Simplified theory of optical nonlinearities in spin-polarized semiconductors

The spin degree of freedom is largely disregarded in existing theories of the density-dependent optical properties of an interacting electron-hole plasma in quasiequilibrium. Here, we extended the pair equation, which is applicable to a bulk semiconductor at elevated temperatures, to calculate optical nonlinearities due to a spin-polarized plasma. We obtained agreement with recent circular dichroism data in laser-excited GaAs by using the plasma density alone as the fitting parameter. The simplicity of our theory, based on the analytical pair-equation formula, makes it ideal for conveniently modelling absorption in a carrier spin-polarized semiconductor.

Quasiequilibrium optical nonlinearities from spin-polarized carriers in GaAs

Semiconductor Bloch equations, which microscopically describe the dynamics of a Coulomb interacting, spin-unpolarized electron-hole plasma, can be solved in two limits: the coherent and the quasiequilibrium regimes. These equations have been recently extended to include the spin degree of freedom and used to explain spin dynamics in the coherent regime. In the quasiequilibrium limit, one solves the Bethe-Salpeter equation in a two-band model to describe how optical absorption is affected by Coulomb interactions within a spin unpolarized plasma of arbitrary density. In this work, we modified the solution of the Bethe-Salpeter equation to include spin polarization and light holes in a three-band model, which allowed us to account for spin-polarized versions of many-body effects in absorption. The calculated absorption reproduced the spin-dependent, density-dependent, and spectral trends observed in bulk GaAs at room temperature, in a recent pump-probe experiment with circularly polarized light. Hence, our results may be useful in the microscopic modeling of density-dependent optical nonlinearities due to spin-polarized carriers in semiconductors.

Simplified theory of optical nonlinearities in spin-polarized bulk GaAs

Apart from their intrinsic physical interest, spin-polarized many-body effects are expected to be important to the working of spintronic devices. A vast literature exists on the effects of a spin-unpolarized electron-hole plasma on the optical properties of a semiconductor. Here, we include the spin degree of freedom to model optical absorption of circularly polarized light by spin-polarized bulk GaAs. Our model is easy to implement and does not require elaborate numerics, since it is based on the closed-form analytical pair-equation formula that is valid in 3d. The efficacy of our approach is demonstrated by a comparison with recent experimental data.

Simplified theory of optical nonlinearities in spin-polarized bulk GaAs

Apart from their intrinsic physical interest, spin-polarized many-body effects are expected to be important to the working of spintronic devices. A vast literature exists on the effects of a spin-unpolarized electron-hole plasma on the optical properties of a semiconductor. Here, we include the spin degree of freedom to model optical absorption of circularly polarized light by spin-polarized bulk GaAs. Our model is easy to implement and does not require elaborate numerics, since it is based on the closed-form analytical pair-equation formula that is valid in 3d. The efficacy of our approach is demonstrated by a comparison with recent experimental data.

Spectrally broadened excitonic absorption and enhanced optical nonlinearities in Dy3+-doped ZnO nanoparticles

We have synthesized Dy3+-doped ZnO nanoparticles at room temperature through the sol-gel method. X-ray diffraction and Scanning electron microscopic studies confirm the crystalline nature of the particles. Excitonic absorption of ZnO shows three different bands, and we observe that incorporation of Dy3+ results in the shifting and broadening of the n=1 absorption band of ZnO. Photoluminescence studies done at the excitation wavelength of 335 nm show broad emission containing five different bands. Open-aperture z-scan studies done at 532 nm using 5 ns laser pulses show an optical limiting behavior, which numerically fits to a three-photon type absorption process. The nonlinearity is essentially resonant, as it is found to increase consistently with Dy3+ concentration. This feature makes Dy3+-doped ZnO a flexible optical limiter for potential device applications.

Hydrogen-bond-directed self-assembly of D-(+)-dibenzoyltartaric acid and 4-aminopyridine: optical nonlinearities and stoichiometry-dependent novel structural features

Attempts to prepare hydrogen-bond-directed nonlinear optical materials from a 1:1 molar mixture Of D-(+)-dibenzoyltartaric acid (DBT, I) and 4-aminopyridine (4-AP, II) resulted in two salts of different stoichiometry. One of them crystallizes in an unusual 1.5:1 (acid:base) monohydrate salt form III while the other one crystallizes as 1:1 (acid:base) salt IV. Crystal structures of both of the salts were determined from single-crystal X-ray diffraction data. The salt III crystallizes in a monoclinic space group C2 with a = 30.339(l), b = 7.881(2), c = 14.355(1) angstrom, beta = 97.48(1)degrees, V = 3403.1(9) angstrom3, Z = 4, R(w) = 0.058, R(w)= 0.058. The salt IV also crystallizes in a monoclinic space group P2(1) with a = 7.500(1), b = 14.968(2), c = 10.370(1) angstrom, beta = 102.67(1)degrees, V = 1135.9(2) angstrom3, Z = 2, R = 0.043, R(w) = 0.043. Interestingly, two DBT molecules with distinctly different conformation are present in the same crystal lattice of salt III. Extensive hydrogen-bonding interactions are found in both of the salts, and both of them show SHG intensity 1.4-1.6 times that of urea.

