Third-order Response Research Articles

A series of terpyridine-based zinc(ii) complexes assembled for third-order nonlinear optical responses in the near-infrared region and recognizing lipid membranes.

Two-photon (TP) microscopy has advantages for biological imaging in that it allows deeper tissue-penetration and excellent resolution compared with one-photon (OP) microscopy. Herein, two-photon activated nonlinear optical (NLO) materials, a terpyridine derivative ligand with a donor-acceptor (D-A) model and its corresponding four zinc(ii) complexes (Z1-Z4), were assembled and fully characterized. Based on their systematic photophysical investigations, it was found that the third-order NLO response in the near-infrared (NIR) region was significantly enhanced for the symmetrical complex Z4 compared with the other asymmetric complexes (Z1-Z3). To further explore its utility in biological systems, Z4 was selected as a two-photon probe for cellular lipid membranes, which was confirmed both by two-photon confocal microscopy and transmission electron microscopy (TEM). Furthermore, it was found that the fluorescence intensity was enhanced for complex Z4 with the addition of bioactive liposomes (1 μg mL-1). Its recognition mechanism was demonstrated by experimental methods, as well as molecular modeling calculations. These findings should open a new pathway for functional metal complexes as lipid membrane targeting probes.

X-ray plane-wave diffraction effects in a crystal with third-order nonlinearity

The two-wave dynamical diffraction in the Laue geometry has been theoretically considered for a plane X-ray wave in a crystal with a third-order nonlinear response to the external field. An analytical solution to the problem stated is found for certain diffraction conditions. A nonlinear pendulum effect is analyzed. The nonlinear extinction length is found to depend on the incident-wave intensity. A pendulum effect of a new type is revealed: the intensities of the transmitted and diffracted waves periodically depend on the incidentwave intensity at a fixed crystal thickness. The rocking curves and Borrmann nonlinear effect are numerically calculated.

Coherent two-dimensional spectroscopy of a Fano model

The Fano lineshape arises from the interference of two excitation pathways to reach a continuum. Its generality has resulted in a tremendous success in explaining the lineshapes of many one-dimensional spectroscopies - absorption, emission, scattering, conductance, photofragmentation - applied to very varied systems - atoms, molecules, semiconductors and metals. Unravelling a spectroscopy into a second dimension reveals the relationship between states in addition to decongesting the spectra. Femtosecond-resolved two-dimensional electronic spectroscopy (2DES) is a four-wave mixing technique that measures the time-evolution of the populations, and coherences of excited states. It has been applied extensively to the dynamics of photosynthetic units, and more recently to materials with extended band-structures. In this letter, we solve the full time-dependent third-order response, measured in 2DES, of a Fano model and give the new system parameters that become accessible.

Effects of finite laser pulse width on two-dimensional electronic spectroscopy

We combine the hierarchical equations of motion method and the equation-of-motion phase-matching approach to calculate two-dimensional electronic spectra of model systems. When the laser pulse is short enough, the current method reproduces the results based on third-order response function calculations in the impulsive limit. Finite laser pulse width is found to affect both the peak positions and shapes, as well as the time evolution of diagonal and cross peaks. Simulations of the two-color two-dimensional electronic spectra also show that, to observe quantum beats in the diagonal and cross peaks, it is necessary to excite the related excitonic states simultaneously.

An Unprecedented M-O Cluster Constructed from Nanosized {[C5NH5]9[H31MoV12O24CoII12(PO4)23(H2O)4]}2- Anions Exhibiting Interesting Nonlinear-Optical Properties.

A novel high-nuclear nanosized cluster modified by conjugated organic ligands (pyridine and imidazole), [C5NH5]8[C3H5N2]2{[C5NH5]9[H31Mo12O24Co12(PO4)23(H2O)4]}·12H2O (1), has been successfully isolated under hydrothermal conditions and structurally characterized. Compound 1 consists of 12 CoII and 12 MoV ions linked by 23 {PO4} groups, exhibiting unprecedented nanosized ship-shaped clusters. The magnetic measurements reveal that compound 1 exhibits dominant antiferromagnetic interactions. Additionally, pyridine and imidazole ligands enhance the delocalized electron effects of clusters, and the third-order nonlinear-optical response of compound 1 is excellent.

