a more hyperopic (p < 0.001) but less astigmatic RPRE (p = 0.01). We further analyzed the relationship between AL/CR with RPRE for children living in small (< 300 ft2), moderate (300–600 ft2), and large home sizes (> 600 ft2). Regardless of the home size, a higher AL/CR remained moderately correlated with a more hyperopic aSER (all p < 0.001). However, a higher AL/CR was associated with a more positive aJ0 only in children living in large homes, and the relationships were not significant for small and moderate home sizes. Linear regression models further indicated that home size was a significant moderator contributing to the relationship between AL/CR and aJ0. In conclusion, our results were consistent with previous studies, showing that children with axial myopia usually lived in smaller homes and had more hyperopic defocus and more positive J0 astigmatism. However, the relationship between peripheral astigmatism and axial refraction was modulated by the home size of Hong Kong schoolchildren. While peripheral astigmatism is hypothesized as a visual cue for axial refractive development in children, extrinsic environmental factors, such as home size, might interfere with the relationship and dominate refractive development.

High-Efficiency Second-Harmonic Generation Using Quasi-Bound State in LiNbO3 Metasurface

We numerically demonstrated a high-efficiency second-harmonic generation (SHG) using quasi-bound state in the continuum (quasi–BIC) in thin film LiNbO3 (TFLN) metasurface. The TFLN possessed exceptionally high second-order nonlinear coefficients, contributing to the enhanced SHG performance. An eccentric cylinder unit cell was presented to achieve high Q–factor resonances associated with the asymmetric parameter introduced. Simulations showed that the high efficiency of the second-harmonic conversion was obtained by using the high Q–factor of the asymmetric dielectric cylinder metasurface, and it achieved a high SHG efficiency of 6.5% at pump intensities as low as 1 MW/cm2 at a normal incident. Furthermore, the simulation results indicated that breaking the symmetry through oblique incidence was more effective in achieving a higher Q–factor compared to altering the structural parameters. Specifically, under 1° oblique incidences, the conversion efficiency could reach 1.2% at an incident power of 1 kW/cm². We have proposed a method to achieve a high conversion efficiency of second-harmonic generation in low-refractive-index materials. Our work not only offers theoretical support but also provides valuable insights for the advancement of efficient nonlinear frequency doubling technology, optical communication, and sensing applications.

Assessment of tight-binding models for high-harmonic generation in zinc blende materials.

Using a simulator for semiconductor Bloch equations (SBEs) accounting for the entire Brillouin zone, we examine the tight-binding (TB) description for zinc blende structure as a model for high-harmonic generation (HHG). We demonstrate that TB models of GaAs and ZnSe exhibit second-order nonlinear coefficients that compare favorably with measurements. For the higher-order portion of the spectrum, we use the results published by Xia et al. in Opt. Express26, 29393 (2018)10.1364/OE.26.029393 and show that the HHG spectra measured in reflection can be closely reproduced by our simulations free of adjustable parameters. We conclude that despite their relative simplicity, the TB models of GaAs and ZnSe represent useful tools to study both the low- and higher-order harmonic response in realistic simulations.

Various exact optical soliton solutions for time fractional Schrodinger equation with second-order spatiotemporal and group velocity dispersion coefficients

Various exact optical soliton solutions for time fractional Schrodinger equation with second-order spatiotemporal and group velocity dispersion coefficients

Multiplexing Linear and Nonlinear Bragg Diffractions through Volume Gratings Fabricated by Femtosecond Laser Writing in Lithium Niobate Crystal