FIELD EMISSION EFFICIENCY OF A CARBON NANOTUBE ARRAY UNDER PARASITIC NONLINEARITIES

Carbon Nanotubes (CNTs) grown on substrates are potential electron sources in field emission applications. Several studies have reported the use of CNTs in field emission devices, including field emission displays, X-ray tube, electron microscopes, cathode-ray lamps, etc. Also, in recent years, conventional cold field emission cathodes have been realized in micro-fabricated arrays for medical X-ray imaging. CNTbased field emission cathode devices have potential applications in a variety of industrial and medical applications, including cancer treatment. Field emission performance of a single isolated CNT is found to be remarkable, but the situation becomes complex when an array of CNTs is used. At the same time, use of arrays of CNTs is practical and economical. Indeed, such arrays on cathode substrates can be grown easily and their collective dynamics can be utilized in a statistical sense such that the average emission intensity is high enough and the collective dynamics lead to longer emission life. The authors in their previous publications had proposed a novel approach to obtain stabilized field emission current from a stacked CNT array of pointed height distribution. A mesoscopic modeling technique was employed, which took into account electro-mechanical forces in the CNTs, as well as transport of conduction electron coupled with electron phonon induced heat generation from the CNT tips. The reported analysis of pointed arrangements of the array showed that the current density distribution was greatly localized in the middle of the array, the scatter due to electrodynamic force field was minimized, and the temperature transients were much smaller compared to those in an array with random height distribution. In the present paper we develop a method to compute the emission efficiency of the CNT array in terms of the amount of electrons hitting the anode surface using trajectory calculations. Effects of secondary electron emission and parasitic capacitive nonlinearity on the current-voltage signals are accounted. Field emission efficiency of a stacked CNT array with various pointed height distributions are compared to that of arrays with random and uniform height distributions. Effect of this parasitic nonlinearity on the emission switch-on voltage is estimated by model based simulation and Monte Carlo method.

On existence of periodic solutions for stable interval plants with odd, sector type nonlinearities

In several systems, the physical parameters of the system vary over time or operating points. A popular way of representing such plants with structured or parametric uncertainties is by means of interval polynomials. However, ensuring the stability of such systems is a robust control problem. Fortunately, Kharitonov's theorem enables the analysis of such interval plants and also provides tools for design of robust controllers in such cases. The present paper considers one such case, where the interval plant is connected with a timeinvariant, static, odd, sector type nonlinearity in its feedback path. This paper provides necessary conditions for the existence of self sustaining periodic oscillations in such interval plants, and indicates a possible design algorithm to avoid such periodic solutions or limit cycles. The describing function technique is used to approximate the nonlinearity and subsequently arrive at the results. Furthermore, the value set approach, along with Mikhailov conditions, are resorted to in providing graphical techniques for the derivation of the conditions and subsequent design algorithm of the controller.

Estimation of nonlinearities from pseudodynamic and dynamic responses of bridge structures using the Delay Vector Variance method

Analysis of the variability in the responses of large structural systems and quantification of their linearity or nonlinearity as a potential non-invasive means of structural system assessment from output-only condition remains a challenging problem. In this study, the Delay Vector Variance (DVV) method is used for full scale testing of both pseudo-dynamic and dynamic responses of two bridges, in order to study the degree of nonlinearity of their measured response signals. The DVV detects the presence of determinism and nonlinearity in a time series and is based upon the examination of local predictability of a signal. The pseudo-dynamic data is obtained from a concrete bridge during repair while the dynamic data is obtained from a steel railway bridge traversed by a train. We show that DVV is promising as a marker in establishing the degree to which a change in the signal nonlinearity reflects the change in the real behaviour of a structure. It is also useful in establishing the sensitivity of instruments or sensors deployed to monitor such changes. (C) 2015 Elsevier B.V. All rights reserved.

Nonlinear Enzyme Kinetics Can Lead to High Metabolic Flux Control Coefficients: Implications for the Evolution of Dominance

In a classic study, Kacser & Burns (1981, Genetics 97, 639-666) demonstrated that given certain plausible assumptions, the flux in a metabolic pathway was more or less indifferent to the activity of any of the enzymes in the pathway taken singly. It was inferred from this that the observed dominance of most wild-type alleles with respect to loss-of-function mutations did not require an adaptive, meaning selectionist, explanation. Cornish-Bowden (1987, J. theor. Biol. 125, 333-338) showed that the Kacser-Burns inference was not valid when substrate concentrations were large relative to the relevant Michaelis constants. We find that in a randomly constructed functional pathway, even when substrate levels are small, one can expect high values of control coefficients for metabolic flux in the presence of significant nonlinearities as exemplified by enzymes with Hill coefficients ranging from two to six, or by the existence of oscillatory loops. Under these conditions the flux can be quite sensitive to changes in enzyme activity as might be caused by inactivating one of the two alleles in a diploid. Therefore, the phenomenon of dominance cannot be a trivial ''default'' consequence of physiology but must be intimately linked to the manner in which metabolic networks have been moulded by natural selection.

