Third-order Harmonics Research Articles

Nonlinear alternating current responses of dipolar fluids.

The frequency-dependent nonlinear dielectric increment of dipolar fluids in nonpolar fluids is often measured by using a stationary relaxation method in which two electric fields are used: The static direct current (dc) field of high strength causing the dielectric nonlinearity, and the probing alternating current (ac) field of low strength and high frequency. When a nonlinear composite is subjected to a sinusoidal electric field, the electric response in the composite will, in general, consist of ac fields at frequencies of higher-order harmonics. Based on the Fröhlich model, we present a theory to investigate the nonlinear ac responses of dipolar fluids containing both polarizable monomers and dimers. In the case of monomers only, our theory reproduces the known results. We obtain the fundamental, second-, and third-order harmonics of the Fröhlich field by performing a perturbation expansion. The even-order harmonics are induced by the coupling between the ac and dc fields, although the system under consideration has a cubic nonlinearity only. The harmonics of the Fröhlich field can be affected by the field frequency, temperature, dispersion strength, and the characteristic frequency of the dipolar fluid, as well as the dielectric constant of the nonpolar fluid. The results are found to be in agreement with recent experimental observations.

Magnetic structure in the zero-applied-field reentrant superconductorErNi1.96Fe0.04B2C0.99

${\mathrm{ErNi}}_{1.96}{\mathrm{Fe}}_{0.04}{\mathrm{B}}_{2}{\mathrm{C}}_{0.99}$ is superconducting at ${T}_{c}=7.3K$ and is shown to partially reenter the normal state between 5.5 and 5.7 K in zero applied field by means of ac-susceptibility $({\ensuremath{\chi}}_{\mathrm{ac}}^{\ensuremath{'}})$ and resistivity measurements. Specific heat ${(C}_{p})$ measurements give a magnetic ordering temperature ${T}_{\mathrm{N}}=5.7\ifmmode\pm\else\textpm\fi{}0.2K.$ Powder neutron diffraction measurements showed that the ${\mathrm{Er}}^{3+}$ magnetic moments adopt below ${T}_{\mathrm{N}}=5.9\ifmmode\pm\else\textpm\fi{}0.2K$ a transverse modulated structure along the $a$ axis $(\mathbf{q}=0.559{\mathbf{a}}^{*}).$ Observation of third-order and fifth-order harmonics indicates a squaring of the structure at lower temperature $(8.2{\ensuremath{\mu}}_{\mathrm{B}}$ at 1.4 K). Although even-order peaks could not be detected in the neutron data, a weak ferromagnetic transition at ${T}_{\mathrm{WFM}}=2.2K$ could be directly evidenced by magnetic susceptibility measurements and ${C}_{p}$ measurements and indirectly evidenced in the thermal variations of the intensity of the first-order magnetic peaks ${(I}_{\mathbf{q}}),$ the magnetic coherence length $({\ensuremath{\xi}}_{m}),$ and the magnetic wave vector (q). The magnetic structure of ${\mathrm{ErNi}}_{1.96}{\mathrm{Fe}}_{0.04}{\mathrm{B}}_{2}{C}_{0.99}$ is nearly identical to that of the parent compound ${\mathrm{ErNi}}_{2}{\mathrm{B}}_{2}\mathrm{C}.$ Precise comparison between the temperature variations of ${I}_{\mathbf{q}},$ ${\ensuremath{\xi}}_{m},$ and ${\ensuremath{\chi}}_{\mathrm{ac}}^{\ensuremath{'}}$ shows that the transverse ${\mathbf{a}}^{*}$-modulated magnetic structure is responsible for the reentrant behavior between 5.5 and 5.7 K. Although it is still pair breaking below 5.5 K, it coexists with superconductivity. ${}^{57}\mathrm{Fe}$ M\ossbauer spectra display no broadening in the temperature range where the reentrant behavior is observed, showing that the transferred hyperfine field at the Fe site, if any, is smaller than 2 kOe.

High-gradient acceleration in a neutrino factory with FFAG rings

High-gradient acceleration is indispensable for muon handling. We need an accelerating field gradient of the order of MV/m in order to accelerate muons up to 30 GeV/c . Because the bunch length of the primary proton beam is 6 ns rms at the top energy of the 50 GeV ring, muons (these are tertiary products from the protons) are also supposed to have the same time structure. An RF cavity of a resonant frequency of about 30 MHz with third-order harmonics can generate a flat-top accelerating field of over 10 ns duration. The size of such a cavity will be as large as 5 m high and 5 m wide.

