Third-order Effects Research Articles

An SBAS Integrity Model to Overbound Residuals of Higher-Order Ionospheric Effects in the Ionosphere-Free Linear Combination

The next generation of satellite-based augmentation systems (SBAS) will support aviation receivers that take advantage of the ionosphere-free dual-frequency combination. By combining signals of the L1 and L5 bands, about 99% of the ionospheric refraction effects on the GNSS (Global Navigation Satellite Systems) signals can be removed in the user receivers without additional SBAS corrections. Nevertheless, even if most of the negative impacts on GNSS signals are removed by the ionospheric-free combination, some residuals remain and have to be taken into account by overbounding models in the integrity computation conducted by safety-of-live (SoL) receivers in airplanes. Such models have to overbound residuals as well, which result from the most rare extreme ionospheric events, e.g., such as the famous “Halloween Storm”, and should thus include the tails of the error distribution. Their application shall lead to safe error bounds on the user position and allow the computation of protection levels for the horizontal and vertical position errors. Here, we propose and justify such an overbounding model for residual ionospheric delays that remain after the application of the ionospheric-free linear combination. The model takes into account second- and third-order ionospheric refraction effects, excess path due to ray bending, and increased ionospheric total electron content (TEC) along the signal path due to ray bending.

Unidirectional Optical Kerr Transmittance in Hierarchical Carbon/Platinum Nanostructures

A strong contrast in the third-order nonlinear optical effects exhibited by hierarchical nanostructures explored in a bidirectional optical circuit is reported. The samples were integrated by multiwall carbon nanotubes and platinum-decorated carbon nanotubes synthetized by an aerosol pyrolysis technique and followed by a chemical vapor deposition method. Coupled and decoupled third-order nonlinear optical properties of the nanocomposites were studied. A nanosecond two-wave mixing experiment at 532 nm wavelength was conducted to analyze the optical Kerr effect in the samples. Multi-photonic interactions were evaluated by a single-beam transmittance as a function of input irradiance and volume fraction of the nanoparticles integrated in the nanohybrids. A two-photon absorption process was identified as the main physical mechanism responsible for the anisotropy in the observed optical nonlinearities. Random carbon nanotube networks in film form were put on top of platinum-decorated carbon nanotubes in order to build up a bilayer sample featuring optical selectivity. The switching of optical signals in propagation through the samples was obtained by an orientation-selectable optical transmittance. Unidirectional optically controlled laser pulses dependent on irradiance and polarization in a two-wave mixing was proposed with potential nanophotonic and nanoelectronic applications. The design of signal processing functions driven by nanohybrid platforms can be contemplated.

Real-time dynamic evolution monitoring of laser-induced exciton phase flips in 2D hybrid semiconductor (C12H25NH3)2PbI4

Real-time monitoring of room-temperature exciton photoluminescence (PL) while irradiated with ultrafast laser excitations (UV and infrared) in long alkyl-chain based (C12H25NH3)2PbI4 inorganic–organic hybrid semiconductors is presented. These naturally self-assembled 2D hybrid structures show strong room-temperature Mott-type excitons confined within the lowest inorganic bandgap, which are highly sensitive to structural phase flips. Under both one-photon (E1PA ≥ Eg) and two-photon (2E2PA ≥ Eg) laser excitations, the exciton PL of unstable phase-II appears initially, and with prolonged laser exposure, the PL peak switches to a new stable blueshifted phase-I peak position. This exciton phase flip demonstrates different laser-induced structural deformations in inorganic quantum wells (PbI6 extended network) associated with orthorhombic (phase-I) and monoclinic (phase-II) unit cells. One-photon absorption induced PL shows the various time dynamics of laser exposure depending on laser characteristics (continuous wave and ultrashort pulsed lasers), mostly influenced by localized heating, ablation effects, and third-order nonlinear effects such as saturation of linear absorption and exciton–exciton annihilation. However, in two-photon absorption induced PL, the near infrared laser excitation reveals the redshifted crumpled excitons from the deeper depth of the sample, which are induced by multiphoton absorption and avalanche ionization. A series of systematic linear and nonlinear steady-state and time-resolved PL studies are presented. A simplified kinetic model further provides an understanding of the real-time evolution of laser-induced excitons and their related phase flips. These laser-induced exciton phase flips and linear and nonlinear optical probing open a new avenue for novel functional properties and nonlinear absorption–based optoelectronic devices.

