Third-order Response Research Articles

Study on modal parameter identification of engineering structures based on nonlinear characteristics

AbstractTo study the nonlinear characteristics of the modal recognition of civil engineering parameters, a method of nonlinear recognition of the parameters of characteristics based on LMD is proposed. The LMD method is applied to decompose the acceleration response signals of the disturbing structure of the building, to obtain the PF components, the instantaneous frequency, and the instantaneous amplitude of each PF component, to determine the modal natural frequency and damping coefficient. To determine the modal parameter based on the LMD, the calculation and analysis results are presented as follows: the frequency of the components fluctuates between the fifth and sixth models, which shows that the components contain the reaction of the fifth and sixth design modes. This is because these two modes (3.101 Hz and 3.147 Hz) are very close to each other, which makes it difficult to distinguish between the responses of these two modes by the LMD method. The frequency of the components is always stable (the first 2.5 s), which indicates that during this period the responses of modes 5e and 6e do not dampen, and the ratio between them in the PF1 components does not differ much. The component frequency curve shows an interesting phenomenon. Starting from about 3.8 s, the frequency curve gradually approaches the first mode, and only the frequency of the first mode is about 6 s, which indicates that the response of the first mode still exists and makes up a significant proportion. Modular response, caused by the damping, is only detected in the first half of the 10 s response, after which it is verified from the nonlinear characteristics of the LMD parameter recognition method that half of the third-order modal response on the scale is very low and almost equal to zero, and despite problems with dense frequency separation mode in the LMD method, the frequency responses of its PF components may reflect the mode combination phenomenon and reflect the duration of each mode throughout the response.

Robustness of sequential third-order response surface design to missing observations

Response surface designs are generally used in process/product optimization studies. Sequential third-order response surface designs are advantageous when the experimenter encounters the significance of lack of fit of a fitted second-order model while establishing the relationship between the input and response variables. In some experimental situations, responses pertaining to certain design points may be destroyed or unobtainable or inaccessible. The unavailability of the observations pertaining to certain experimental run(s) affects the design property and affects the analysis of variance. In this paper, we have examined the robustness of sequential third-order rotatable design and investigated the loss of information when one or two observations pertaining to experimental run(s) is (are) missing, which are at different radii from the design centre. It has been found that the maximum loss of information occurs when the observation at the design points which are at higher radii from the design centre is lost and the design has the minimum efficiency.

Structure-dependent optical nonlinearity of indium tin oxide

We use post-deposition vacuum annealing of epsilon-near-zero (ENZ) indium tin oxide (ITO) nanolayers in order to modify their structural properties and enhance the third-order optical nonlinear response around the ENZ wavelength. We find that room temperature magnetron sputtering deposition results in polycrystalline thin films with an intrinsic tensile strain and a ⟨110⟩ fiber axis preferentially oriented normal to the substrate. Moreover, we demonstrate that post-deposition vacuum annealing treatments produce a secondary anisotropic phase characterized by compressive strain that increases with the annealing temperature. Finally, we use the Z-scan optical technique to accurately measure the complex nonlinear susceptibility χ(3) and the intensity-dependent refractive index change Δn for samples with different structural properties despite featuring similar ENZ wavelengths. Our intensity-dependent analysis demonstrates that an enhancement of the optical nonlinearity can be achieved by tuning the structure of ENZ nanolayers with values as large as χR(3)=(5.2 ± 0.3)×10−17m2/V2. This study unveils the importance of structural control and secondary phase formation in ITO nanolayers with ENZ optical dispersion properties for the engineering of integrated highly nonlinear devices and metamaterials that are compatible with the scalable silicon photonics platform.

Constitutive Model Parameter Identification Based on Optimization Method and Formability Analysis for Ti6Al4V Alloy.

