Macroscopic Nonlinearity Research Articles

Theoretical insight on structure, electronic, and optical properties of two d 0–d 10 electron transition-metal oxyhalides SHG materials

Materials containing mixed anions, particularly, oxyhalides containing asymmetric functional building units, may lead to the discovery of excellent nonlinear optical (NLO) materials. In the present work, the geometric structure, mechanical properties, electronic structure and optical properties of two d 0–d 10 electron transition-metal oxyhalides Cs2CdV2O6Cl2 and Cs3CdV4O12Br have been systematically determined based on density functional theory. The asymmetric functional building units [V2O7], [V4O13], [CdO2Cl4] and [CdO4Br2] exhibit varying degrees of second-order Jahn−Teller distortions, contributing differently to the macroscopic nonlinearity. Mechanical properties reveal that the two oxyhalides are structurally and mechanically stable. Detailed electronic and optical properties of the two oxyhalides are provided. Optical anisotropy character is exhibited along different polarization vectors, giving a large birefringence for satisfying the phase-matching condition. Maximum absolute values of static second harmonic generation (SHG) coefficients are 4.47 pm V−1 for Cs2CdV2O6Cl2 and 3.72 pm V−1 for Cs3CdV4O12Br, suggesting that Cs2CdV2O6Cl2 and Cs3CdV4O12Br are potential NLO crystals with large SHG coefficients. In particular, unique 3D framework structures give a polar structure superposition of individual moments for asymmetric functional building units. Thus, maximum magnitudes of the total microscopic dipole are achieved, having the largest influence on the SHG response. This study elucidates the relationship between the structure and properties of transition-metal oxyhalides, providing valuable insights for designing NLO materials with excellent performance.

Stabilizing persistent currents in an atomtronic Josephson junction necklace

Arrays of Josephson junctions are at the forefront of research on quantum circuitry for quantum computing, simulation, and metrology. They provide a testing bed for exploring a variety of fundamental physical effects where macroscopic phase coherence, nonlinearities, and dissipative mechanisms compete. Here we realize finite-circulation states in an atomtronic Josephson junction necklace, consisting of a tunable array of tunneling links in a ring-shaped superfluid. We study the stability diagram of the atomic flow by tuning both the circulation and the number of junctions. We predict theoretically and demonstrate experimentally that the atomic circuit withstands higher circulations (corresponding to higher critical currents) by increasing the number of Josephson links. The increased stability contrasts with the trend of the superfluid fraction – quantified by Leggett’s criterion – which instead decreases with the number of junctions and the corresponding density depletion. Our results demonstrate atomic superfluids in mesoscopic structured ring potentials as excellent candidates for atomtronics applications, with prospects towards the observation of non-trivial macroscopic superpositions of current states.

Experimental and density functional theory investigation of 1-(4-Bromophenyl)-3-(4-ethoxyphenyl)-prop-2-en-1-one (EBC) single crystals for high second-order nonlinear optical applications

Theoretical calculation and characterization on the D-π-A-π-D type of organic nonlinear optical crystals 1-(4-Bromophenyl)-3-(4-ethoxyphenyl)-prop-2-en-1-one (EBC) were studied. The EBC single crystals with a size of 8 × 2 × 2 mm3 were successfully grown using slow cooling method in the methanol solution. Quantum chemical calculations for the experimental structure of the EBC molecule were performed at B3LYP/6-31G basis set using the density functional theory. The powder XRD, FT-IR and 1H NMR spectral of EBC molecule were investigated theoretically and experimentally, which can specify the used enantiopure starting materials, suggest the absence of impurity. The EBC crystals exhibit a large macroscopic nonlinearity, and it is revealed that the second harmonic generation efficiency (SHG) is 20 times that of KDP. Their thermal stability, UN-Vis-NIR spectrum, and the relationship between dielectric properties at different frequencies and temperature had also been investigated. In addition, the molecular electrostatic potential, frontier molecular orbitals, global reactivity descriptors, natural bond orbital, Hirshfeld surface and 2D-fingerprint were analyzed to get a better understanding of the molecular properties.