Experimental observation of third-order effect in magnetic small-angle neutron scattering

A recent theory [Metlov and Michels, Phys. Rev. B 91, 054404 (2015)] predicts a qualitatively new effect in the magnetic small-angle neutron scattering (SANS) cross section of statistically-isotropic disordered ferromagnetic media. The effect is due to the third-order terms in the amplitude of the inhomogeneities. Here, its existence is demonstrated both numerically via large-scale micromagnetic simulations and analyzed experimentally in a two-phase iron-based nanocomposite. The previous model is extended to an arbitrary spatial defect profile, which allows us to describe the experimental field dependence of the third-order SANS effect quantitatively.

Observation of spatial self-phase modulation induced via two competing mechanisms.

Two spatial self-phase modulation (SSPM) patterns were observed in suspensions of Bi2TeSe2 nanosheets. Two mechanisms were found to produce SSPM with different occurrence times and power dependence. The Type I (narrow) rings are attributed to the coherent third-order nonlinear optical Kerr effect, which induces self-diffraction in 2D materials, and the Type II (wide) rings are assigned to the contribution of a thermal effect. The nonlinear refractive index of Bi2TeSe2 is found to be 2.30×10-5cm2W-1 at 700 nm. The findings described here provide an explanation for the formation of rings in 2D systems due to SSPM.

Single-shot diagnosing of spatiotemporal couplings in ultrashort laser pulses by spatiospectral imaging of a third-order nonlinear process.

The impact of spatiotemporal couplings (STCs) on the focal-spot intensity of ultra-intense femtosecond lasers scales up with the larger beam sizes and shorter pulse duration typically implemented to reach petawatt (PW) intensities. The repetition rate of such facilities (${ \lt }{10}\;{\rm Hz}$<10Hz) makes single-shot diagnosing of STCs mandatory. We present here a new, to the best of our knowledge, spatiotemporal diagnostic technique based on the comparison of the spatiospectral intensity of a pulse and its nonlinear third-order effect, in this case, cross-polarized wave generation (XPW), with an imaging spectrometer. The measured XPW spectrum displays specific couplings that depend on both amplitude and phase STCs of the initial pulse to be characterized. We confirm experimentally the ability of our new approach to diagnose common STCs in a laser pulse on the fly.

Technology Focus: Completions (April 2020)

Technology Focus We must standardize our completion configuration for all our wells. We cannot wait 6 months to accumulate production data to use in optimizing treating parameters on future wells. Can you predict first-year oil production? Can you predict annular pressure buildup in your high-pressure/high-temperature well? Sound familiar? Today, completion optimization relies heavily on our experience with the last well, domain knowledge [subject-matter experts (SMEs)], or perhaps simple curve fitting using the data from multiple wells. All are time-honored methods but have fundamental limitations. As SMEs, humans can articulate the “what” but, when many variables are in play (e.g., unconventional completions), are frequently challenged in pinpointing the “whys.” Historical mathematical models are better but suffer from multiple assumptions about second- and third-order effects. While adequate in some cases, historical models are challenged when predicting outcomes in highly complex completions. Enter machine learning. Digitization, big data, artificial intelligence, analytics, machine learning (ML), and automation are mentioned frequently as solutions for today’s complex technical challenges. ML is particularly fascinating because numerical models are used that can learn and be trained to predict future outcomes accurately. The synopses in this feature show how ML can provide accurate prediction of annular pressure buildup, first-year oil production, and (in conjunction with novel casing accessories) the time and location of water breakthrough along a lateral wellbore. Digitization is a trend that will forever change how engineers and scientists tackle the most complex problems in our industry. ML can advance optimization in many complex completions significantly by delivering high-accuracy predictions. When ML is applied successfully, the numbers do not lie. Recommended additional reading at OnePetro: www.onepetro.org. SPE 196169 Subsurface-Driven Connectivity Descriptions in the Montney and the Duvernay Inform the Applicability of Single-Point vs. Multipoint Well Architectures by Ben Stephenson, Shell, et al. SPE 197968 Strategic Engineering Application for Long Lateral Wells by Ahmed Kiyoumi, Abu Dhabi National Oil Company, et al. SPE 196179 Evaluating Precision of Fluid/Casing Design for Annular Pressure Buildup Application Using Machine-Learning Tools by Sandeep D. Kulkarni, Indian Institute of Technology, et al.