An L-band geophysical model function for SAR wind retrieval using JERS-1 SAR

An L-band geophysical model function is developed using Japanese Earth Resources Satellite-1 (JERS-1) synthetic aperture radar (SAR) data. First, we estimate the SAR system noise, which has been a serious problem peculiar to the JERS-1 SAR. It is found that the system noise has a feature common in all the SAR images and that the azimuth-averaged profile of noise can be expressed as a parabolic function of range. By subtracting the estimated noise from the SAR images, we can extract the relatively calibrated ocean signals. Second, using the noise-removed SAR data and wind vector data from the NASA Scatterometer and buoys operated by the Japan Meteorological Agency, we generate a match-up dataset, which consists of the SAR sigma-0, the incidence angle, the surface wind speed, and wind direction. Third, we investigate the sigma-0 dependence on incidence angle, wind speed, and wind direction. While the incidence angle dependence is negligible in the present results, we can derive distinct sigma-0 dependence on wind speed and direction. For wind speeds below 8 m/s, the wind direction dependence is not significant. However, for higher wind speeds, the upwind-downwind asymmetry becomes very large. Finally, taking into account these characteristics, a new L-band-HH geophysical model function is produced for the SAR wind retrieval using a third-order harmonics formula. Resultant estimates of SAR-derived wind speed have an rms error of 2.09 m/s with a negligible bias against the truth wind speed. This result enables us to convert JERS-1 SAR images into the reliable wind-speed maps.

Theoretical calculation and experimental study on the third-order nonlinearity parameter C/A for organic liquids and biological fluids.

In the present paper we deal with calculating and measuring the third-order nonlinearity parameter C/A for organic liquids and biological fluids. For the organic liquids, the second-order derivative of sound speed with respect to pressure at constant entropy is discussed in terms of thermodynamic parameters, and a formula for calculating C/A is established. Calculated results of C/A for various organic liquids demonstrate that omitting the second-order derivative of sound speed with respect to sound pressure in an isentropic process, could overestimate the value of C/A about 20%-30%. For measuring C/A, the finite-amplitude insert substitution technique is employed. A theoretical description of the sound pressure amplitude for the third-order harmonics is obtained using the perturbation method, in which the sound pressure amplitude of the third-order harmonics is shown approximately as a parabolic function of the propagation distance in the medium. By measuring and comparing the sound pressure amplitudes of the third-order harmonics when inserting a test sample, the reference liquid, and a comparative liquid, respectively, the value of C/A for the sample liquid is determined with reference to known C/A values of reference and comparative liquids. An experimental setup is developed, and the measured values of C/A for the organic liquids agree with the predicted ones calculated by the thermodynamic methods. Furthermore, the finite-amplitude method is extended to measure the C/A parameter for biological fluids, and the measured values of C/A for several biological fluids are also presented.

Third-order harmonic generation by self-guided femtosecond pulses in air.

Strong third-order harmonic (TH) emission is observed with a conversion efficiency higher than 10(-3) from a plasma channel formed by self-guided femtosecond laser pulses propagating in air. The main characteristics of TH emission in various conditions and the phase-matching condition between the fundamental and the TH wave are investigated. An optimized condition is found, under which the TH conversion efficiency is maximized. Our experimental results show that radiation of the emission in ultraviolet wavelength range makes a major attribution to TH emission, whereas the effects of self-phase modulation are not important when intense laser pulses interact with gaseous media.

ＫＣｌ基板上に作製されたバナジルフタロシアニン薄膜の熱処理による成長機構と分子配向及び非線形光学特性の評価

Vanadyl-Phthalocyanine (VOPc) thin films are prepared by a molecular beam epitaxy on KCl substrate. The nonlinear optical properties, VOPc molecular orientation and growing mechanism on KCl substrate of VOPc thin film are investigated with UV/VIS spectra, the images observed by SEM and AFM and the second-order harmonic (SH) and third-order harmonic (TH) intensities measured by Maker-fringe. The VOPc thin film treated with a thermal treatment changes from pseudo-epitaxy to epitaxy. Moreover, the surface of the thin film is a plate-like-crystal and smooth. These suggest that the VOPc molecules on KCl substrate are parallel to KCl substrate. The SH and TH intensities of VOPc thin films are increased with thermal treatment. It is closely related to the phase-morpholpgy of VOPc thin film. Therefore, the VOPc thin film epitaxially grown improves the SH and TH intensities.