Polar and Helical Isomorphous Crystals of Proline Derivatives: Influence of a Fluorine Atom on the Electric Susceptibility

Two novel nonlinear optical isomorphous crystals of proline derivatives with alkyne functionality have been obtained (Boc-L-ProNH(CH2)2CCH and Boc-cis-4-fluoro-L-ProNH(CH2)2CCH). Both derivatives, which differ only by the substitution of a H atom to a F atom, adopt the same polar and columnar right-handed helix arrangement in the crystalline state. In addition, adjacent polar helical columns all point in the same direction, thus generating a macrodipole and a crystalline system conducive for second harmonic generation (SHG) properties. This isomorphous crystal system constitutes an interesting tool to study the effect of the fluorine atom on the dipole moment and on the first hyperpolarizability. Starting from the PBC optimized geometries of the crystals, the macroscopic second-order nonlinearity, χ(2), of the newly synthesized crystals has been estimated by quantum chemical calculations. These χ(2) responses are of the same order of magnitude as those of inorganic proline derivatives while smaller than those observed in crystals of push–pull π-conjugated molecules.Graphic

A Correlation Study between Dendritic Structure and Macroscopic Nonlinearity for Second-Order Nonlinear Optical Materials

To study the effect of dendritic structure on the macroscopic nonlinearities, four types of dendritic nonlinear optical (NLO) materials containing the same isophorone-bridged chromophores are prepa...

Wide‐Bandgap Organic Crystals: Enhanced Optical‐to‐Terahertz Nonlinear Frequency Conversion at Near‐Infrared Pumping

AbstractEnhanced terahertz (THz) wave generation is demonstrated in nonlinear organic crystals through refractive index engineering, which improves phase matching characteristics substantially. Unlike conventional low‐bandgap nonlinear organic crystals, the newly designed benzimidazolium‐based HMI (2‐(4‐hydroxy‐3‐methoxystyryl)‐1,3‐dimethyl‐1H‐benzoimidazol‐3‐ium) chromophore possesses a relatively wide bandgap. This reduces the optical group index in the near‐infrared, allowing better phase matching with the generated THz waves, and leads to high optical‐to‐THz conversion. A unique feature of the HMI‐based crystals, compared to conventional wide‐bandgap aniline‐based crystals, is their remarkably larger macroscopic optical nonlinearity, a one order of magnitude higher diagonal component in macroscopic nonlinear susceptibility than NPP ((1‐(4‐nitrophenyl)pyrrolidin‐2‐yl)methanol) crystals. The HMI‐based crystals also exhibit much higher thermal stability, with a melting temperature Tm above 250 °C, versus aniline‐based crystals (116 °C for NPP). With pumping at the technologically important wavelength of 800 nm, the proposed HMI‐based crystals boost high optical‐to‐THz conversion efficiency, comparable to benchmark low‐bandgap quinolinium crystals with state‐of‐the‐art macroscopic nonlinearity. This performance is due to the excellent phase matching enabled by decreasing optical group indices in the near‐infrared through wide‐bandgap chromophores. The proposed wide‐bandgap design is a promising way to control the refractive index of various nonlinear organic materials for enhanced frequency conversion processes.

Organic σ‐Hole Containing Crystals with Enhanced Nonlinear Optical Response and Efficient Optical‐to‐THz Frequency Conversion

AbstractA new approach for the molecular design of highly efficient nonlinear optical organic crystals is proposed by introducing substituents that form σ‐holes on both nonlinear optical cationic chromophores and aromatic anions. Introducing chlorinated substituents, in which a relatively positive σ‐hole and a negative belt coexist, provides selective reduction capability of specific π–π intermolecular interactions and simultaneous multiple secondary bonding capabilities. This leads to a crystalline state with enhanced first‐order hyperpolarizability βcrystal of chromophores that favors parallel chromophore alignment and suppression of molecular vibrations, which are optimal characteristics for electro‐optic and nonlinear optical applications, including efficient THz wave generation. Compared to benchmark nonhalogenated and fluorinated analogous crystals with state‐of‐the‐art macroscopic optical nonlinearity, σ‐hole containing chloro‐quinolinium crystals exhibit up to two times higher macroscopic nonlinear optical response and remarkably different crystal characteristics. As a result, a 0.16 mm thick chloro‐quinolinium crystal exhibits ≈22 times higher optical‐to‐THz conversion efficiency than the widely used 1.0 mm thick ZnTe inorganic crystal. Moreover, chloro‐quinolinium crystals exhibit very broad THz spectra, up to 8 THz with significantly different THz spectral shape compared to benchmark organic crystals, which is attributed to different phase matching between optical and THz frequencies and molecular vibration motions.