Titanium alloy is widely applied in aerospace, medical, shipping and other fields due to its high specific strength and low density. The purpose of this study was to analyze the formability of Ti6Al4V alloys at elevated temperatures. An accurate constitutive model is the basic condition for accurately simulating the plastic forming of materials, and it is an important basis for optimizing the parameters of the hot forging forming process. In this study, the optimization algorithm was used to accurately identify the high-temperature constitutive model parameters of Ti6Al4V titanium alloy, and the hot working diagram was established to optimize the hot forming process parameters. The optimal forming conditions of Ti6Al4V titanium alloy are given. Ti6Al4V alloy was subjected to high-temperature compression tests at 800–1000 °C and at strain rates of 0.01–5 s−1 on a Gleeble-1500D thermal/mechanical simulation machine. Each parameter of the Hansel–Spittel constitutive model was taken as an independent variable, and the accumulated error between the stress calculated by the constitutive model and the stress obtained by experimentation was used as an objective function. Based on response surface methodology, an inverse optimization method for identifying the parameters of the high-temperature constitutive model of Ti6Al4V alloy is proposed in this paper. An orthogonal test design was adopted to obtain sample point data, and a third-order response surface approximate model was established. The genetic algorithm (GA) was applied to reversely optimize the parameters of the constitutive model. To verify the accuracy of the optimized constitutive model, the average absolute relative error (AARE) and correlation coefficient (R) were used to evaluate the reliability of optimized constitutive model. The R value of the model was 0.999, and the AARE value was 0.048, respectively, indicating that the established high-temperature constitutive model for Ti6Al4V alloy has good calculation accuracy. The flow stress behavior of the material could be accurately delineated. Meanwhile, in order to study the formability of Ti6Al4V alloy, the hot processing map of the alloy, based on a dynamic material model, was established in this paper. The optimum hot working domains of the Ti6Al4V alloy were determined within 840–920 °C/0.01–0.049 s−1 and 940–980 °C/0.11–1.65 s−1; the hot processing map was verified in combination with the microstructure, and the fine and equiaxed grains and a large amount of β phase could be found at 850 °C/0.01 s−1.

Ultra‐miniaturized filtering power divider chip on integrated passive device technology using complex isolation network

In this letter, an ultra-miniaturized filtering power divider (FPD) chip based on integrated passive device (IPD) technology using a complex isolation network is proposed. Three lumped L represents inductor, C represents capacitor (LC) tanks and two electromagnetic hybrid coupling units are used to realize the third-order quasi-elliptical filtering response with high-frequency selectivity and wide stopband, which are designed and realized by using the IPD process to achieve ultra-miniaturized size. In addition, the complex impedance is utilized to form the isolation network, so good in-band isolation can be easily achieved. Moreover, the working principle and design method of this proposed FPD is well illustrated, a prototype with 3-dB fractional bandwidth of 19.3% at 2.6 GHz (f0) is in final designed and fabricated. The isolation is higher than 16 dB within the passband, and upper-stopband attenuation higher than 20 dB is extended to 40 GHz (15.4f0). It occupies only 2.76 mm × 2.0 mm, that 0.023λ0 × 0.017λ0, where λ0 is the free-space wavelength at f0.

Assembling of Perylene, Naphthalene, and Pyromellitic Diimide-Based Materials and Their Third-Order Nonlinear Optical Properties

π-conjugated aromatic diimides with chemical stability, heat resistance, and redox activity have attracted more attention due to their excellent fluorescence quantum yield in solution. The planar perylene diimide (PDI) derivatives generally have aggregation-induced emission quenching in the solid state, while the cyclic trimers based on pyromellitic diimides (PMDIs), naphthalene diimides (NDIs), and PDIs can increase the fluorescence quantum yield in the solid state and have large two-photon absorption cross section, which can be used as excellent nonlinear optical (NLO) materials. Therefore, this paper will study the effects of multiple assembly modes of the three monomers on the NLO responses of materials. It was found that the assembly modes of 2PMDI-1NDI and 2NDI-1PDI exhibit larger third-order NLO response (γ) values, which was due to the larger conjugate surface of PDI effectively reducing the energy gap between the HOMO and LUMO. Compared with other assembly methods, 2PMDI-1NDI and 2NDI-1PDI were conducive to causing redshifts (150 nm) in the absorption spectrum. Therefore, the larger conjugate surface of PDI and the assembly mode of the isosceles triangle were more favorable for intramolecular charge transfer, thus improving its NLO properties.

