Diffraction of light bv two parallel superposed supersonic waves, one being the second harmonic, the other the third harmonic of the same fundamental. Description of two methods leading to approximate solutions in finite form

The weak first-order Néel transition in Cr was explained by Young and Sokoloff (1974) as being associated with the strain-wave second harmonic of the spin-density wave (SDW). Kotani (1975) developed a theory of higher harmonics of the SDW in Cr and its dilute alloys, which indicates an inverse relation between the amplitude of the strain wave and the value of the incommensurability parameter, δ=1−Q, Q being the SDW wave vector. This effect was observed by Iida et al. (1981), who found that the strain-wave amplitude A2/S1 relative to that of the SDW decreases as V is doped into Cr and δ increases, but remains roughly constant in CrMn alloys as δ decreases and the system approaches commensurability. The ratio S3/S1 of the amplitudes of the third harmonic and the fundamental, on the other hand, increases progressively more rapidly as δ decreases. The present work confirms that the magnitude of the first-order step in S1 at the Néel transition is roughly the same in Cr+0.18 at % Re as in pure Cr (Lebech and Mikke 1972), the values of δ at the transition being 0.32 and 0.35, respectively, whereas in Cr+0.2 at % V having δ=0.42 the Néel transition is continuous.

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A 35 MHz/105 MHz Dual-Element Focused Transducer for Intravascular Ultrasound Tissue Imaging Using the Third Harmonic

10.20944/preprints201806.0234.v1 ◽

2018 ◽

Author(s):

Junsu Lee ◽

Ju-Young Moon ◽

Jin Ho Chang

Keyword(s):

Intravascular Ultrasound ◽

Second Harmonic ◽

Harmonic Imaging ◽

Tissue Imaging ◽

Fractional Bandwidth ◽

Third Harmonic ◽

The Third ◽

Frequency Transducer ◽

Ultrasound Energy ◽

Ivus Imaging

The superharmonic imaging of tissue has the potential for high spatial and contrast resolutions, compared to the fundamental and second harmonic imaging. For this technique, the spectral bandwidth of an ultrasound transducer is divided for transmission of ultrasound and reception of its superharmonics (i.e., higher than the second harmonic). Due to the spectral division for the transmission and reception, transmitted ultrasound energy is not sufficient to induce superharmonics in media without using contrast agents, and it is difficult that a transducer has a -6-dB fractional bandwidth of higher than 100%. For the superharmonic imaging of tissue, thus, multi-frequency array transducers are the best choice if available; transmit and receive elements are separate and have different center frequencies. However, the construction of a multi-frequency transducer for intravascular ultrasound (IVUS) imaging is particularly demanding because of its small size of less than 1 mm. Here, we report a recently developed dual-element focused IVUS transducer for the third harmonic imaging of tissue, which consists of a 35-MHz element for ultrasound transmission and a 105-MHz element for third harmonic reception. For high quality third harmonic imaging, both elements were fabricated to have the same focus at 2.5 mm. The results of tissue mimicking phantom tests demonstrated that the third harmonic images produced by the developed transducer had higher spatial resolution and deeper imaging depth than the fundamental images.

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Effect of plasma channel non-uniformity on resonant third harmonic generation

Laser and Particle Beams ◽

10.1017/s0263034613000311 ◽

2013 ◽

Vol 31 (3) ◽

pp. 531-537 ◽

Cited By ~ 4

Author(s):

Anuraj Panwar ◽

Chang-Mo Ryu ◽

Ashok Kumar

Keyword(s):

Laser Pulse ◽

Harmonic Generation ◽

Plasma Channel ◽

Second Harmonic ◽

Third Harmonic Generation ◽

Laser Frequency ◽

The Self ◽

Third Harmonic ◽

The Third ◽

Self Focusing

AbstractWe study the generation of resonant third harmonic laser radiation in a density non-uniform rippled plasma channel. An introduction of plasma channel non-uniformity strongly enhances the self-focusing and compression of main laser pulse at lower powers. In a deeper plasma channel, self-focusing is less sensitive to laser amplitude variation but increases compression. Plasma density ripple ‘nq’ leading to resonant third harmonic generation when kq = 4ω2p/3meω0cγ0, where ‘ω’p is electron plasma frequency, ‘ω0’ is laser frequency, and ‘γ0’ is the electron Lorentz factor. Third harmonic is produced through the beating of ponderomotive force induced second harmonic density oscillations and the oscillatory velocity of electrons at main laser frequency. The self-focusing and compression of the fundamental pulse periodically enhances the intensity of the third-harmonic pulse at lower powers of main laser. In a deeper plasma channel, the third harmonic power is less effective by self-focusing and the compression of main laser, and increase with main laser pulse power.

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Some aspects of the fluid dynamics of laser welding

Journal of Fluid Mechanics ◽

10.1017/s0022112083000075 ◽

1983 ◽

Vol 126 ◽

pp. 123-146 ◽

Cited By ~ 63

Author(s):

John Dowden ◽

Michael Davis ◽

Phiroze Kapadia

Keyword(s):

Fluid Dynamics ◽

Energy Source ◽

Approximate Solutions ◽

The Other ◽

Liquid Motion ◽

Solid States ◽

The Third ◽

Flow Round ◽

Liquid States ◽

Solid And Liquid States

When a laser beam is used as the energy source for welding two pieces of metal together, a hole is formed perpendicular to the plane of the workpiece. The latter is moved relative to the laser and metal is transferred from the front to the rear by fluid flow round the hole. The equations governing the process are set out and the conditions at the two boundaries in the problem (one between the hole and the molten metal, and the other between the liquid and the solid states of the metal) are considered.Approximate solutions of the problem for low welding speeds are obtained for four different models. The first is one in which the viscosity is taken to be constant. In the second, the viscosity is allowed to depend linearly on temperature. The third model divides the liquid into a region in which the cooler part is taken to be viscous and the hotter part inviscid; the fourth model is then constructed as a limit, with the liquid motion considered as wholly inviscid. It is found that the motion is not irrotational in this last model. The models all display a downstream displacement of the boundary between the solid and liquid states, in agreement with observations. An expression for the minimum power of the laser is calculated.