6MNEP: a molecular cation with large hyperpolarizability and promise for nonlinear optical applications

The featured organic push-pull chromophores 6MNEP-T and 6MNEP-4NBS show from 1.6 to 2.5 times larger calculated macroscopic nonlinearities compared with benchmark organic nonlinear optical crystals.

Optical and biological characteristics of novel organic single crystal 4-chloro N-methyl 4-stilbazolium tosylate

When compared with inorganic materials, the molecular organic materials acquire significant interest because of their considerable nonlinear optical properties, virtual unlimited design possibilities and extremely fast response times. Amongst them, organic crystals which are based on the charged chromophores and substantial Coulomb interaction have a number of benefits over non-ionic species, like first-order hyperpolarizability or greater molecular nonlinearity, durable stability and having a larger capability to override the dipole–dipole interactions and therefore it forms a non-centro symmetric macroscopic packing. For instance, DAST (4-N, N-dimethylamino-4′-N′-methyl-stilbazolium tosylate), the organic salt crystal, is one of the finest nonlinear optical materials having larger second-order nonlinear optical susceptibilities. Even though benchmark stilbazolium crystals display a great macroscopic nonlinearity and noble crystal characteristics, improving these physical properties comprising the environmental stability is a provocative topic. Based on this, the present paper discusses the growth of cationic substituted DAST namely 4-chloro -N-methyl 4-stilbazolium tosylate (CMST). Knoevenagel reaction method was used to synthesis CMST salt using Dean-Stark apparatus. The synthesized salt of CMST was dried at 100 °C for 24 h. The dried CMST salt was used to grow the crystals after three recrystallization process. Based on the solubility curve new solvent, mixture of methanol and acetonitrile was used to grow the crystals at room temperature by slope nucleation method. Structure of the grown crystals was characterized using single crystal XRD and FTIR. The compositional analysis was carried out using NMR and CHN analysis. Luminescence characteristics was studied using photoluminescence spectrum. The dielectric characteristics ware carried out from room temperature to 250 °C. Invitro analysis was carried out in the cancer cell line to study it’s anti-cancer activity.

Damage prediction via nonlinear ultrasound: A micro-mechanical approach

Nonlinear constitutive mechanical parameters, predominantly governed by micro-damage, interact with ultrasound to generate harmonics that are not present in the excitation. In principle, this phenomenon therefore permits early stage damage identification if these higher harmonics can be measured. To understand the underlying mechanism of harmonic generation, a nonlinear micro-mechanical approach is proposed here, that relates a distribution of clapping micro-cracks to the measurable macroscopic acoustic nonlinearity by representing the crack as an effective inclusion with Landau type nonlinearity at small strain. The clapping mechanism inside each micro-crack is represented by a Taylor expansion of the stress-strain constitutive law, whereby nonlinear terms arise. The micro-cracks are considered distributed in a macroscopic medium and the effective nonlinearity parameter associated with compression is determined via a nonlinear Mori-Tanaka homogenization theory. Relationships are thus obtained between the measurable acoustic nonlinearity and the Landau-type nonlinearity. The framework developed therefore yields links with nonlinear ultrasound, where the dependency of measurable acoustic nonlinearity is, under certain hypotheses, formally related to the density of micro-cracks and the bulk material properties.

Structure-property analysis of julolidine-based nonlinear optical chromophores for the optimization of microscopic and macroscopic nonlinearity.

Four NLO chromophores with different acceptors and modified julolidine donors were facilely synthesized to tune their intramolecular charge-transfer energy gaps for the investigation of the structure-property relationships. The photophysical properties of the UV-Vis absorption spectra, fluorescence spectra and solvatochromism were measured and analyzed to understand the effect of electron-donating strength and electron-withdrawing strength on intramolecular charge-transfer. Density functional theory calculations were carried out to investigate the electron density of the frontier orbitals, energy gap, molecular microscopic dipole moment and hyperpolarizability. The change tendency of the microscopic hyperpolarizability in different dielectric environments in association with the solvatochromism in absorption was analyzed. Meanwhile, the macroscopic electro-optic performance in relation to molecular structure variation and microscopic properties was further analyzed, revealing that chromophores with a larger solvatochromism exhibited higher microscopic hyperpolarizability and macroscopic electro-optic coefficients. Our investigation of the structure-property relationship gave a reliable insight into molecular design for high performance nonlinear optical chromophores.