矢量光场激发三阶非线性光学效应的研究进展（特邀）

Polarization-structured intense laser interacting with nonlinear optical material results in many novel third-order nonlinear optical effects, reflects the nonlinear optical property of the material, and modulates the propagation behavior of the beam itself. Herein, the research progress of third-order nonlinear optical effects excited by vectorial light fields was reviewed. Firstly, the basic theory of third-order nonlinear optical effects excited by arbitrary polarized lights was briefly introduced, such as nonlinear Schrodinger equation, beam propagation equation, and isotropic and anisotropic third-order nonlinear optical coefficients. The Z-scan techniquefor characterizing third-order nonlinear optical coefficients was also introducd. Under the weak focusing condition, the expressions for the focal field of three types of vectorial light fields were provided, i.e., radially polarized beams, hybridly polarized beams, and lemon-type Poincare beams. Secondly, the isotropic and/or anisotropic third-order nonlinear optical effects excited by a variety of vectorial light fields was revisited, includinganisotropic nonlinear optical effects induced by radially polarized beams, isotropic and anisotropic Kerr nonlinearities excited by hybridly polarized beams, isotropic and anisotropic nonlinear optical effects induced by lemon-type Poincare beams. Lastly, the prospects of their applications of vectorial light fields in nonlinear polarizationrotation, beam shaping, controllable field collapsing filaments, and optical limiting were briefly discussed.

矢量光场激发三阶非线性光学效应的研究进展（特邀）

矢量光场激发三阶非线性光学效应的研究进展（特邀）

Formation Rules and Dynamics of Photoinduced χ(2) Gratings in Silicon Nitride Waveguides.

Silicon nitride has emerged as a prominent platform for building photonics integrated circuits. While its nonlinear properties based on third-order effects have been successfully exploited, an efficient second harmonic generation in standard stoichiometric silicon nitride (Si3N4) waveguides can also be achieved after all-optical poling, as was recently shown. The root of such a phenomenon has been attributed to the inscription of a self-organized periodic space-charge grating along the waveguide, allowing an effective χ(2) and automatic quasi-phase-matching of pump and second harmonic. However, the different parameters and their role in increasing the efficiency of the process are still not fully comprehended. In this work, we use optical means to identify the general conditions of mode matching occurring during all-optical poling. The overlap integral between pump and second harmonic optical modes is shown to be the governing parameter in determining the features of the χ(2) gratings. Two-photon microscopy measurements of the χ(2) gratings reveal the presence of a secondary periodicity in some of the waveguides used in the study. According to overlap integral simulations, such an effect can occur due to mode mixing in the waveguide bends. From a study of poling dynamics, we observe that poling efficiency and rate increase as a function of optical pump power and waveguide length. However, in order to initiate poling, a critical pump intensity, which is lower for longer waveguides, must be coupled into a waveguide. Temporal and thermal stability tests reveal the nature of charge traps responsible for grating inscription. After applying thermally activated hopping as a conductivity mechanism in our samples, we show that only shallow traps seem to be activated during the all-optical poling process.

Eye-safe diamond Raman laser

Stimulated Raman scattering, as a third-order nonlinear effect, is an effective approach to expand the laser spectral region. To obtain a high power output of a Raman laser with a specific wavelength, novel Raman gain media and laser structures have been continuously studied, and in recent years, diamonds have received an increased interest from researchers owing to their extremely high Raman gain coefficient, high thermal conductivity, and wide transmission spectrum. Diamond Raman lasers (DRLs) have enabled the achievement of a laser input in the visible to the mid-infrared band. In particular, lasers with outputs in the 1.5 μm band have the characteristics of an atmospheric window and being eye-safe, which are critical for applications in the medical, distance measurement, radar, and other such domains. Consequently, researchers are constantly improving the methods to output a higher power laser at 1.5 μm, and the DRLs offer the potential to realize a high power and high beam quality in this band. This paper provides a review of the research status of eye-safe DRLs and suggests opportunities for future development and applications.

