Value Of Nonlinear Coefficient Research Articles

Rare earth oxides effects on both the threshold voltage and energy absorption capability of ZnO varistors

Rare earth oxides: Pr 6O 11, Y 2O 3, La 2O 3, Ce 2O 3 and Nd 2O 3 are added with contents of 0.01–0.5 wt.% to ZnO standard and antimony-rich varistor compositions. It is found that the rare earth oxide: REO, allows reaching large energy absorption capability value for the high threshold voltage ZnO-based varistors. A 30% maximum increase in threshold voltage is observed with the addition of 0.1 wt.% REO. However, degradation is accentuated with REO addition. Between 0 and 0.1 wt.% of REO the degradation remain still acceptable, but beyond 0.1% it becomes strong, up to 20% and energy absorption capability remains more than 100 J/cm 3. It is practically constant whatever the REO percentage. Results from standard composition are exploited for the second composition by optimization of Sb 2O 3 and REO concentrations in order to control the growth of the ZnO grains while maintaining the energy absorption capability above 100 J/cm 3. On the one hand, a high threshold voltage 300 V/mm ensured by antimony oxide, and on the other hand, a good capacity for absorption in energy 107 J/cm 3 ensured by the REO, whereas it had fallen to 52 J/cm 3 because of the great quantity of Sb 2O 3. Satisfactory values of non-linearity coefficient ( α) between 40 and 52 are obtained. These results are explained by the presence of extra-pyrochlore phase suggesting less bismuth oxide in the ceramics, especially at grain boundaries. Varistors present more active grains and hence a larger conduction section which account for large absorption capability.

Nonlinear‐Optical Susceptibility of Hilgardite‐Like Borates M2B5O9X (M: Pb, Ca, Sr, Ba; X: Cl, Br).

AbstractFor Abstract see ChemInform Abstract in Full Text.

Two new poly(arylene ether sulfone)s containing second-order nonlinear optical chromophores

Two new poly(arylene ether sulfone)s, P1 and P2, with pendant nonlinear optical (NLO) chromophores (60 and 84%, respectively) have been easily prepared by post-esterification reaction of poly(arylene ether sulfone) P under mild conditions. P1 and P2 are readily soluble in common organic solvents at room temperature and thermally stable up to 200 °C in both air and argon. The glass transition temperatures (T g's) of P1 and P2 are 174 and 189 °C, respectively. The resonant nonlinear optical coefficient (d 33) values were estimated to be 29.2 and 16.5 pm/V for P1 and P2, respectively, by in situ second harmonic generation (SHG) measurements at 1064 nm fundamental wavelength. By using the approximation two-level model, the nonresonant NLO coefficient (d 33(∞)) values of P1 and P2 were estimated to be 6.6 and 4.8 pm/V, respectively.

TiO 2 ceramic varistor modified with tantalum and barium

The non-linear current ( I)–voltage ( V) characteristics of titanium dioxide doped with small quantities of tantalum and barium (99.9 TiO 2 + 0.1 Ta and 99.4 TiO 2 + 0.1 Ta + 0.5 Ba, all are in at.%) were investigated. These samples have the non-linear coefficient ( α) values of (20–30) with high breakdown voltages ( E B ∼ 400–700 V mm −1). The pentavalent tantalum acts as donor and increases the electronic conductivity. The higher electrical conductivity and decrease in the breakdown field strength with barium addition is attributed to higher density. The acceptor like surface states formed by barium ions segregate to grain boundaries due size misfit to thereby modifying the electrical barrier characteristics of grain boundaries.

Nonlinear-optical susceptibility of hilgardite-like borates [formula omitted][formula omitted]; [formula omitted

Usage of non-centrosymmetric boron oxide derivative crystals as nonlinear elements may be a key solution of pressing problem of obtaining powerful radiation at shorter wavelengths via frequency multiplication of solid state laser radiations. It is shown that Pb 2B 5O 9Br and some other members of hilgardite-like borohalogenides demonstrate in powder form, high non-linear optical activity in the SHG experiments. An attempt is made using the Philips–Van Vechten–Levine–Xue bond theory to calculate second-order nonlinear coefficients for isostructural to mineral hilhardite noncentrosymmetric crystals M 2 B 5 O 9 X with M = Pb , Sr, Ba, Eu, Ca and X = Cl , Br. Theoretically obtained values of nonlinear optical coefficients d i j k only partly correlate with the results of SHG measurements. In particular, the experiments distinctively show sharp increase of nonlinear activity along the series Ca < Sr < Ba < Pb and Cl < Br of metal boro-halogenides, while theoretical estimations give substantially more slack composition dependences. Analysis of contribution of different boron–oxygen bonds to optical nonlinearities of the compounds reveals important role of planar BO 3 triangles, though this factor is yet unable to explain enormously high SHG output from Pb 2B 5O 9Br.