Third-Order Harmonic Generation in Atmospheric Air withFocused Intense Femtosecond Laser Pulses

Generation of third-order harmonics at 800 nm of femtosecond laser pulses isstudied in neutral atmospheric air and in plasma of optical breakdown in air. Itsefficiency is measured at different fundamental laser intensities. A maximumefficiency is observed at the intensity when optical breakdown in atmospheric airstarts. The factors that exhibit the main effects on the harmonic generation, includingself-focusing in a neutral air and self-focusing in plasma, are discussed. PACS: 42. 65. Jx, 42. 65. Ky

Harmonic distortion in 1.55-μm vertical-cavity lasers

We investigate second and third order harmonics in the analog modulation response of InP-GaAs fused 1.55-μm vertical-cavity lasers (VCLs). These devices exhibit the lowest threshold current as well as the highest temperature of continuous-wave operation of any electrically pumped long wavelength VCL. Near the resonance frequency, harmonic distortion is dominated by electron-photon interaction, and it is close to the distortion measured with in-plane lasers. At low frequencies, distortions seem to be dominated by carrier transport effects. At 1 GHz modulation frequency, we measure a maximum spur-free dynamic range of 64 dB Hz <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> 2/ for second-order harmonic distortion and 81-dB Hz <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> 3/ for third-order harmonic distortion.

Magnetic structure ofHoBe13in an applied magnetic field

The magnetic structure of ${\mathrm{HoBe}}_{13}$ and its evolution under an applied magnetic field have been examined using neutron diffraction and bulk magnetization measurements on a single crystal. In the absence of an external field this cubic compound orders at ${T}_{N}=5.7(1)\mathrm{K}$ into a regular helical magnetic structure with propagation vector $\mathbf{k}=[00\frac{1}{3}].$ Third-order harmonics appear at 4.4(1) K and are attributed to a deformation of the helical structure below this temperature. When a magnetic field is applied along a [001] axis two magnetic transitions occur. First the magnetic domain with propagation vector parallel to the field is favored and, with the addition of the induced ferromagnetic component, by about 4 kG we have a single-domain conical structure. The surprising observation was that at higher fields (15 kG at 1.4 K) the other two domains reappear and become the preferred ones. This reentrant behavior is due to the change of the magnetic structure to a canted arrangement, involving a ferromagnetic component along the applied field and a transverse collinear antiferromagnetic component. When the magnetic field is applied along a [110] axis only one transition is observed from the helical to the conical structure. The magnetic phase diagram of ${\mathrm{HoBe}}_{13}$ has been constructed.

Seismic response of multi-layered basins with velocity gradients upon incidence of plane shear waves

A boundary integral scheme based on boundary-integral discrete-wave-number approach has been developed to compute the seismic response of two-dimensional irregular-shaped basins with horizontal soil layers. Each layer exhibits a linear gradient of shear wave velocity with depth. The approach combines the boundary-integral representation of the seismic wave field outside the basin with plane wave representation of the seismic wave field inside the basin. The propagation throughout the layers is performed by matrix propagators in which the effect of the vertical variation of the velocity is incorporated by using confluent hyper-geometric functions of the Whittaker type. Our method is tested against other well-accepted solutions for the case of a circular basin with excellent agreement. Test of the ground response for a semi-circular basin with radius a shows that stable solutions are obtained if the chosen model parameters satisfy following conditions: (1) the distance from the sources to the interface is greater than 0.1a; (2) the distance between the sources is smaller than a quarter of the incident wavelength; and (3) the discrete wave-number step is smaller than 2π/4a. The computation of ground response of basins with a sharp interface and several horizontal deposits leads to the following main results: (1) the amplification of a basin with velocity gradients is larger than that of a basin with homogeneous layers; (2) the frequencies of the second- and third-order harmonics for a basin with velocity gradients are lower than those of a basin with homogeneous layers; and (3) the response amplitude of the basin with velocity gradients attenuates more slowly in time domain than when layers are homogeneous. Since these results have been obtained for realistic values of basin geometrical and mechanical consideration, they should find some interest in earthquake engineering or seismic microzonation studies.