Impact of laser-ionized liquid nonlinear characteristics on the efficiency of terahertz wave generation.

The generation of terahertz (THz) radiation during the propagation of subpicosecond pulses in liquid media is investigated using a theoretical model considering the relative contribution of Kerr and plasma nonlinearity. The dependences of the THz emission generation efficiency on the contribution of plasma nonlinearity with a fixed third-order nonlinearity value revealed the existence of weak and strong ionization modes. It is shown that the transition between these modes is determined by the ratio of plasma to Kerr nonlinearity coefficients and the pump energy. In the strong ionization mode and with the fixed contribution of plasma nonlinearity, the optical-to-THz conversion efficiency decreases with increasing Kerr nonlinearity due to the redistribution of the pump energy for the third-order effects. These results contribute to estimating the potential of liquid media as highly efficient THz sources.

Nonlinear Elastic Effects on High-Strength Concrete Stress Invariants

Abstract Computational modeling of concrete behavior and most failure criteria for concrete strongly rely on the use of invariants of stress. These invariants allow a straightforward geometric interpretation of stress states and concrete failure surfaces in the three-dimensional Haigh-Westergaard stress space. Although second-order linear elastic relations have been traditionally applied to evaluate stresses in concrete, the magnitudes of concrete third-order parameters based on finite deformation theory—Murnaghan parameters l, m, n—are such that, if nonlinear stress-strain relations are considered, the stress invariants’ magnitudes are directly affected. In this work, acoustoelastic stress-strain relations for a general triaxial stress state and ultrasonically calculated second- and third-order elastic parameters are used in the evaluation of three high-strength concrete mixtures with compressive strengths: f′c = 43.0, 44.8, and 56.0 MPa (6.2, 6.5, and 8.1 ksi, respectively). The results demonstrate that nonlinear elastic effects introduce anisotropy when uniaxial stresses are applied and the magnitudes of concrete elastic and shear moduli change because of the applied stress field. When triaxial loads are considered, all stress invariants—first (I1), second (I2), and third (I3)—also undergo variations in their magnitudes. The stress-induced anisotropy due to uniaxial loading application and also the changes in the stress invariants’ magnitudes calls attention to the importance of considering nonlinear third-order effects in cement-based materials’ stress-strain relations and failure criteria.

Nonlinear optical response spatial self-phase modulation in MoTe2: correlations between χ(3) and mobility or effective mass.

We report on an unambiguous observation of the third-order nonlinear optical effect, spatial self-phase modulation (SSPM), in a MoTe2 dispersion. The values of the third-order nonlinear optical coefficients effectively for one-layer MoTe2, χone-layer(3), are obtained through the SSPM method at excitation wavelengths 473, 532, 750, and 801nm, respectively. The wind-chime model is used to explain the ring formation time. The wavelength dependence of χone-layer(3) compares well with the photo-absorption spectra. Significantly, we find a correlation between χ(3) and the carrier mobility μ or effective mass m*, which again further supports the laser-induced ac electron coherence in 2D materials.

Electoral rules, strategic entry and polarization

How does electoral rule disproportionality affect the structure of the party system (i.e. the number and the policy platforms of the competing parties)? By studying a model where both party entry and platform choice are endogenous we are able to provide a unified theory: An increasing electoral rule disproportionality exhibits: a) a first-order negative effect on platform polarization, b) a second-order negative effect on the number of parties (as polarization decreases, centrist parties are squeezed between other contenders and prefer not to enter), and c) an additional third-order negative effect on polarization via the reduction of the number of parties. We then conduct a laboratory experiment and strongly confirm the theoretical predictions of the model.

