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At least 577 records · Page 32
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Extraction of Pairs of Harmonics from Trigonometric Polynomials by Phase-Amplitude Operators

We propose a method for extracting the sums of two harmonics from trigonometric polynomials T{sub n}(t) by the method of amplitude-phase transformations. Such transformations send polynomials T{sub n}(t) to similar polynomials by two simplest operations: multiplication by a real constant X and shift by a real phase λ, i.e., T{sub n}(t) → X ・ T{sub n}(t − λ). The harmonics are extracted by adding similar polynomials.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

On the Radius of Starlikeness for Harmonic Mappings

In this paper, we obtain a criterion of starlikeness for the image of the disk with center at the origin and radius r ∈ (0, 1) under a univalent harmonic mapping by a function that maps the unit disk onto a convex domain. This criterion is similar to the criterion of image convexity, and it is expressed in terms of starlikeness in one direction. As a corollary, we obtain a new estimate for the radius of starlikeness of the class of univalent harmonic mappings that take the unit disk onto a convex domain.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Nonlinear Second Harmonics of Localized Shear Waves in an Anisotropic Layer Between Anisotropic Half Spaces Under the Conditions of Imperfect Contact

We construct a numerical-analytic solution of the problem of generation of the nonlinear second harmonics in the course of propagation of elastic symmetric localized shear waves in the crystalline layer of cubic system of the m3m class located between the crystalline half spaces of the same type and the same class of anisotropy under the conditions of imperfect sliding contact of components of the waveguide. We determine the analytic form of the functions of wave motions for nonlinear anharmonic perturbations in the form of longitudinal-shear-type waves. We also perform the numerical investigations of the amplitude-frequency characteristics of the second harmonics for monochromatic localized waves in a layer of a single crystal of germanium between the half spaces from the single crystal of silicon.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

Conversion of a Chirp Pulse Into the Second Harmonic in a KDP Crystal

Results of investigation of conversion of radiation with the wavelength λ = 950 nm and pulse duration of 100 ps into the second harmonic are reported. It is demonstrated that the second harmonic pulse duration is half the pulse duration at the fundamental frequency. The converted radiation linewidth remains unchanged. The beam quality factor М{sup 2} increases from 1.16 to 1.56. The maximal conversion efficiency is 12.2%.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2011

Quantization and instability of the damped harmonic oscillator subject to a time-dependent force

We consider the one-dimensional motion of a particle immersed in a potential field U(x) under the influence of a frictional (dissipative) force linear in velocity (-{gamma}x) and a time-dependent external force (K(t)). The dissipative system subject to these forces is discussed by introducing the extended Bateman's system, which is described by the Lagrangian: L=mxy-U(x+1/2 y)+U(x-1/2 y)+({gamma})/2 (xy-yx)-xK(t)+yK(t), which leads to the familiar classical equations of motion for the dissipative (open) system. The equation for a variable y is the time-reversed of the x motion. We discuss the extended Bateman dual Lagrangian and Hamiltonian by setting U(x{+-}y/2)=1/2 k(x{+-}y/2){sup 2} specifically for a dual extended damped-amplified harmonic oscillator subject to the time-dependent external force. We show the method of quantizing such dissipative systems, namely the canonical quantization of the extended Bateman's Hamiltonian H. The Heisenberg equations of motion utilizing the quantized Hamiltonian H surely lead to the equations of motion for the dissipative dynamical quantum systems, which are the quantum analog of the corresponding classical systems. To discuss the stability of the quantum dissipative system due to the influence of an external force K(t) and the dissipative force, we derived a formula for transition amplitudes of the dissipative system with the help of the perturbation analysis. The formula is specifically applied for a damped-amplified harmonic oscillator subject to the impulsive force. This formula is used to study the influence of dissipation such as the instability due to the dissipative force and/or the applied impulsive force. - Highlights: > A method of quantizing dissipative systems is presented. > In order to obtain the method, we apply Bateman's dual system approach. > A formula for a transition amplitude is derived. > We use the formula to study the instability of the dissipative systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Pisot q-coherent states quantization of the harmonic oscillator