Five-level Non-Sequential Third-Order Response Surface Designs and their Efficiencies

New non-sequential third-order response surface designs are proposed with good optical properties. They are suitable as one-stage experimental designs for use in modeling third-order effects. The new designs are presented for cuboidal region in k dimensions and the technique employed in the construction of the non-sequential designs on the cuboidal region is flexible for use in regions that may be non-cuboidal. The new non-sequential designs lay importance on the use of axial points and two or three other blocks of points selected from a discrete design region such that the design is non-singular. For a continuous design region, uniform grids are formed over the entire design region. Five grid levels are utilized in this work thus resulting in 5^k grid points from which blocks of points are selected to form the desired non-sequential designs. The goodness of the designs is assessed via optimality and efficiency criteria and the new designs possess good optimality properties and are very high by G-efficiency.

Growth and characterization of barium bis para-nitrophenolate para-nitrophenol tetrahydrate single crystal for NLO applications

Single crystals of barium bis para-nitrophenolate para-nitrophenol tetrahydrate (BBPNT) was grown using slow evaporation technique with the crystal dimensions of 15 × 10 × 6 mm3. The structure of the BBPNT crystal was examined by X-ray diffraction and the functional groups present in the compound were identified using FTIR spectrum. The optical and electrical properties were characterized by UV–Vis spectrum and dielectric studies respectively. Thermal properties of the grown crystal were investigated by using thermo-gravimetric (TG) and differential thermal analyses (DTA). The mechanical behavior of the grown crystal was studied using Vickers microhardness test. Using the Kurtz-Perry powder method, the second-harmonic generation efficiency was found to be 15.75 times greater than to that of KDP. Third-order nonlinear response was studied using Z-scan technique with a He-Ne laser (632.8 nm) and NLO parameters such as intensity dependent refractive index, nonlinear absorption coefficient and third-order susceptibility were also estimated. In the PL spectra, a broad band observed at 525 nm suggests its applications for fabricating green laser and new tunable laser system. The laser damage threshold value of BBPNT was found to be 5.09 GW/cm2 using an Nd: YAG laser.

Flexible Vertex Engineers the Controlled Assembly of Distorted Supramolecular Tetrahedral and Octahedral Cages.

Designing and building unique cage assemblies attract increasing interest from supramolecular chemists but remain synthetically challenging. Herein, we propose the use of a flexible vertex with adjustable angles to selectively form highly distorted tetrahedral and octahedral cages, for the first time, in which the flexible vertex forms from the synergistic effect of coordination and covalent interactions. The inherent interligand angle of the vertex can be modulated by guest anions present, which allows for the fine-tuning of different cage geometries. Furthermore, the reversible structural transformation between tetrahedral and octahedral cages was achieved by anion exchange monitored by mass spectrometric technique, the smaller anions favoring tetrahedral cages, while the larger anions supporting octahedral cages. Additionally, the KBr-based cage thin films exhibited prominent enhancement of their third-order NLO responses in two or three orders of magnitude compared to those obtained for their corresponding solutions. This work not only provides a new methodology to build irregular polyhedral structures in a controlled and tunable way but also provides access to new kinds of promising functional optical materials.