Optical parametric amplification in all-silica triangular-core photonic crystal fibers

The present analysis demonstrates that photonic crystal fibers can be designed to enhance their properties for optical parametric amplification. In particular, it is possible to achieve high nonlinear coefficient values and flattened dispersion curves around 1550 nm to fully exploit the four-wave-mixing effect. These results have been obtained for triangular-core photonic crystal fibers without the need of modifying the refractive-index profile by adding dopants in the fiber cross section.

Synthesis and Crystal Structures of Phenylethynylpyridinium Derivatives for Second‐Order Nonlinear Optics.

AbstractFor Abstract see ChemInform Abstract in Full Text.

Low voltage varistors based on CeO 2

The nonlinear current ( I)–voltage ( V) characteristics of cerium dioxide containing few dopants such as a donor (Nb 2O 5 or Ta 2O 5 (0.5 at.%) and a rare earth element oxide (La 2O 3) or alkaline earth element oxide (BaO) (0.5 at.%) shows promising values of nonlinear coefficient ( α) values (∼5–6) with very low breakdown voltages ( E B ∼10–20 V mm −1). The pentavalent tantalum or niobium acts as donor and increases the electronic conductivity. The oxygen adsorbed at the grain boundary acceptors states during sintering and cooling leads to the formation of grain boundary barrier.

Synthesis and Crystal Structures of Phenylethynylpyridinium Derivatives for Second-Order Nonlinear Optics

Abstract Several salts of 1-methyl-4-[4-(dimethylamino)phenylethynyl]pyridinium 1, whose ethenyl analogue 2 is the cation of DAST (1-methyl-4-{2-[4-(dimethylamino)phenyl]ethenyl}pyridinium p-toluenesulfonate), were synthesized, and these properties were investigated. From a molecular-orbital calculation, the hyperpolarizability (β) of 1 was calculated to be about 80% of that of 2. The absorption maximum wavelength of 1 is shorter than that of 2. Six SHG active salts based on cation 1, including iodide and 4-substituted benzenesulfonates, were obtained in total. Among them, the crystal structures of p-chlorobenzenesulfonate salt (1c) and p-toluenesulfonate salt (1e) could be analyzed. As a result, these two have almost the same structures, and the off-diagonal second-order nonlinear optical coefficient (d) values were estimated to be about twice as large as those of DAST.

Recent research developments in SnO 2-based varistors

This paper discusses some advances in research conducted on SnO 2-based electroceramics. The addition of different dopants, as well as several thermal treatments in oxidizing and inert atmospheres, were found to influence the microstructure and electrical properties of SnO 2-based varistor ceramics. Measurements taken by impedance spectroscopy revealed variations in the height and width of the potential barrier resulting from the atmosphere in which thermal treatments were performed. High nonlinear coefficient values, which are characteristic of high-voltage and commercial ZnO varistors, were obtained for these SnO 2-based systems. All the systems developed here have potentially promising varistor applications.

Design and synthesis of a new nonlinear optical poly(phthalazinone ether ketone)

This paper reports a new nonlinear optical (NLO) poly(phthalazinone ether ketone) P1 with a high molar density (80%) of chromophore. It has been synthesized by Heck reaction between a brominated poly(phthalazinone ether ketone) P and the NLO chromophore 4. P1 exhibited excellent thermal properties and good solubility due to the presence of the kinked non-planar moiety, phenyl phthalazinone, along the polymer backbones. DSC indicated that the glass transition temperature ( T g) of P1 was 188 °C, and TGA indicated that P1 was thermally stable up to 290 °C in both air and argon. The structures of P and P1 were characterized, and the poled films of P1 revealed a second-order nonlinear optical coefficient ( d 33) value of 16.9 pm/V by in situ second harmonic generation measurements at 1064 nm fundamental wavelength.