We revisit the quantized version of the harmonic oscillator obtained through a q-dependent family of coherent states. For each q, 0<q<1, these normalized states form an overcomplete set that resolves the unity with respect to an explicit measure. We restrict our study to the case in which q{sup -1} is a quadratic unit Pisot number, since then the q-deformed integers form Fibonacci-like sequences of integers. We then examine the main characteristics of the corresponding quantum oscillator: localization in the configuration and in the phase spaces, angle operator, probability distributions and related statistical features, time evolution and semi-classical phase space trajectories. - Highlights: Black-Right-Pointing-Pointer Quantized version of the harmonic oscillator (HO) through a q-family of coherent states. Black-Right-Pointing-Pointer For q,0<q<1 these normalized states form an overcomplete set that resolves the unity with respect to an explicit measure. Black-Right-Pointing-Pointer q-Deformed numbers are Fibonacci-like integer sequences (1/q a quadratic unit Pisot number). Black-Right-Pointing-Pointer We examine the main physical characteristics of the corresponding quantum oscillator.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Reconsidering harmonic and anharmonic coherent states: Partial differential equations approach

This article presents a new approach to dealing with time dependent quantities such as autocorrelation function of harmonic and anharmonic systems using coherent states and partial differential equations. The approach that is normally used to evaluate dynamical quantities involves formidable operator algebra. That operator algebra becomes insurmountable when employing Morse oscillator coherent states. This problem becomes even more complicated in case of Morse oscillator as it tends to exhibit divergent dynamics. This approach employs linear partial differential equations, some of which may be solved exactly and analytically, thereby avoiding the cumbersome noncommutative algebra required to manipulate coherent states of Morse oscillator. Additionally, the arising integrals while using the herein presented method feature stability and high numerical efficiency. The correctness, applicability, and utility of the above approach are tested by reproducing the partition and optical autocorrelation function of the harmonic oscillator. A closed-form expression for the equilibrium canonical partition function of the Morse oscillator is derived using its coherent states and partial differential equations. Also, a nonequilibrium autocorrelation function expression for weak electron–phonon coupling in condensed systems is derived for displaced Morse oscillator in electronic state. Finally, the utility of the method is demonstrated through further simplifying the Morse oscillator partition function or autocorrelation function expressions reported by other researchers in unevaluated form of second-order derivative exponential. Comparison with exact dynamics shows identical results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Dissipative quantum trajectories in complex space: Damped harmonic oscillator

Dissipative quantum trajectories in complex space are investigated in the framework of the logarithmic nonlinear Schrödinger equation. The logarithmic nonlinear Schrödinger equation provides a phenomenological description for dissipative quantum systems. Substituting the wave function expressed in terms of the complex action into the complex-extended logarithmic nonlinear Schrödinger equation, we derive the complex quantum Hamilton–Jacobi equation including the dissipative potential. It is shown that dissipative quantum trajectories satisfy a quantum Newtonian equation of motion in complex space with a friction force. Exact dissipative complex quantum trajectories are analyzed for the wave and solitonlike solutions to the logarithmic nonlinear Schrödinger equation for the damped harmonic oscillator. These trajectories converge to the equilibrium position as time evolves. It is indicated that dissipative complex quantum trajectories for the wave and solitonlike solutions are identical to dissipative complex classical trajectories for the damped harmonic oscillator. This study develops a theoretical framework for dissipative quantum trajectories in complex space.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Macroscopic detection of deformed QM by the harmonic oscillator

Based on the nonperturbative analysis, we show that the classical motion of harmonic oscillator derived from the deformed QM is manifestly in contradiction with observations (to the first order in deformation parameter as it has been pointed out in Bawaj et al. (2015)). For this reason, we take an alternate way for estimating the effect and discuss its possible observational manifestations in macrophysics. - Highlights: • The classical motion of harmonic oscillator is derived from deformed QM. • The classical limit is obviously inconsistent with observations. • The reason for this inconsistency is explained. • An alternate estimate of the effect is provided.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