Prediction Variance Properties of Third-Order Response Surface Designs in the Hypersphere

The variance dispersion graphs (VDGs) and the fraction of design space (FDS) graphs are two graphical methods that effectively describe and evaluate the points of best and worst prediction capability of a design using the scaled prediction variance properties. These graphs are often utilized as an alternative to the single-value criteria such as D- and E- when they fail to describe the true nature of designs. In this paper, the VDGs and FDS graphs of third-order orthogonal uniform composite designs (OUCD₄) and orthogonal array composite designs (OACD₄) using the scaled-prediction variance properties in the spherical region for 2 to 7 factors are studied throughout the design region and over a fraction of space. Single-valued criteria such as D-, A- and G-optimality are also studied. The results obtained show that the OUCD₄ is more optimal than the OACD₄ in terms of D-, A- and G-optimality. The OUCD₄ was shown to possess a more stable and uniform scaled-prediction variance throughout the design region and over a fraction of design space than the OACD₄ although the stability of both designs slightly deteriorated towards the extremes.

Effect of intravalley and intervalley electron-hole exchange on the nonlinear optical response of monolayer MoSe2

The coherent third-order nonlinear response of monolayer transition-metal dichalcogenide semiconductors, such as ${\mathrm{MoSe}}_{2}$, is dominated by the nonlinear exciton response, as well as biexciton and trion resonances. The fact that these resonances may be spectrally close together makes identification of the signatures, for example in differential transmission (DT), challenging. Instead of focusing on explaining a given set of experimental data, a systematic study aimed at elucidating the roles of intravalley and intervalley long-range electron-hole $(e\ensuremath{-}\mathrm{h})$ exchange on the DT spectra is presented. Previous works have shown that the $e\ensuremath{-}\mathrm{h}$ long-range exchange introduces a linear leading-order term in the exciton dispersion. Based on a generalized Lippmann-Schwinger equation, we show that the presence of this linear dispersion term can reduce the biexciton binding energy to zero, contrary to the conventional situation of quadratic dispersion where an arbitrarily weak (well-behaved) attractive interaction always supports bound state(s). The effects of spin scattering and the spin-orbit interaction caused by $e\ensuremath{-}\mathrm{h}$ exchange are also clarified, and the DT line shape at the exciton and trion resonance is studied as a function of $e\ensuremath{-}\mathrm{h}$ exchange strength. In particular, as the exciton line shape is determined by the interplay of linear exciton susceptibility and the bound-state two-exciton resonance in the $T$ matrix, the line shape at the trion is similarly determined by the interplay of the linear trion susceptibility and the bound-state exciton-trion resonance in the $T$ matrix.

Insighting the functionally modified C60 fullerenes as an efficient nonlinear optical materials: A quantum chemical study

It is well-known that π-conjugation plays an important role to tune the nonlinear optical (NLO) response of donor-π-conjugated-acceptor compounds. Fullerenes (C60) are one of a few compounds who are abounded with π-conjugation and perhaps are the largest π-conjugation compounds. In the present study, we systematically designed C60 derivatives (2 (fulleropyrrolidine) and 2a-2c (fulleropyrrolidine tetrathiafulvalene derivatives where 2a, 2b and 2c are with n = 0, n = 1 and n = 2) through the use of pyrrolidine and tetrathiafulvalene moieties. We applied density functional theory (DFT) methods to calculate their respective geometrical structures, electronic properties, linear and nonlinear optical response properties along with their respective UV–Visible spectra using CAM-B3LYP functional and 6-31G* basis set. The isotropic polarizability (αiso) and anisotropic polarizability (αaniso) of 2c was found to be 131.52 × 10-24 and 47.01 × 10-24 esu, respectively. Amongst our designed compounds, the maximum second-order nonlinear optical polarizability amplitude (β//) of 2c was found to be 15.69 × 10-30 esu. Interestingly, 2c shows the highest third-order nonlinear polarizability amplitude <γ> of 284.29 × 10-36 esu that is about three times higher than parent compound 1. Additionally, frontier molecular orbitals (FMOs), molecular electrostatic potential maps (MEPs), transition density matrix (TDM) analysis indicate more effective charge redistribution from donor moiety to acceptor fragments. The density of states (DOS) diagrams reveal distinct electronic contributions of various fragments in the formation of HOMO and LUMO orbitals resulting in efficient intramolecular charge transfer (ICT) and robust third-order NLO response properties of functionalized fullerene derivatives. The current study may arouse the attention of the scientific society to utilize the extensive π-conjugation of functionalized fullerenes for designing efficient NLO materials.