Seismic response of multi‐layered basins with velocity gradients upon incidence of plane shear waves

A boundary integral scheme based on boundary-integral discrete-wave-number approach has been developed to compute the seismic response of two-dimensional irregular-shaped basins with horizontal soil layers. Each layer exhibits a linear gradient of shear wave velocity with depth. The approach combines the boundary-integral representation of the seismic wave field outside the basin with plane wave representation of the seismic wave field inside the basin. The propagation throughout the layers is performed by matrix propagators in which the effect of the vertical variation of the velocity is incorporated by using confluent hyper-geometric functions of the Whittaker type. Our method is tested against otherwell-accepted solutions for the case of a circular basin with excellent agreement. Test of the ground response for a semi-circular basin with radius a shows that stable solutions are obtained if the chosen model parameters satisfy following conditions: (1) the distance from the sources to the interface is greater than 0·1a; (2) the distance between the sources is smaller than a quarter of the incident wavelength; and (3) the discrete wave-number step is smaller than 2π/4a. The computation of ground response of basins with a sharp interface and several horizontal deposits leads to the following main results: (1) the amplification of a basin with velocity gradients is larger than that of a basin with homogeneous layers; (2) the frequencies of the second- and third-order harmonics for a basin with velocity gradients are lower than those of a basin with homogeneous layers; and (3) the response amplitude of the basin with velocity gradients attenuates more slowly in time domain than when layers are homogeneous. Since these results have been obtained for realistic values of basin geometrical and mechanical consideration, they should find some interest in earthquake engineering or seismic microzonation studies. © 1998 John Wiley & Sons, Ltd.

Determination of the incommensurately modulated structure of (perylene)Co(mnt)2(CH2Cl2)0.5 by direct methods

For the organic conductor (perylene)Co(mnt)(2)-(CH2Cl2)(0.5), where mnt is maleonitriledithiolate, the incommensurate displacive modulation is determined using X-ray diffraction data for main reflections and first- and second-order satellites, collected at a temperature of 283 K. The lattice parameters of the unit cell of the average structure are: a = 6.5441 (13), b = 11.7173 (15), c = 16.4251 (17) Angstrom, alpha = 92.092 (11), beta = 95.343 (16), gamma = 94.67 (2)degrees, with V = 1248.6(3)Angstrom(3) and Z = 2. The components of the modulation wavevector are given by: q(1) = 0.211 (13), q(2) = -0.1374(5), q(3) = -0.368(2). The symmetry of the modulated structure is given by the (3+1)-dimensional superspace group P ($) over bar 1 (q(1), q(2), q(3)). Direct methods were used to obtain a starting model for the modulation. The subsequent refinement converged to R = 0.126 for 2835 observed (I/sigma > 2.5) reflections. Partial R factors are 0.111 for 1450 main reflections, 0.143 for 1188 first-order satellites and 0.263 for 197 second-order satellites. The modulation is described by sawtooth-shaped functions for the Co and S atoms and by rigid-body modulations, up to third-order harmonics, for the perylene units and parts of the mnt fragments. The largest amplitudes were found for the Co (0.77 Angstrom) and S atoms (0.48-0.63 Angstrom) and were mainly directed along the a axis. The four equatorial Co-S distances are only slightly affected by the modulation, but the two apical Co-S distances show large variations with distances ranging from 2.05 to 3.86 Angstrom. These variations are out of phase. This causes the coordination of the Co atom to vary from a distorted octahedral coordination by six S atoms to a region with fivefold coordination and vice versa. The valence of the Co atom, as calculated by the bond-valence method, varies between 2.92 and 3.57. The stacking of the Co(mnt)(2) units can be described by oligomeric packages of four or five dimerized Co(mnt)(2) units.

Effects of higher-order harmonics on phase determination in an ultrasonic interferometer.