A THEORETICAL STUDY ON THE INFLUENCE OF AGGREGATE GRADATION ON THE TENSILE STRENGTH OF 2-DIMENSIONAL MODEL CONCRETE

The size effect and macroscopic mechanical nonlinearity of concrete are caused by its inherent heterogeneity. Considering the mesoscopic structure, concrete is treated as a composite material consisting of aggregate, mortar matrix and an interfacial transition zone (ITZ). The double-line elastic-damage model has been borrowed to describe the mechanical properties of the mortar matrix and the ITZs. Aggregate is assumed to be elastic, so it cannot be damaged. Then, a general expression of the length of the fracture crack propagation path and a theoretical solution for the uniaxial tensile strength for different graded concretes are established. Finally, the theoretical resolution is compared with the simulation results at meso-scale and the rationality of the theoretical formulae for crack length and tensile strength from the present work is thereby validated.

Tuning the nonlinear optical properties of BODIPYs by functionalization with dimethylaminostyryl substituents

Two difluoroboradiazaindacene (BODIPY) scaffolds with attached dimethylaminostyryl substituents were synthesized. Guest-host polymeric films were produced by incorporating these chromophores into polymethylmethacrylate matrices. The second and third nonlinear optical properties of the resulting polymer composites were studied by means of the Maker fringe technique using a laser generating at 1064 nm with a 30 ps pulse duration. The macroscopic and microscopic nonlinearities were found to be comparatively high and dependent on the number of dimethylaminostyryl substituents attached to BODIPY core. The development of integrated optics makes such nonlinear films of particular interest, since they can be used in the creation of efficient nonlinear devices.

Preparation of polymer films containing multi-branched chromophores for enhanced nonlinear optical activity

Two new multi-branched chromophores were synthesized via esterification from monochromophores to achieve ideal macroscopic nonlinear optical activities. Molecular chemical structures of chromophores were confirmed by 1H NMR, FT-IR spectroscopy, elemental analysis, mass spectrometry and UV–visible absorption spectra. Monochromophore N1 and bichromophore DN were doped into poly (4-vinylphenol) to fabricate guest-host polymer films Film-N1 and Film-DN with high molecular loading density (up to 30 wt%). And the maximum second harmonic generation coefficients (d33) of polymer films Film-N1 and Film-DN reached to 25 pm V−1 and 39 pm V−1, respectively. In contrast, six-branched dendritic chromophore SN was utilized directly to prepare thin film Film-SN without any polymer matrix due to its large molecular weight (about 3183 Da) and the d33 value of Film-SN was up to 208 pm V−1. Compared with Film-N1, films containing multi-branched chromophores Film-DN and Film-SN exhibited about 1.6-fold and 8.3-fold enhancement in the d33 value indicating the multi-branched chromophore could significantly promote the macroscopic optical nonlinearity through the site-isolation effect.

Synthesis, crystal structures and properties of new quinolinium derivatives

Four phenyl-substituted quinolinium salts with different counter anions, C27H27NO4S, C26H25NO5S, C25H22NO5SCl, and C25H22NO5SBr, were synthesized and their single crystals were successfully grown from methanol solution by slow evaporation. Single crystal X-ray diffraction analyses showed that C27H27NO4S crystal belongs to the noncentrosymmetric orthorhombic space group Pna21, and the other three crystals belong to centrosymmetric monoclinic space group P21/n. Their first order hyperpolarization and macroscopic nonlinearity were analyzed and physical properties were characterized by UV–vis absorption spectroscopy, and differential scanning calorimetric and thermal gravimetric analysis.

Sum frequency generation image reconstruction: aliphatic membrane under spherical cap geometry.

The article explores an opportunity to approach structural properties of phospholipid membranes using Sum Frequency Generation microscopy. To establish the principles of sum frequency generation image reconstruction in such systems, at first approach, we may adopt an idealistic spherical cap uniform assembly of hydrocarbon molecules. Quantum mechanical studies for decanoic acid (used here as a representative molecular system) provide necessary information on transition dipole moments and Raman tensors of the normal modes specific to methyl terminal - a typical moiety in aliphatic (and phospholipid) membranes. Relative degree of localization and frequencies of the normal modes of methyl terminals make nonlinearities of this moiety to be promising in structural analysis using Sum Frequency Generation imaging. Accordingly, the article describes derivations of relevant macroscopic nonlinearities and suggests a mapping procedure to translate amplitudes of the nonlinearities onto microscopy image plane according to geometry of spherical assembly, local molecular orientation, and optical geometry. Reconstructed images indicate a possibility to extract local curvature of bilayer envelopes of spherical character. This may have practical implications for structural extractions in membrane systems of practical relevance.