A Proposal for Concurrent Estimation of Static and Dynamic Nonlinearity of ADC

Despite great advances in very large scale integrated-circuit design and manufacturing, performance of even the best available high-speed, high-resolution analog-to-digital converter (ADC) is known to deteriorate while acquiring fast-rising, high-frequency, and nonrepetitive waveforms. Waveform digitizers (ADCs) used in high-voltage impulse recordings and measurements are invariably subjected to such waveforms. Errors resulting from a lowered ADC performance can be unacceptably high, especially when higher accuracies have to be achieved (e.g., when part of a reference measuring system). Static and dynamic nonlinearities (estimated independently) are vital indices for evaluating performance and suitability of ADCs to be used in such environments. Typically, the estimation of static nonlinearity involves 10-12 h of time or more (for a 12-b ADC) and the acquisition of millions of samples at high input frequencies for dynamic characterization. ADCs with even higher resolution and faster sampling speeds will soon become available. So, there is a need to reduce testing time for evaluating these parameters. This paper proposes a novel and time-efficient method for the simultaneous estimation of static and dynamic nonlinearity from a single test. This is achieved by conceiving a test signal, comprised of a high-frequency sinusoid (which addresses dynamic assessment) modulated by a low-frequency ramp (relevant to the static part). Details of implementation and results on two digitizers are presented and compared with nonlinearities determined by the existing standardized approaches. Good agreement in results and time savings achievable indicates its suitability.

A Proposal for Concurrent Estimation of Static and Dynamic Nonlinearity of ADC

Despite great advances in very large scale integrated-circuit design and manufacturing, performance of even the best available high-speed, high-resolution analog-to-digital converter (ADC) is known to deteriorate while acquiring fast-rising, high-frequency, and nonrepetitive waveforms. Waveform digitizers (ADCs) used in high-voltage impulse recordings and measurements are invariably subjected to such waveforms. Errors resulting from a lowered ADC performance can be unacceptably high, especially when higher accuracies have to be achieved (e.g., when part of a reference measuring system). Static and dynamic nonlinearities (estimated independently) are vital indices for evaluating performance and suitability of ADCs to be used in such environments. Typically, the estimation of static nonlinearity involves 10-12 h of time or more (for a 12-b ADC) and the acquisition of millions of samples at high input frequencies for dynamic characterization. ADCs with even higher resolution and faster sampling speeds will soon become available. So, there is a need to reduce testing time for evaluating these parameters. This paper proposes a novel and time-efficient method for the simultaneous estimation of static and dynamic nonlinearity from a single test. This is achieved by conceiving a test signal, comprised of a high-frequency sinusoid (which addresses dynamic assessment) modulated by a low-frequency ramp (relevant to the static part). Details of implementation and results on two digitizers are presented and compared with nonlinearities determined by the existing standardized approaches. Good agreement in results and time savings achievable indicates its suitability.

Inelastic Postbuckling of Columns of Variable Flexural Rigidity

Effects of large deformation and inelasticity are considered in formulating the behavior of columns of variable cross section subjected to an axial compressive load. Simple, approximate methods are used to obtain numerical results. The combined effect of the nonlinearities is shown to be of a hardening type for small column deflections

Nonlinear secondary whirl of an overhung rotor

Gravity critical speeds of rotors have hitherto been studied using linear analysis, and ascribed to rotor stiffness asymmetry. Here, we study an idealized asymmetric nonlinear overhung rotor model of Crandall and Brosens, spinning close to its gravity critical speed.Nonlinearities arise from finite displacements, and the rotor's staticlateral deflection under gravity is taken as small. Assuming small asymmetry and damping, slow modulations of whirl amplitudes are studied using the method of multiple scales. Inertia asymmetry appears only at second order. More interestingly, even without stiffness asymmetry, the gravity-induced resonance survives through geometric nonlinearities. The gravity resonant forcing does not influence the resonant mode at leading order, unlike the typical resonant oscillations. Nevertheless,the usual phenomena of resonances, namely saddle-node bifurcations, jump phenomena and hysteresis, are all observed. An unanticipated periodic solution branch is found. In the three-dimensional space oftwo modal coefficients and a detuning parameter, the full set of periodic solutions is found to be an imperfect version of three mutually intersecting curves: a straight line,a parabola and an ellipse.