The effect of higher-order harmonic components on phase determination were analyzed to improve the accuracy of transient time measurement in an ultrasonic interferometer with a quadrature detector system. Under ideal conditions the locus of output signals of the phase sensitive detector forms a circle on the phase plane as the frequency changes and any nonideal factor would distort the circle, leading to erratic phase determination. This analysis has shown that the nth-order contribution to the phase is mostly determined by the product of the amplitudes of corresponding components of the reference and echo signals fed to the phase detector. The distortion parameters were obtained by least-squares fitting of the data to the distorted circle in the phase plane, and compared with those roughly estimated from the frequency components of the reference and echo signals. The exemplary numerical phase corrections for the third-order harmonics were carried out, so as to illustrate the improvement in the accuracy of the ultrasonic interferometer.

A model for the effect of stress on the low-frequency harmonic content of the magnetic induction in ferromagnetic materials

A simple model used previously by the authors to explain stress variation of magnetic hysteresis is now employed to explain the effect of stress on the amplitudes of the first- and third-order harmonics of the magnetic induction signal resulting from application of an ac magnetic field of low frequency to a steel specimen. An improved expression for the effective field contribution Hσ due to stress has been derived from thermodynamic considerations.

Magnetic ordering in MnSe2

Abstract Neutron diffraction experiments on polycrystalline samples of MnSe2 performed in the temperature range 1.8 to 54K show a first-order magnetic phase transition at TN=49 K. The existence of the third-order harmonics below TN shows the magnetic structure of MnSe2 to be of commensurate square-wave type given by the wave vectors k= [ 1 301 ] and 3k=[010].

Radiative transfer in three-dimensional rectangular enclosures containing inhomogeneous, anisotropically scattering media

Radiative transfer in a three-dimensional rectangular enclosure containing radiatively participating gases and particles is studied using the first- and third-order spherical harmonics approximations. Inhomogeneities in the radiative properties of the medium, as well as in the radiation characteristics of the boundaries, are allowed for. The scattering phase function is represented by the delta-Eddington approximation, and it is assumed to be a function of the location in order to account for density variation of the particles in the medium. Numerical solutions of the model equations are obtained using a finite difference scheme. For the purpose of validating the P 3-approximation, the results are compared with those based on Hottel's zonal method.

Mascons and the moon's orientation

This letter reports the discovery of a relation between the moments of inertia of the mascons (taken about the moon's center) and the moon's moments of inertia. It is found that the principal axes of the mascons alone are nearly parallel to those of the moon. Possible explanations of this parallelism are discussed. If the mascons are associated with a layer of uncompensated basalt on the moon's nearside, then the parallelism can be adequately explained on the grounds that the mascons and basalts together determined the moon's orientation. On the other hand, the third-order harmonics of the moon's gravity field indicate that the excess mass controlling the moon's orientation is on the farside. It thus appears that the mascons have been emplaced in special sites whose position was controlled by the processes which produced the farside highlands.

Longitude variations of the Earth's gravity field as sensed by the drift of three synchronous satellites

Analysis of the tracking record of three synchronous satellites over a 2-year period has clearly revealed the effects of second- and third-order longitude components in the earth's gravity potential field. These components are shown to be largely responsible for small but well-measured longitude drift accelerations experienced by three nearly geostationary satellites at a fair number of locations around the equator. The acceleration record appears complete enough to define separately and with accuracy the second- and third-order tesseral harmonics of the field under reasonable assumptions as to the effects of neglected harmonics. The results are: J22 = −(1.816 ± 0.020) × 10−6, λ22 = −(15.4 ± 0.3)°, J33 = −(0.171 ± 0.017) × 10−6, λ33 = (24.9 ± 3.3)°, J31 = −(1.4 ± 0.21.0) × 10-6, λ31 = −(168 + 26)°.

The latest achievements of physical geodesy

That the accuracy of computing the undulations in the geoid is not yet as high as is desired is not due to the method itself but to the lack of gravity data. The masses of the great formations are 85 to 90 per cent isostatically compensated. The flattening ratio value, 1/298.3, obtained by the satellite method has also been obtained several times by gravity and arc-measuring methods. At the Institute of Geodesy, Photogrammetry and Cartography we have been conservative; we have used only the gravimetric method and have not extrapolated gravity anomalies more than 15° from the computation point. Uotila obtained by spherical harmonic analysis third-order harmonics similar to those obtained by O'Keefe from satellite data. The undulations associated with the pear-shaped form are of the order of ±15 meters. O'Keefe's geoid heights at the north and south poles are brought about solely by the fact that the flattening value he used (1/299.8) does not correspond to the real facts.