Two phenomenological constants explain similarity laws in stably stratified turbulence.

In stably stratified turbulent flows, the mixing efficiency associated with eddy diffusivity for heat, or equivalently the turbulent Prandtl number (Pr(t)), is fraught with complex dynamics originating from the scalewise interplay between shear generation of turbulence and its dissipation by density gradients. A large corpus of data and numerical simulations agree on a near-universal relation between Pr(t) and the Richardson number (R(i)), which encodes the relative importance of buoyancy dissipation to mechanical production of turbulent kinetic energy. The Pr(t)-R(i) relation is shown to be derivable solely from the cospectral budgets for momentum and heat fluxes if a Rotta-like return to isotropy closure for the pressure-strain effects and Kolmogorov's theory for turbulent cascade are invoked. The ratio of the Kolmogorov to the Kolmogorov-Obukhov-Corrsin phenomenological constants, and a constant associated with isotropization of the production whose value (= 3/5) has been predicted from Rapid Distortion Theory, explain all the macroscopic nonlinearities.

Nonlinear current-voltage characteristics of conductive polyethylene composites with carbon black filled pet microfibrils

Current-voltage electrical behavior of in situ microfibrillar carbon black (CB)/poly(ethylene terephthalate) (PET)/polyethylene (PE) (m-CB/PET/PE) composites with various CB concentrations at ambient temperatures was studied under a direct-current electric field. The current-voltage (I-V) curves exhibited nonlinearity beyond a critical value of voltage. The dynamic random resistor network (DRRN) model was adopted to semi-qualitatively explain the nonlinear conduction behavior of m-CB/PET/PE composites. Macroscopic nonlinearity originated from the interfacial interactions between CB/PET micro fibrils and additional conduction channels. Combined with the special conductive networks, an illustration was proposed to interpret the nonlinear I-V characteristics by a field emission or tunneling mechanism between CB particles in the CB/PET microfibers intersections.

Meso-element equivalent method for the simulation of macro mechanical properties of concrete

A meso-element equivalent method is proposed to investigate the macro mechanical properties of concrete. The randomly distributed aggregates with different sizes and shapes are built by using the Monte Carlo simulation approach, and they are discretized into a finite number of identical elements with a characteristic element size. Each meso-element formed is then processed to be a homogeneous and isotropic unit based on homogenization theory of composite materials. There are two key issues emphasized in the present research, they are the equivalence of the mechanical behaviors of the aggregated concrete material and the determination of the mesh-element size, respectively. The classical Voigt parallel approach is applied to establish the equivalent mechanical behaviors of the meso-elements containing the two-phase medium composed of aggregates and mortar matrix. Since the macroscopic nonlinearity of concrete material is essentially attributed to the inherent heterogeneities, the non-homogeneity of concrete is described by the dispersion coefficient of the effective elastic moduli of concrete meso-elements. And the characteristic element size is introduced and determined by means of a statistical analysis of the aggregate sizes and taken as an appropriate mesh size of concrete specimens. The proposed approach reflects the fact that the concrete nonlinearity originates from the inherent heterogeneity. Several two-dimensional samples of concrete specimens are carried out to verify the feasibility and the accuracy of the proposed meso-element equivalent method. Furthermore, the damage process and the deformation of a three-dimensional four-point bending concrete beam are studied. The numerical results show the high efficiency and accuracy of the proposed method. Compared with other meso-mechanical methods, the advantage of the present meso-element equivalent method is that the degrees of freedom of the concrete specimens reduce significantly, making the computational efficiency improved drastically, especially for three-dimensional problems, while the accuracy of the numerical results is acceptable.

Co-crystal structure selection of nonlinear optical analogue polyenes

We demonstrate co-crystallization of analogous phenolic polyene molecules that form non-isomorphic single-component crystal structures for nonlinear optical applications. The analogous polyene molecules form similar main supramolecular hydrogen-bond interactions with neighboring molecules resulting in polar linear molecular chains, but form different crystal space groups in single component crystals, which have a different orientation of these molecular chains due to subtle variations of weak intermolecular interactions. The resulting co-crystal structure is isomorphous with one of the single-component crystals. In co-crystallization with competition between two analogous crystal structures, the solubility plays an important role to select the equilibrium crystal structure of co-crystals. The phenolic polyene co-crystals retain optimal molecular ordering with large macroscopic nonlinearity of single component crystals for nonlinear optical applications.