Third-order terahertz response of gapped, nearly-metallic armchair graphene nanoribbons

We use time dependent perturbation theory to study the terahertz nonlinear response of gapped intrinsic and extrinsic nearly-metallic armchair graphene nanoribbons of finite length under an applied electric field. Generally, the nonlinear conductances exhibit contributions due to single-photon, two-photon, and three-photon processes. The interference between each of these processes results in remarkably complex behavior for the third-order conductances, including quantum dot signatures that should be measurable with a relatively simple experimental configuration. Notably, we observe sharp resonances in the isotropic third-order response due to the Van Hove singularities in the density of states at one-, two-, and three-photon resonances. However, these resonances are absent in the anisotropic third-order response; a result of the overall symmetry of the system.

Multi-objective optimization of heat exchanger in an automotive exhaust thermoelectric generator

Currently, thermoelectric generator optimization mainly focuses on the transformation or improvement of a heat exchanger. This study aims to eliminate the contradiction between the thermal and pressure performances of a heat exchanger through the mathematical optimization of the fin distribution. To evaluate the thermal properties and pressure losses of a heat exchanger, five fin parameters and four optimization targets (i.e. average temperature, temperature gradient in longitudinal direction, temperature gradient in transverse direction and average static pressure drop from the inlet to the outlet of the heat exchanger) are proposed. An L16 (45) orthogonal array computational fluid dynamics simulation is employed, and the influence of the five fin parameters on thermal and pressure performances is explored. Results show that fin height has the most significant effect (34%) on the average temperature increase. The influence of fin interval distance on the four targets contradicts that of the fin height. Accordingly, the fin interval distance is the only parameter that is good for the pressure drop decrease. The fin angle shows a homogeneous effect on the four targets as well as interval distance, except for the significant decrease of longitudinal temperature difference. Four surrogate models are constructed via a third-order response surface approach to extract the variation regularity between the five parameters and four targets. Finally, an archive-based micro genetic algorithm is used to obtain the optimal fin parameters. Although the horizontal temperature difference after optimization is reduced, the average temperature is improved from 222.46°C to 226.4°C, whereas the longitudinal temperature difference is decreased from 29.36°C to 28.9°C. Moreover, the pressure drop is decreased by approximately 20%, which may be significant for the global improvement of a thermoelectric generator system.

Spirooxazine-Fulgide Biphotochromic Molecular Switches with Nonlinear Optical Responses across Four States

A new type of prototypical biphotochromic switches combining spirooxazine and fulgide has been synthesized, and their nonlinear optical (NLO) responses have been theoretically studied on the basis of density functional theory (DFT). Our DFT calculations show that the introduction of a fulgide fragment (E and C) into the spirooxazine host can largely enhance the static second- and third-order NLO responses. Moreover, the photoisomerization of spirooxazine derivatives (SO-E and SO-C) brings forth a pronounced change in the geometry accompanied by the formation of a larger π-conjugated system, and thus the corresponding merocyanine derivatives (PMC-E and PMC-C) obtain ∼3.5-times enhancement of static second- and third-order NLO responses. Nevertheless, the difference in NLO responses between the E-form series (SO-E and PMC-E) and the C-form series (SO-C and PMC-C), respectively, is not substantial, which means the fulgide fragment in the prototypical biphotochromic system does not considerably differentiate ...