The harmonic oscillator in a space with a screw dislocation

Highlights: •Quantum-mechanical systems with screw dislocation are receiving considerable interest. •The harmonic oscillator with screw dislocation is not completely separable. •The screw dislocation removes the degeneracy. •The variational method is useful for obtaining eigenvalues and eigenfunctions. •The spectrum exhibits a rich structure of avoided crossings. -- Abstract: We obtain the eigenvalues of the harmonic oscillator in a space with a screw dislocation. By means of a suitable nonorthogonal basis set with variational parameters we obtain sufficiently accurate eigenvalues for an arbitrary range of values of the space-deformation parameter. The energies exhibit a rich structure of avoided crossings in terms of such model parameter.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Generalized ladder operators for the perturbed harmonic oscillator

In this paper, we construct corrections to the raising and lowering (i.e. ladder) operators for a quantum harmonic oscillator subjected to a polynomial type perturbation of any degree and to any order in perturbation theory. We apply our formalism to a couple of examples, namely q and p{sup 4} perturbations, and obtain the explicit form of those operators. We also compute the expectation values of position and momentum for the above perturbations. This construction is essential for defining coherent and squeezed states for the perturbed oscillator. Furthermore, this is the first time that corrections to ladder operators for a harmonic oscillator with a generic perturbation and to an arbitrary order of perturbation theory have been constructed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Evaluating route to impact convergence of the harmonic balance method for piecewise-smooth systems

Here in this work, we investigate the applicability of the harmonic balance method (HBM) to predict periodic solutions of a single degree-of-freedom forced Duffing oscillator with freeplay nonlinearity. By studying the route to impact, which refers to a parametric study as the contact stiffness increases from soft to hard, the convergence behavior of the HBM can be understood in terms of the strength of the non-smooth forcing term. HBM results are compared to time-integration results to facilitate an evaluation of the accuracy of nonlinear periodic responses. An additional contribution of this study is to perform convergence and stability analysis specifically for isolas generated by the non-smooth nonlinearity. Residual error analysis is used to determine the approximate number of harmonics required to get results accurate to a given error tolerance. Hill’s method and Floquet theory are employed to compute the stability of periodic solutions and identify the types of bifurcations in the system.

42 ENGINEERING↗
DOE OSTI2013

Large scale synthesis, second-harmonic generation, and piezoelectric properties of a noncentrosymmetric vanadium phosphate, Li₂VPO₆

The phase pure large scale synthesis, second-harmonic generation, and piezoelectric properties of a vanadium phosphate, Li₂VPO₆ are reported. The material has been synthesized by a standard solid-state reaction using Li₂CO₃, V₂O₅, and NH₄H₂PO₄ as reagents. The phase purity and crystal structure of the reported material have been confirmed by powder X-ray and neutron diffractions. The material crystallizes in orthorhombic space group Pna2₁ (no. 33) with a=10.32581(7) Å, b=4.63728(3) Å, c=8.56606(5) Å, and Z=4. The noncentrosymmetric layered structure is composed of distorted VO₆ octahedra and PO₄ tetrahedra. The V⁵⁺ cations distort either along the approximate [1 0 1] or [-1 0 1] directions attributable to the alignment of distorted VO₆ octahedra, resulting in a polar structure. Powder second-harmonic generating (SHG) measurements on Li₂VPO₆ using 1064 nm radiation, indicate the material has a SHG efficiency of approximately 10 times that of α-SiO₂ and is not phase-matchable (type 1). Converse piezoelectric measurements for the material reveal a piezoelectric coefficient, d₃₃, of 12 pm V⁻¹. - Graphical abstract: A net moment arising from the alignment of the distorted VO₆ octahedra is responsible for the SHG and piezoelectricity for the noncentrosymmetric vanadium phosphate, Li₂VPO₆. Highlights: • Large scale synthesis of a NCS vanadium phosphate, Li₂VPO₆ is reported. • Li₂VPO₆ exhibits a SHG efficiency of 10× that of α-SiO₂. • Li₂VPO₆ reveals a piezoelectric coefficient, d₃₃, of 12 pm V⁻¹. • A net moment is arising from the alignment of the VO₆ octahedra in Li₂VPO₆.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Structural characterization of particle systems using spherical harmonics