Diagrammatic theory of linear and nonlinear optics for composite systems

We present a general formalism to model and calculate linear and nonlinear optical processes in composite systems, based on a graphical representation of light-matter interactions by loop diagrams associated with Feynman rules. Through this formalism, we recover the usual second-order response of a simple system by drawing four times fewer loop diagrams than doubled-sided ones. For composite systems, we introduce coupling Hamiltonians between subsystems (for example, a molecule and a substrate), graphically represented by virtual bosons. In this way, we enumerate all the diagrams describing the second-order response of the system and show how to select those relevant for the calculation of the molecular second-order hyperpolarizabilities under the influence of the substrate, including effective second-order contributions from the molecular third-order response. As it applies to all nonlinear processes and an arbitrary number of interacting partners, this representation provides a general frame for the calculation of the nonlinear response of arbitrarily complex systems.

Novel Third-Order Nonlinear Optical Materials with Craig-Möbius Aromaticity.

Electron delocalization in aromatic materials significantly impacts their third-order nonlinear optics (NLO). Despite organometallic complexes with Craig-Möbius aromaticity attracting great attention for their unusual physicochemical properties, their third-order NLO have been little studied to date. Herein, 12 Craig-Möbius aromatic organometallics with a stable structure similar to osmapentalyne, namely, carbolong complexes, are screened by DFT. They exhibit high third-order NLO responses because of the d and p electron delocalization in the organometallic ring. Furthermore, electron-hole distribution analyses draw a conclusion that extending the conjugated plane will increase the π-conjugation system to enhance the local excitation in the plane, and the introduction of typical aromatic ligands can result in the organometallic ring-to-ligand charge transfer (RLCT), which are effective methods to improve the third-order NLO response. This study opens a new window in the application of Craig-Möbius aromatic complexes and provides a new approach for third-order NLO materials design.

Demonstrating the Potential of Alkali Metal-Doped Cyclic C6O6Li6 Organometallics as Electrides and High-Performance NLO Materials.

In this report, the geometric and electronic properties and static and dynamic hyperpolarizabilities of alkali metal-doped C6O6Li6 organometallics are analyzed via density functional theory methods. The thermal stability of the considered complexes is examined through interaction energy (Eint) calculations. Doping of alkali metal derives diffuse excess electrons, which generate the electride characteristics in the respective systems (electrons@complexant, e–@M@C6O6Li6, M = Li, Na, and K). The electronic density shifting is also supported by natural bond orbital charge analysis. These electrides are further investigated for their nonlinear optical (NLO) responses through static and dynamic hyperpolarizability analyses. The potassium-doped C6O6Li6 (K@C6O6Li6) complex has high values of second- (βtot = 2.9 × 105 au) and third-order NLO responses (γtot = 1.6 × 108 au) along with a high refractive index at 1064 nm, indicating that the NLO response of the corresponding complex increases at a higher wavelength. UV–vis absorption analysis is used to confirm the electronic excitations, which occur from the metal toward C6O6Li6. We assume that these newly designed organometallic electrides can be used in optical and optoelectronic fields for achieving better second-harmonic-generation-based NLO materials.

Design of compact microstrip bandpass filter with two switchable operating passbands

A new bandpass filter (BPF) with two switchable operating passbands has been proposed. The BPF topology is formed by switchable resonators and stepped-impedance resonators. The two operating bands can be switched on and off independently. For verification, a switchable BPF with a third-order Chebyshev bandpass response was designed and fabricated using microstrip technology. The developed BPF was measured to verify the predicted and simulated results. A close agreement was observed between them. The proposed switchable BPF has good in-band and out-of-band performances. Besides, the attenuation is > 30 dB as the passband is switched off.