Crystal growth and DFT insight on sodium para-nitrophenolate para-nitrophenol dihydrate single crystal for NLO applications

Single crystals of sodium para-nitrophenolate para-nitrophenol dihydrate (SPPD) were grown by slow evaporation technique and its structure has been studied by FT-IR, FT-Raman and single crystal X-ray diffraction techniques. The optical and electrical properties were characterized by UV-Vis spectrum, and dielectric studies respectively. SPPD was thermally stable up to 128 °C as determined by TG-DTA curves. Using the Kurtz-Perry powder method, the second-harmonic generation efficiency was found to be five times 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. The molecular geometry from X-ray experiment in the ground state has been compared using density functional theory (DFT) with appropriate basis set. The first-order hyperpolarizability also calculated using DFT approaches. Stability of the molecule arising from hyperconjugative interactions leading to its nonlinear optical activity and charge delocalization were analyzed using natural bond orbital technique. HOMO-LUMO energy gap value suggests the possibility of charge transfer within the molecule. Based on optimized ground state geometries, Natural bond orbital (NBO) analysis was performed to study donor-acceptor interactions.

First-principles study of the terahertz third-order nonlinear response of metallic armchair graphene nanoribbons

We compute the terahertz third-order nonlinear conductance of metallic armchair graphene nanoribbons using time-dependent perturbation theory. Significant enhancement of the intrinsic third-order conductance over the result for instrinsic 2D single-layer graphene is observed over a wide range of temperatures. We also investigate the nonlinear response of extrinsic metallic acGNR with |E_F|<<200 meV. We find that the third-order conductance exhibits a strong Fermi level dependence at low temperatures. A third-order critical field strength of between 1 and 5 kV/m is computed for the Kerr conductance as a function of temperature. For the third-harmonic conductance, the minimum critical field is computed to be about about 5 kV/m.

Origin of Dispersive Line Shapes in Plasmonically Enhanced Femtosecond Stimulated Raman Spectra

A theoretical model is described to explain the observed dispersive-like vibrational line shapes reported in previous studies of plasmonically enhanced (PE) femtosecond stimulated Raman spectroscopy (FSRS). These Raman line shapes are rationalized in terms of interference or heterodyne terms between the PE stimulated Raman response from the molecules located in the plasmonically enhancing regions of Au nanoparticles and the nonlinear emission/scattering due to the resonant surface plasmon resonance (SPR) of these nanoparticles. The treatment of the FSRS signal response follows the standard perturbative polarization approach apart from the familiar g4 field enhancement factor found in spontaneous SERS description, where g represents the local electromagnetic field enhancement due to proximity with the plasmonic nanoparticles. The SPR contribution is modeled as a PE resonant two-level system. The heterodyne cross-term between these two complex third-order responses is large because both of the components ar...

Nonlinear optical conductivity ofU(1)spin liquids with large spinon Fermi surfaces

In this paper we study the nonlinear current response of $U(1)$ spin liquids with large spinon Fermi surfaces under the perturbation of a time-dependent ac electric field $\mathbf{E}(t)$ within the framework of an effective $U(1)$ gauge theory. In particular, the third-order nonlinear current response to ac electric fields is derived. We show that as in the case of linear current response, an in-gap power-law ($\sim\omega^{\eta}$) response is found for the nonlinear current at low frequency. The nonlinear susceptibility may also induce through process of third harmonic generation propagating EM wave with frequency $3\omega$ inside the spin liquids.

The effect of buccal-lingual slot dimension size on third-order torque response.

The focus of the presented study was to investigate the effect of buccal-lingual (B-L) orthodontic bracket slot dimension on third-order torque mechanics. Three types of orthodontic brackets and two archwire sizes were considered. Ortho Classic H4 (0.026″ B-L slot, passive), Ormco Damon Q (0.028″ B-L slot, passive), and In-Ovation R (0.028″ slot, active) brackets were tested using 0.017″ × 0.025″ and 0.019″ × 0.025″ beta-titanium archwires. An in vitro orthodontic torque simulator (OTS) was used to rotate archwires relative to a single bracket while recording forces and moments in three directions. For each bracket-archwire combination, a total of n = 47 samples were tested. Repeated measures analysis of variance between brackets was conducted for third-order torque values at 3° increments between 9° and 30° during loading and unloading for each archwire size. Statistically significant differences between H4 and Q brackets were only found for 0.017″ × 0.025″ archwires during loading, and 0.019″ × 0.025″ archwires during unloading. Conversely, differences between H4 and R brackets were found for both archwires during loading and unloading phases. Finally, when using a 0.017″ × 0.025″ archwire the H4 brackets reached the 5 Nmm threshold before R and Q brackets; however, there was little difference found when using a 0.019″ × 0.025″ archwire. The concept of using a smaller B-L bracket slot dimension in orthodontic treatment showed it may theoretically allow for more options, primarily using smaller archwires to correct third-order rotational misalignments. However, it is suspected that bracket material limitations and added loading on the door currently prevent this from being clinically applicable.