Many important properties of particulate materials are heavily influenced by the size and shape of the constituent particles. Thus, in order to control and improve product quality, it is important to develop a good understanding of the shape and size of the particles that make up a given particulate material. In this paper, we show how the spherical harmonics expansion can be used to approximate particles obtained from tomographic 3D images. This yields an analytic representation of the particles which can be used to calculate structural characteristics. We present an estimation method for the optimal length of expansion depending on individual particle shapes, based on statistical hypothesis testing. A suitable choice of this parameter leads to a smooth approximation that preserves the main shape features of the original particle. To show the wide applicability of this procedure, we use it to approximate particles obtained from two different tomographic 3D datasets of particulate materials. The first one describes an anode material from lithium-ion cells that consists of sphere-like particles with different sizes. The second dataset describes a powder of highly non-spherical titanium dioxide particles. - Highlights: • Complex particle shapes are described analytically by spherical harmonics expansion. • The optimal length of the expansion is estimated for each particle individually. • Characteristics like, e.g., particle surface areas can be calculated efficiently. • The method is applied to two tomographic datasets of particulate materials.

36 MATERIALS SCIENCE↗
DOE OSTI2012

Harmonic decomposition of two particle angular correlations in Pb Pb collisions at s_NN = 2.76 TeV

Angular correlations between unidentified charged trigger (t) and associated (a) particles are measured by the ALICE experiment in Pb-Pb collisions at {radical}s{sub NN} = 2.76 TeV for transverse momenta 0.25 < p{sub T}{sup t,a} < 15 GeV/c, where p{sub T}{sup t} > p{sub T}{sup a}. The shapes of the pair correlation distributions are studied in a variety of collision centrality classes between 0 and 50% of the total hadronic cross section for particles in the pseudorapidity interval |{eta}| < 1.0. Distributions in relative azimuth {Delta}{phi}{triple_bond}{phi}t-{phi}a are analyzed for |{Delta}{eta}|{triple_bond}|{eta}t-{eta}a| > 0.8, and are referred to as 'long-range correlations'. Fourier components Vn{Delta} {triple_bond} <cos(n{Delta}{phi})> are extracted from the long-range azimuthal correlation functions. If particle pairs are correlated to one another through their individual correlation to a common symmetry plane, then the pair anisotropy V{sub n{Delta}}(p{sub T}{sup t},p{sub T}{sup a}) is fully described in terms of single-particle anisotropies vn(pT) as V{sub n{Delta}}(p{sub T}{sup t},p{sub T}{sup a}) = v{sub n}(p{sub T}{sup t})v{sub n}(p{sub T}{sup a}). This expectation is tested for 1 {le} n {le} 5 by applying a global fit of all V{sub n{Delta}}(p{sub T}{sup t},p{sub T}{sup a}) to obtain the best values vn{l_brace}GF{r_brace}(p{sub T}). It is found that for 2 {le} n {le} 5, the fit agrees well with data up to p{sub T}{sup a} {approx} 3-4 GeV/c, with a trend of increasing deviation as p{sub T}{sup t} and p{sub T}{sup a} are increased or as collisions become more peripheral. This suggests that no pair correlation harmonic can be described over the full 0.25 < pT < 15 GeV/c range using a single vn(pT) curve; such a description is however approximately possible for 2 {le} n {le} 5 when p{sub T}{sup a} < 4 GeV/c. For the n = 1 harmonic, however, a single v{sub 1}(pT) curve is not obtained even within the reduced range p{sub T}{sup a} < 4 GeV/c.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Chirality-Dependent Second Harmonic Generation of MoS 2 Nanoscroll with Enhanced Efficiency