The femtosecond-laser-writing technique provides a flexible method for fabrication of nonlinear photonic crystals in three dimensions, providing structures that enable efficient complex nonlinear wave interactions and modulation for applications including nonlinear holography, nonlinear beam shaping, and waveguide-integrated wavelength conversion. However, the tightly focused laser pulse inevitably causes structural modification and then changes the local refractive index, resulting in additional linear modulation of the interacting waves. Here, we use the same periodic distributions of the refractive index and the second-order nonlinear coefficient for grating arrays engineered in lithium niobate crystals by femtosecond laser writing to achieve polarization-dependent linear and nonlinear Bragg diffractions simultaneously. The experimental results show that the linear and nonlinear diffraction efficiencies range up to 31% and 2.9 × 10−5, respectively, for grating arrays with dimensions of 100 μm (x) × 100 μm (y) × 100 μm (z). This work paves the way toward the realization of the multiplexing of linear and nonlinear optical modulations in a single structure for potential applications that include multidimensional optical data storage and optical coding.

A homogenized model accounting for dispersion, interfaces and source points for transient waves in 1D periodic media

A homogenized model is proposed for linear waves in 1D microstructured media. It combines second-order asymptotic homogenization (to account for dispersion) and interface correctors (for transmission from or towards homogeneous media). A new bound on a second-order effective coefficient is proven, ensuring well-posedness of the homogenized model whatever the microstructure. Based on an analogy with existing enriched continua, the evolution equations are reformulated as a dispersive hyperbolic system. The efficiency of the model is illustrated via time-domain numerical simulations. An extension to Dirac source terms is also proposed.

Lattice Study of the Equation of State of a Rotating Gluon Plasma

The effect of uniform rotation on the equation of state of gluodynamics has been studied in lattice simulation. To this end, the system has been considered in the corotating reference frame, where the rotation can be modeled as an external gravitational field. The free energy of the studied system in the case of sufficiently slow rotation can be expanded in a power series in the angular velocity. The moment of inertia given by the second-order coefficient of this expansion has been calculated and its dependence on the temperature and the dimensions of the rotating system has been determined. Our results indicate that the moment of inertia of gluodynamics is negative up to the temperature T * ~ 1.5Tc, where Tc is the critical temperature of the confinement/deconfinement phase transition, and becomes positive at temperatures T > T *. The negative moment of inertia has been attributed to the thermodynamic instability of the gluon plasma with respect to uniform rotation.

Energy-Harvesting Performance in a LaYFe2O6/P(VDF-HFP) Nanocomposite by Boosting the Magnetoelectric Effect

The present work reports an enhanced magnetoelectric (ME) effect at room temperature (RT) and above in a nanocomposite of LaYFe2O6/poly(vinylidene fluoride)–hexafluoropropylene [LaYFe2O6/P(VDF-HFP)], which is prepared by the solution-casting method. Field-emission scanning electron microscopy, X-ray diffraction, and Fourier transform infrared spectroscopy reveal excellent phase-to-phase connectivity and an enhanced beta-phase fraction in the PVDF matrix by the incorporation of 10 wt % antiferromagnetic nanoparticles (NPs). This is also substantiated by the improved ferroelectric (electric-field-dependent polarization) response by a 10 wt % sample. At RT, this nanocomposite manifests a first-order ME coupling coefficient of ∼2.92 mV cm–1 Oe–1 and a second-order ME coupling coefficient of ∼0.051 μV cm–1 Oe–2 (significantly 1 order higher than that of pristine LaYFe2O6). The enhanced ME coefficient at RT and above makes it a viable candidate to address the challenges of ME-based device applications. A flexible, portable, lightweight, cost-effective magnetoelectric nanogenerator (MENG) fabricated from the nanocomposite film is able to harvest the wasted magnetic energy with an efficiency of 1.5%. As a demonstration, the harvested electric energy is stored in a capacitor, which, in turn, is used to power a light-emitting diode (LED). The present work hence suggests the deployment of this material for self-powered wearable devices.