Optical phase-change in plasmonic nanoparticles by a two-wave mixing

Described herein is the optical phase-change and photothermal phenomena induced by a two-wave mixing configuration in a nonlinear optical material. For experimental analysis of these findings, the third-order nonlinear optical response exhibited by bimetallic Au–Pt nanoparticles embedded in a TiO2 matrix was studied. A vectorial two-wave mixing technique was conducted to explore the automatic generation of polarized self-diffraction by the participation of the optical Kerr effect in the samples. Fractional derivative calculations allowed us to identify the physical mechanism responsible for photothermal influence on the third-order nonlinear optical effects in the nanosystems. A 532 nm wavelength emitted by the second harmonic of a nanosecond Nd:YAG laser system was employed as an optical source in our measurements. Based on the importance of the vectorial nature of light for dictating the amplitude of the beams and splitting properties, within this work is highlighted the attractive energy transfer functions and phase modulation that can be envisioned by photothermally-controlled interactions.

Results of Microscopic Self-Consistent Theory of Quasiparticle—Phonon Interaction in Nuclei

A self-consistent approach in the problem of taking into account quasiparticle-phonon interaction provides a high predictive power and is free from adjustable parameters (this is of crucial importance for astrophysics). Moreover, it is consistent and makes it possible to take into account new effects. A brief survey of the results obtained within this approach on the basis of Skyrme or Fayans functionals by employing the smallness parameter g2, where g is the phonon-production amplitudes, with allowance for tadpole effects is presented. The contribution of quasiparticle-phonon interaction to ground-state electromagnetic moments of odd nuclei; second-order anharmonic effects in g2, including quadrupole moments of the first 2+ and 3− states and EL transitions between one-phonon states; third-order anharmonic effects; pygmy dipole and giant resonances; and the contribution of quasiparticle-phonon interaction to radiative properties of nuclear reactions are considered. For magic and semimagic nuclei, additional effects and structures arising in nuclear features because of quasiparticle-phonon interaction are discussed along with new—that is, three- and four-quasiparticle ground-state—correlations. Earlier unknown values of the above features, including the features of the pygmy dipole resonance in neutron-rich nickel isotopes, are predicted. It is shown that, in all of the aforementioned problems, the contributions of quasiparticle-phonon interaction is sizable, is of fundamental importance, and is necessary for explaining experimental data.

Designing one-dimensional magnetized plasma photonic crystals for compensating second- and third-order dispersion effects in ultra-short pulse lasers

The dispersion compensation ability of a one-dimensional photonic crystal composed of dielectric and magnetized cold plasma materials has been theoretically investigated, based on the simple transfer matrix method in the near infrared region. Group delay, group velocity dispersion and third-order dispersion of the considered multilayer structure are deduced, and the propagating pulse shape correction in terms of external magnetic field is investigated for TE mode at normal incidence. The numerical simulations show that, for initially chirped ultra-short pulses, the external magnetic field controls both the pulse width and ripple. It is found that with the increasing of static magnetic field applied on the plasma layers, the pulse propagating through the structure reaches its minimum duration at shorter lengths of the crystal. The results of this study may be utilized to develop dispersion engineered ultra-short pulse laser systems. Moreover, the outcomes may also be useful in designing compact size tunable pulse compressors and pulse shapers.

A particle swarm optimization method for interpreting self-potential anomalies

Abstract This paper describes the use of the particle swarm optimization (PSO) method for interpreting observed self-potential anomalies measured along a profile. First, the technique applies the second moving average to the observed self-potential data in order to eradicate the possible influence of the regional anomaly (up to the third-order polynomial effect) via the filter of consecutive window lengths (s-values) and to calculate the residual anomaly. Following that, the PSO method is applied to the residual response to infer the source parameters: amplitude coefficient (K), depth (z), polarization angle (θ) and the shape factor (q) of the underlying buried target. The technique has been applied to three different theoretical and two field examples from the USA and Turkey. Comparisons have shown that the source parameters retrieved from the technique described here are in good agreement with the available geologic and geophysical information.

Erratum: Third-order effect in magnetic small-angle neutron scattering by a spatially inhomogeneous medium [Phys. Rev. B 91 , 054404 (2015)

Erratum: Third-order effect in magnetic small-angle neutron scattering by a spatially inhomogeneous medium [Phys. Rev. B <b>91</b> , 054404 (2015)