On Some Two- and Three-dimensional D-minimax Designs for Estimating Slopes of a Third-order Response Surface

Design of experiments is considered for the situation where estimation of the slopes of a response surface is the main interest. Under the D-minimax criterion, the objective is to minimize the generalized variance of the estimated axial slopes at a point maximized over all points in the region of interest in the factor space. For the third-order model over spherical regions, the D-minimax designs are derived in two and three dimensions. The efficiencies of some two- and three-dimensional designs available in the literature are also investigated.

Multiband High-Order Bandstop 3-D Frequency-Selective Structures

A general methodology for the design of multiband high-order three-dimensional (3-D) frequency-selective structures (FSSs) is proposed. The methodology is based on employing multiple resonators inside a unit cell (UC) to obtain a multiband response, and by controlling the coupling between identical resonators, a high-order filtering performance is achieved. This provides more transmission zeros in the operating bands, which lead to improved bandwidth and high selectivity. Detailed analysis for the coupling between identical resonators is provided as well as equivalent circuit models to explain the operating principle. Three structures are designed, fabricated, and measured to verify the proposed methodology. The first structure is a triband second-order FSS with center frequencies at 9.6, 13.4, and 17.5 GHz and their $-3-\text{dB}$ fractional bandwidths of 13.5%, 8.5%, and 12.6%, respectively. The second structure is designed to have a dual-band third-order response with center frequencies at 13.2 and 19.6 GHz and their $-3\text{-}{\rm dB}$ fractional bandwidths of 16% and 13.3%, respectively. The last structure is designed to exhibit a dual-band second-order response under both TE and TM polarizations with center frequencies at 11.2 and 13.8 GHz and $-3\text{-}{\rm dB}$ fractional bandwidths of 5.5% and 4%, respectively.

Multi-Order Investigation of the Nonlinear Susceptibility Tensors of Individual Nanoparticles.

We use Hyper Rayleigh Scattering and polarization resolved multiphoton microscopy to investigate simultaneously the second and third-order nonlinear response of Potassium Niobate and Bismuth Ferrite harmonic nanoparticles. We first derive the second-to-third harmonic intensity ratio for colloidal ensembles and estimate the average third-order efficiency of these two materials. Successively, we explore the orientation dependent tensorial response of individual nanoparticles fixed on a substrate. The multi-order polarization resolved emission curves are globally fitted with an analytical model to retrieve individual elements of susceptibility tensors.

Efficient Third Harmonic Generation in a Metal–Organic Framework

As a recently emerged class of inorganic–organic hybrid crystals, metal–organic frameworks (MOFs) have been investigated for their capabilities for doubling light frequency. We report, for the first time, our observation of an efficient coherent up-conversion via third harmonic generation (THG) in a MOF. It is achieved by utilizing a MOF with a constituent ligand that possesses significant third-order nonlinear optical (NLO) responses. Our THG measurements at fundamental wavelengths ranging from 1200 to 1600 nm show that the MOF constructed with the An2Py ligand exhibits an effective χ(3) value that is 3 orders of magnitude greater than α-quartz. Our findings demonstrate a new avenue to realize efficient third-order NLO responses by utilizing MOFs consisting of strong third-order NLO ligands.