Fabrication of low-loss III-V Bragg-reflection waveguides for parametric down-conversion

Entangled photon pairs are an important resource for many types of quantum protocols. Semiconductor Bragg-reflection waveguides are a promising photon-pair source due to mature fabrication, integrability, large transparency window in the telecom wavelength range, integration capabilities for electro-optical devices as well as a high second-order nonlinear coefficient. To increase performance, we improved the fabrication of Bragg-reflection waveguides by employing fixed-beam-moving-stage optical lithography, low-pressure, and low chlorine concentration etching, and resist reflow. The reduction in sidewall roughness yields a low optical loss coefficient for telecom wavelength light of αreflow = 0.08 (6) mm−1. Owing to the decreased losses, we achieved a photon-pair production rate of 8800 (300) (mW · s · mm)−1, which is 15-fold higher than in previous samples.

Influence of the blade size on the dynamic characteristic damage identification of wind turbine blades

Abstract In this article, the sensitivity coefficients of dynamic characteristic damage identification of blades with different sizes were investigated. The results show that the first third-order vibration modes of the blade before and after damage are consistent, and the wind turbine blade size has no significant effect on the vibration mode; with the increase of the blade size, the first-, third- and fourth-order natural frequency sensitivity coefficients decrease gradually, while the second-, fifth- and sixth-order natural frequency sensitivity coefficients increase gradually; as the blade size increases, the third-order displacement mode sensitivity coefficient of the blade gradually increases, which indicates that the displacement modes identification effect is better with the increase of the blade size. With the increase of the blade size, the first- and third-order strain modal sensitivity coefficients increase gradually, which indicates that when using first- and third-order strain modes for damage identification, the larger the blade size, the better the identification effect; with the increase of the blade size, the second-order strain modal sensitivity coefficient decreases gradually, which indicates that when using second-order strain mode for damage identification, the larger the blade size, the worse the identification effect. This research could provide a theoretical basis for the application of the dynamic characteristic damage identification method in the damage identification of wind turbine blades of different sizes.

Solving the homogeneous BVP of second order linear FDEs with fuzzy parameters under granular differentiability concept1

In this paper, the second-order fuzzy homogeneous differential equation is transformed into a more special simplest form under the condition that the solution of the boundary value problem of the equation exists and is unique. Then the eigenvalues of the boundary value problem of the second-order simplest fuzzy homogeneous differential equation are studied and the theorems that make the eigenvalues exist are proposed and then illustrated with examples. Finally, it is proved that when the second-order fuzzy coefficient p ˜ ( t ) in the second-order fuzzy homogeneous differential equation is a fuzzy number, the solution set of its corresponding second-order granular homogeneous differential equation becomes larger, that is, the solution set of fuzzy differential equations with real numbers is a subset of the solution set with fuzzy coefficients as fuzzy numbers.

The Polarimetric Radar Scattering Properties of Oriented Aggregates

Abstract The scattering properties of aggregates are studied herein. Early aggregates (&lt;7 monomers) of branched planar crystals and mature aggregates (up to 100 monomers) of columns are randomly generated with varying assumptions about the monomer attachment processes and the orientation behavior during collection. The resulting physical properties of the aggregates correspond well with prior in situ and retrieved sizes and shapes. Assumed azimuthally uniform orientations during collection and monomer pivoting upon attachment resulted in flatter and denser aggregates. The column aggregates had lower density and more spherical shapes than the branched planar crystal aggregates. The scattering properties were calculated using the discrete dipole approximation for a set of orientation angles and transformed to spectral coefficients representing modes of orientation angle variability. The zeroth- and second-order coefficients dominate this variability, with the zeroth-order coefficients representing the scattering properties for randomly oriented particles. The second-order coefficients for backscatter showed differences between horizontal and vertical polarization increasing with density, and these coefficients for specific differential phase increase with both mass and density. Similarly, coefficients for the copolar covariance decreased with density. Rapid changes in the contributions to the radar moments from the second-order coefficients from low to moderate density were observed, likely due to the increasing presence of horizontally aligned monomers in the aggregate structure. Differences in how differential reflectivity and correlation coefficient evolve with the orientation distribution parameters suggest that these measurements, along with specific differential phase and reflectivity, provide complementary information about aggregate sizes, shapes, and orientation distributions.