THERMAL POSTBUCKLING OF SLENDER ELASTIC RODS WITH HINGED ENDS CONSTRAINED BY A LINEAR SPRING

This paper presents the critical buckling temperature and a closed-form analytical solution for the thermal postbuckling behavior of uniformly heated slender elastic rods. The boundary conditions are assumed hinged and nonmovable at one end, whereas at the other end longitudinal displacement is constrained by a linear spring. The thermal strain–temperature relationship is considered nonlinear and the material is assumed to be linearly elastic, homogeneous, and isotropic. Large displacements are included; hence, the formulation is geometrically nonlinear. A set of six first-order nonlinear ordinary differential equations with boundary conditions defined at both ends yields a complex boundary-value problem. The buckling and postbuckling solutions are respectively accomplished by assuming infinitesimal rotations and employing complete elliptical integrals. The results are presented in nondimensional graphs obtained for different values of spring stiffness, slenderness ratios, and nonlinear thermal strain coefficients. It is shown that these three parameters govern the buckling and postbuckling behavior.

Synthesis and properties of a ROMP backbone polymer with efficient, laterally appended nonlinear optical chromophores

The synthesis and properties of a new ROMP backbone polymer bearing lateral donor–acceptor-substituted (E)-diethynylethene ((E)-hex-3-ene-1,5-diyne) chromophores are described. The polymer with an average of 40 monomeric repeat units is readily soluble in common organic solvents such as tetrahydrofuran, dichloromethane and chloroform. Good optical-quality films were obtained by spin coating. The third-order susceptibility χ(3) at a wavelength of 1907 nm was determined to be 100 times greater than that of fused silica. After electrical poling, the polymer also showed a significant second-order nonlinear optical coefficient (d33) value, which decays by a factor of two over a period of one month at room temperature.

A numerical study of 1-D nonlinear P-wave propagation in solid

Two central schemes of finite difference (FD) up to different accuracy orders of space sampling step Δx (Fourth order and Sixth order respectively) were used to study the 1-D nonlinear P-wave propagation in the nonlinear solid media by the numerical method. Distinctly different from the case of numerical modeling of linear elastic wave, there may be several difficulties in the numerical treatment to the nonlinear partial differential equation, such as the steep gradients, shocks and unphysical oscillations. All of them are the great obstacles to the stability and convergence of numerical calculation. Fortunately, the comparative study on the modeling of nonlinear wave by the two FD schemes presented in the paper can provide us with an easy method to keep the stability and convergence in the calculation field when the product of the absolute value of nonlinear coefficient and the value of ϖu/ϖx are small enough, namely, the value of βϖu/ϖx is much smaller than 1. Several results are founded in the numerical study of nonlinear P-wave propagation, such as the waveform aberration, the generation and growth of harmonic wave and the energy redistribution among different frequency components. All of them will be more violent when the initial amplitudeA 0 is larger or the nonlinearity of medium is stronger. Correspondingly, we have found that the nonlinear P-wave propagation velocity will change with different initial frequencyf of source wave or the wave velocityc (equal to the P-wave velocity in the same medium without considering nonlinearity).

Linear and third-order nonlinear optical absorption of amorphous Ge nanoclusters embedded in Al2O3 matrix synthesized by electron-beam coevaporation

Amorphous germanium (α-Ge) nanoclusters embedded in Al2O3 matrix are synthesized on fused-quartz glass substrate at room temperature by vacuum electron-beam coevaporation. Linear optical transmittance measurements reveal an indirect optical absorption edge with a blueshift as large as 1.6 eV due to the quantum confinement effects. The Z-scan method is used to study the third-order nonlinear absorption process of the synthesized samples, which clearly show a two-photon nonlinear process. Results also suggest that Ge nanocluster density or size is of great influence to the value of nonlinear absorption coefficient β.