Second-Order Adjoint Sensitivity and Uncertainty Analysis of a Heat Transport Benchmark Problem—I: Analytical Results

This work presents an illustrative application of the second-order adjoint sensitivity analysis methodology (2nd-ASAM) to a heat transport benchmark problem that simulates the radial heat conduction in a heated fuel rod together with the axial heat transport along the coolant channel surrounding the rod. This paradigm benchmark is sufficiently simple to admit an exact solution, thereby making transparent the mathematical derivations underlying the 2nd-ASAM, and also for performing solution verification of computational fluid dynamics simulation tools such as the FLUENT Adjoint Solver, a code that has been used for computing thermal-hydraulic processes within the G4M Reactor. The G4M Reactor is an innovative small modular fast reactor cooled by lead-bismuth eutectic.The benchmark problem has six thermal-hydraulic parameters representative of the G4M Reactor, as well as of a test section that is under design for analyzing thermal-hydraulic phenomena expected within the reactor’s core. Thus, the benchmark exhibits 6 first-order and 21 second-order sensitivities for the temperature distribution at any location within the heated rod (and/or on its surface) and just as many sensitivities for the temperature distribution at any location within the coolant. Locations of particular importance are those where the rod temperature attains its maximum along the rod’s axis or on the rod’s surface, as well as the coolant’s exit, where the coolant temperature attains its maximum.The general theory underlying the 2nd-ASAM indicates that for a physical system comprising Nα parameters, the computation of all of the first- and second-order response sensitivities requires Nα large-scale computations involving correspondingly constructed adjoint systems, which we called second-level adjoint sensitivity systems (2nd-LASS). In practice, however, the actual number of large-scale adjoint computations can be significantly smaller; in particular, all 54 first- and second-order rod and coolant temperature sensitivities for the benchmark presented in this work were obtained using only seven independent adjoint computations. Furthermore, the construction and solution of the 2nd-LASS require very little additional effort beyond the construction of the first-level adjoint sensitivity system (1st-LASS) needed for computing the first-order sensitivities. Very significantly, only the sources on the right side of the differential operator needed to be modified; the left side of the respective differential equations (and hence the solver in large-scale practical applications) remained unchanged from the 1st-LASS and from the original equations when these are linear in the unknown state function.This work also shows that the second-order sensitivities have the following impacts on the computed moments of the response distribution: (a) they cause the expected value of the response to differ from the computed nominal value of the response, (b) they contribute to the response variances and covariances, and (c) they contribute decisively to causing asymmetries in the response distribution. Indeed, neglecting the second-order sensitivities would nullify the third-order response correlations stemming from normally distributed parameters and hence would nullify the skewness of the response; consequently, events occurring in a response’s long and/or short tails could be missed.

Nonlinear optics of complex plasmonic structures: linear and third-order optical response of orthogonally coupled metallic nanoantennas

We investigate the polarization-resolved linear and third-order optical response of plasmonic nanostructure arrays that consist of orthogonally coupled gold nanoantennas. By rotating the incident light polarization direction, either one of the two eigenmodes of the coupled system or a superposition of the eigenmodes can be excited. We find that when an eigenmode is driven by the external light field, the generated third-harmonic signals exhibit the same polarization direction as the fundamental field. In contrast, when a superposition of the two eigenmodes is excited, third-harmonic can efficiently be radiated at the perpendicular polarization direction. Furthermore, the interference of the coherent third-harmonic signals radiated from both nanorods proves that the phase between the two plasmonic oscillators changes in the third-harmonic signal over $$3\pi$$ when the laser is spectrally tuned over the resonance, rather than over $$\pi$$ as in the case of the fundamental field. Finally, almost all details of the linear and the nonlinear spectra can be described by an anharmonic coupled oscillator model, which we discuss in detail and which provides deep insight into the linear and the nonlinear optical response of coupled plasmonic nanoantennas.

Some new augmented fractional Box–Behnken designs

ABSTRACTThe augmented Box–Behnken designs are used in the situations in which Box–Behnken designs (BBDs) could not estimate the response surface model due to the presence of third-order terms in the response surface models. These designs are too large for experimental use. Usually experimenters prefer small response surface designs in order to save time, cost, and resources; therefore, using combinations of fractional BBD points, factorial design points, axial design points, and complementary design points, we augment these designs and develop new third-order response surface designs known as augmented fractional BBDs (AFBBDs). These AFBBDs have less design points and are more efficient than augmented BBDs.