Materials with high second harmonic generation (SHG) efficiency and reduced dimensions are favorable for integrated photonics and nonlinear optical applications. Here, we fabricate MoS 2 nanoscrolls with different chiralities and study their SHG performances. As a 1D material, MoS 2 nanoscroll shows reduced symmetry and strong chirality dependency in the polarization-resolved SHG characterizations. This SHG performance can be well explained by the superposition theory of second harmonic field of the nanoscroll walls. MoS 2 nanoscrolls with certain chiralities and diameters in our experiment can have SHG intensity up to 95 times stronger than that of monolayer MoS 2 , and the full potential can still be further exploited. The same chirality-dependent SHG can be expected for nanoscrolls or nanotubes composed of other noncentrosymmetric 2D materials, such as WS 2 , WSe 2 , and hBN. Here, the characterization and analysis results presented here can also be exploited as a nondestructive technique to determine the chiralities of these nanoscrolls and nanotubes.

42 ENGINEERING↗
DOE OSTI2018

Enhanced Second-Harmonic Generation Using Broken Symmetry III–V Semiconductor Fano Metasurfaces

All-dielectric metasurfaces, two-dimensional arrays of subwavelength low loss dielectric inclusions, can be used not only to control the amplitude and phase of optical beams, but also to generate new wavelengths through enhanced nonlinear optical processes that are free from some of the constraints dictated by the use of bulk materials. Recently, high quality factor (Q) resonances in these metasurfaces have been revealed and utilized for applications such as sensing and lasing. The origin of these resonances stems from the interference of two nanoresonator modes with vastly different Q. Here we show that nonlinear optical processes can be further enhanced by utilizing these high-Q resonances in broken symmetry all-dielectric metasurfaces. As a result, we study second harmonic generation from broken symmetry metasurfaces made from III–V semiconductors and observe nontrivial spectral shaping of second-harmonic and multifold efficiency enhancement induced by high field localization and enhancement inside the nanoresonators.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2022

Heteroanionic Control of Exemplary Second-Harmonic Generation and Phase Matchability in 1D LiAsS 2– x Se x

The isostructural heteroanionic compounds β-LiAsS 2–x Se x (x = 0, 0.25, 1, 1.75, 2) show a positive correlation between selenium content and second-harmonic response and greatly outperform the industry standard AgGaSe 2 . These materials crystallize in the noncentrosymmetric space group Cc as one-dimensional $\frac{1}{∞}$ [AsQ 2 ] - (Q = S, Se, S/Se) chains consisting of corner-sharing AsQ3 trigonal pyramids with charge-balancing Li + atoms interspersed between the chains. LiAsS 2–x Se x melts congruently for 0 ≤ x ≤ 1.75, but when the Se content exceeds x = 1.75, crystallization is complicated by a phase transition. This behavior is attributed to the β- to α-phase transition present in LiAsSe 2 , which is observed in the Se-rich compositions. The band gap decreases with increasing Se content, starting at 1.63 eV (LiAsS 2 ) and reaching 1.06 eV (β-LiAsSe 2 ). Second-harmonic generation measurements as a function of wavelength on powder samples of β-LiAsS 2–x Se x show that these materials exhibit significantly higher nonlinearity than AgGaSe 2 (d 36 = 33 pm/V), reaching a maximum of 61.2 pm/V for LiAsS 2 . In comparison, single-crystal measurements for LiAsSSe yielded a d eff = 410 pm/V. LiAsSSe, LiAsS 0.25 Se 1.75 , and β-LiAsSe 2 show phase-matching behavior for incident wavelengths exceeding 3 μm. The laser-induced damage thresholds from two-photon absorption processes are on the same order of magnitude as AgGaSe 2 , with S-rich materials slightly outperforming AgGaSe 2 and Se-rich materials slightly underperforming AgGaSe 2 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