Response probability structure of a structurally nonlinear fluttering airfoil in turbulent flow

The stationary probability structure for the aeroelastic response of a structurally nonlinear fluttering airfoil subject to random turbulent flow is examined numerically. The airfoil is modelled as a two-dimensional flat plate with degrees of freedom in torsion and heave (vertical displacement). The nonlinearity is a hardening cubic stiffness force in the torsional direction. The aerodynamic force and moment are assumed to be linear, thus limiting the analysis to small oscillations; unsteady effects are retained. Furthermore, both parametric and external random coloured excitations are considered. It is found that depending on the value of turbulence variance and nonlinear cubic stiffness coefficient, the pitch marginal probability density functions (PDF) exhibits uni-, bi- or double bi-modality; the nature of the bi-modality is not unique. An explanation of the behaviour is provided via an analysis of the joint PDF in pitch and pitch rate for which both the deterministic and random responses are examined. More generally, it is found that the random excitation effectively ‘decouples’ the nonlinear responses such that the pitch, pitch rate, heave and heave rate marginal PDFs transition from uni- to bi-modality at different airspeeds. It is argued that a fundamental cause of the observed behaviour is the synergy between the nonlinearity and the random external excitation.

Low‐Voltage Varistor Based on (Sn,Ti)O2 Ceramics

A description is given of the nonohmic behavior obtained in (SnxTi1−x)O2‐based systems. A matrix founded on (SnxTi1−x)O2‐based systems doped with Nb2O5 leads to a low‐voltage varistor system with nonlinear coefficient values of ∼9. The presence of the back‐to‐back Schottky‐type barrier is observed based on the voltage dependence of the capacitance. When doped with CoO, the (SnxTi1−x)O2‐based system presents higher nonlinear coefficient values (&gt;30) than does the SnO2‐based varistor system.

Third order optical characterisation of a π-conjugated polydiacetylene by Maker fringes technique

Conjugated polymers are promising photonic materials due to the high values of non-linear optical coefficients when compared to inorganic compounds. A key point in view of applications is the figure of merit defined as the ratio between the non-linear optical and the absorption coefficients. We report on the NIR measurement of the third order optical susceptibility ( χ (3)) by third harmonic generation in polydiacetylene (poly-[1,6-bis-(3,6-dihexadecyl- N-carbazolyl)-2,4-hexadiyne], polyDCHD-HS). Samples are prepared as thin films by spin-coating technique and the χ (3) is evaluated by Maker fringes method in the spectral range from 1200 to 2000 nm. The absorption coefficient has been derived from measurements in CS 2 solution. Spectra of χ (3) show typical resonant behaviour due to the multi-photon processes and are strictly related to the absorption spectra in the visible range. Values of χ (3) are in the range of 10 −11 esu. The absorption coefficient is as low as 0.25 cm −1 at 1.5 μm showing the good figure of merit of polyDCHD-HS.

Acousto-optic study of nonlinear acoustic properties of layered materials

The investigation of acoustic properties in layered crystals KY(MoO4)2 and Si20Te80 isotropic alloy with nanocrystallite inclusions has been carried out. The acousto-optic and pulse-echo techniques were used. The measurements of ultrasound velocity and attenuation, and also sound wave spectrum evolution along different crystallographic axes in wide ranges of frequency (14-1800 MHz) temperatures (90-300 K) and sound intensities (0.04-100 W cm-2) were fulfilled. Extremely large values of nonlinear coefficients and anharmonicity constants of longitudinal photon modes across the layers and crystallite boundaries have been found. It has been shown that anharmonicity of the bonding force across the layers determines the anisotropy of the mechanical strength in layered crystals.

Effect of non-Newtonian behaviour of lubricant and bearing flexibility on the performance of slot-entry journal bearing

This work describes the theoretical study concerning the effect of non-linear behaviour of the lubricant on the performance of a slot-entry journal bearing. The analysis considers the generalized Reynolds equation governing the flow of lubricant having variable viscosity in the clearance space and the three dimensional elasticity equations governing the displacement field in the bearing shell, and equation of flow of lubricant through slot restrictor. The non-Newtonian lubricant is assumed to follow the cubic shear stress law ( τ ̄ + K ̄ τ ̄ 3=γ⨪ ). Bearing performance characteristics have been presented for a typically selected values of non-linearity factor ( K̄) and deformation coefficient ( C ̄ d ). It has been observed that the combined effect of non-linearity factor ( K̄) and bearing flexibility ( C ̄ d ) affects the performance characteristics of slot-entry journal bearing quite significantly.