Vascular region-specific changes in arterial tone in rats with type 2 diabetes mellitus: Opposite responses of mesenteric and femoral arteries to acetylcholine and 5-hydroxytryptamine

AimsType 2 diabetes mellitus (T2DM) ranks in the top 10 causes of mortality worldwide. The key factor of T2DM vascular complications is endothelial dysfunction. It is characterized by the vessels motor activity disruption and endothelium-derived factors imbalance. The blood vessels morphological and molecular heterogeneity greatly affects the changes occurring in T2DM. Therefore, we conducted a comparative study of vascular bed changes occurring in T2DM. Main methodsMale Wistar rats were fed a high-fat diet for 20 weeks, followed by a single streptozotocin injection (20 mg/kg). T2DM was confirmed with an oral glucose tolerance test. Key findingsA dose-dependent contraction study showed an increase in third-order mesenteric arterioles response to serotonin but not to phenylephrine. These vessels also exhibited a decrease in acetylcholine-dependent relaxation and an increase in guanylate cyclase function. At the same time, the femoral arteries showed a tendency for increased acetylcholine-dependent relaxation. The blood plasma analysis revealed low bioavailable nitric oxide and high levels of endothelin-1 and ROS. SignificanceThis knowledge, in conjunction with the features of the T2DM course, can allow further targeted approaches development for the prevention and treatment of vascular complications occurring in the disease.

Diagrammatic approach to classical coherent two-dimensional infrared spectroscopy

The authors develop a diagrammatic theory for the classical description of nonlinear response functions of anharmonic oscillators. Based on the theory, the authors demonstrate that the third-order response of a weakly anharmonic system can be qualitatively described using classical dynamics, clarifying the boundary of classical and purely quantum phenomena in relation to observations of molecular coherence.

Hydrodynamic nonlinear response of interacting integrable systems

We develop a formalism for computing the nonlinear response of interacting integrable systems. Our results are asymptotically exact in the hydrodynamic limit where perturbing fields vary sufficiently slowly in space and time. We show that spatially resolved nonlinear response distinguishes interacting integrable systems from noninteracting ones, exemplifying this for the Lieb-Liniger gas. We give a prescription for computing finite-temperature Drude weights of arbitrary order, which is in excellent agreement with numerical evaluation of the third-order response of the XXZ spin chain. We identify intrinsically nonperturbative regimes of the nonlinear response of integrable systems.

Synthesis, characterization and nonlinear optical response of polyelectrolyte-stabilized copper hydroxide and copper oxide colloidal nanohybrids

In the present work, the synthesis and characterization of polyelectrolyte-stabilized copper-based nanohybrids with tunable sizes and chemical composition are reported. More precisely, highly stable poly(sodium-4-styrenesulfonate) PSS-Cu(OH)2 and PSS-CuO/Cu(OH)2 nanohybrids are synthesized and characterized in terms of their chemical composition and morphology by X-ray Photoelectron Spectroscopy (XPS) and Atomic Force Microscopy (AFM) respectively. Moreover, their nonlinear optical (NLO) response is systematically investigated by means of the Z-scan technique under different excitation conditions, i.e., 50 fs, 800 nm and 4 ns, 532 nm laser pulses. The findings denote that the size and chemical composition of nanoparticles, defining the surface plasmon resonance frequency, along with the excitation laser parameters (pulse duration and wavelength) affect greatly the NLO response of these nanohybrids. To the best of our knowledge it is the first time that such copper-based nanohybrids are synthesized and investigated towards their third-order NLO response. The results suggest an efficient strategy for preparing copper hydroxide and copper oxide colloidal nanohybrids exhibiting at-will NLO properties for specific optoelectronic and photonic applications.