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The Third Harmonic in Solar Radio Bursts

Symposium - International Astronomical Union ◽

10.1017/s0074180900234360 ◽

1974 ◽

Vol 57 ◽

pp. 289-290

Author(s):

V. V. Zheleznyakov ◽

E. Ya. Zlotnik

Keyword(s):

Second Harmonic ◽

Plasma Waves ◽

Number Density ◽

Solar Radio Bursts ◽

Third Harmonic ◽

The Third ◽

Linear Dimensions ◽

Image Position ◽

Second Harmonic Radiation ◽

Ambient Electron

Generation of third harmonic plasma emission by coalescence of second harmonic radiation with a plasma wave is more favourable than by direct coalescence of three plasma waves. The predicted ratio of the intensities at the third (III) and second (II) harmonics is IIIIω/IIIω ~ ωLWlL/Nmc3, where ωL is the plasma frequency, Wl is the energy density in plasma waves, L the linear dimensions of the source and N the ambient electron number density. The intensity at the second harmonic is where LN(∼1010 cm at ωL ∼ 2π × 108 s−1) is the typical dimension of coronal inhomogeneities.

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Spectral analysis of geomagnetic data from Kandilli Observatory, Istanbul

Annals of Geophysics ◽

10.4401/ag-3833 ◽

1997 ◽

Vol 40 (6) ◽

Author(s):

A. H. Bilge ◽

Y. K. Tulunay

Keyword(s):

Daily Variation ◽

Second Harmonic ◽

Field Variation ◽

Maximal Power ◽

Third Harmonic ◽

The Third ◽

Geomagnetic Data ◽

Deterministic Components ◽

Equal Power ◽

Solar Daily Variation

The geomagnetic field variation spectra for periods longer than 2 h are analysed using the data obtained at the Kandilli Observatory in Istanbul, Turkey. Among the deterministic components, only the harmonics of the solar daily variation (Si) and the second harmonic of the lunar daily variation (L2) were observed. The seasonal dependence of the D component is analysed; the first harmonic of the solar daily variation (S1) has maximum power in summer, decreasing symmetrically towards the winter; the second harmonic (S2) has equal power in spring, summer and fall, while the third harmonic (S3) has maximal power in spring and fall.

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Spatial structure of first and higher harmonic internal waves from a horizontally oscillating sphere

Journal of Fluid Mechanics ◽

10.1017/s0022112010005719 ◽

2011 ◽

Vol 671 ◽

pp. 364-383 ◽

Cited By ~ 9

Author(s):

E. V. ERMANYUK ◽

J.-B. FLÓR ◽

B. VOISIN

Keyword(s):

Spatial Structure ◽

Linear Theory ◽

Second Harmonic ◽

Oscillation Amplitude ◽

Buoyancy Frequency ◽

Harmonic Waves ◽

Third Harmonic ◽

The Third ◽

Higher Harmonic ◽

Oscillating Sphere

An experimental study is presented on the spatial structure of the internal wave field emitted by a horizontally oscillating sphere in a uniformly stratified fluid. The limits of linear theory and the nonlinear features of the waves are considered as functions of oscillation amplitude. Fourier decomposition is applied to separate first harmonic waves at the fundamental frequency and higher harmonic waves at multiples of this frequency. For low oscillation amplitude, of 10% of the sphere radius, only the first harmonic is significant and the agreement between linear theory and experiment is excellent. As the oscillation amplitude increases up to 30% of the radius, the first harmonic becomes slightly smaller than its linear theoretical prediction and the second and third harmonics become detectable. Two distinct cases emerge depending on the ratio Ω between the oscillation frequency and the buoyancy frequency. When Ω > 0.5, the second harmonic is evanescent and localized near the sphere in the plane through its centre perpendicular to the direction of oscillation, while the third harmonic is negligible. When Ω < 0.5, the second harmonic is propagative and appears to have an amplitude that exceeds the amplitude of the first harmonic, while the third harmonic is evanescent and localized near the sphere on either side of the plane through its centre perpendicular to the direction of oscillation. Moreover, the propagative first and second harmonics have radically different horizontal radiation patterns and are of dipole and quadrupole types, respectively.

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Bond Model of Second- and Third-Harmonic Generation in Body- and Face-Centered Crystal Structures

Advances in Materials Science and Engineering ◽

10.1155/2018/7153247 ◽

2018 ◽

Vol 2018 ◽

pp. 1-11 ◽

Cited By ~ 1

Author(s):

Hendradi Hardhienata ◽

Tony Ibnu Sumaryada ◽

Benedikt Pesendorfer ◽

Adalberto Alejo-Molina

Keyword(s):

Harmonic Generation ◽

Spatial Dispersion ◽

Second Harmonic ◽

Third Harmonic Generation ◽

Face Centered Cubic ◽

Third Harmonic ◽

The Third ◽

Bond Model ◽

Face Centered ◽

Cubic Systems

In this work, we describe the third- and fourth-rank tensors of body- and face-centered cubic systems and derive the s- and p-polarized SHG far field using the simplified bond-hyperpolarizability model. We also briefly discuss bulk nonlinear sources in such structures: quadrupole contribution, spatial dispersion, electric-field second-harmonic generation, and third-harmonic generation, deriving the corresponding fourth rank tensor. We show that all the third- and fourth-rank tensorial elements require only one independent fitting parameter.

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