Soliton generation via continuous stokes acoustic self-scattering of hypersonic waves in a paramagnetic crystal

A new mechanism is proposed for continuous frequency down-conversion of acoustic waves propagating in a paramagnetic crystal at a low temperature in an applied magnetic field. A transverse hypersonic pulse generating a carrier-free longitudinal strain pulse via nonlinear effects is scattered by the generated pulse. This leads to a Stokes shift in the transverse hypersonic wave proportional to its intensity, and both pulses continue to propagate in the form of a mode-locked soliton. As the transverse-pulse frequency is Stokes shifted, its spectrum becomes narrower. This process can be effectively implemented only if the linear group velocity of the transverse hypersonic pulse equals the phase velocity of the longitudinal strain wave. These velocities are renormalized by spin-phonon coupling and can be made equal by adjusting the magnitude of the applied magnetic field. The transverse structure of the soliton depends on the sign of the group velocity dispersion of the transverse component. When the dispersion is positive, planar solitons can develop whose transverse component has a topological defect of dark vortex type and longitudinal component has a hole. In the opposite case, the formation of two-component acoustic “bullets” or vortices localized in all directions is possible.     

On the propagation of hypersonic solitons in a strained paramagnetic crystal

Nonlinear dynamics of a subnanosecond transverse elastic pulse in a low-temperature paramagnetic crystal placed into a magnetic field and statically strained in the same direction is investigated. Paramagnetic impurities implanted into the crystal have an effective spin of 3/2, and the pulse propagates at right angles to the magnetic field. In the general case, the structure of the pulse is such that the approximation of slowly varying envelopes, which is standard for quasi-monochromatic signals, is inapplicable. Under certain conditions, the pulse propagation in the 1D case is described by the Konno-Kameyama-Sanuki integrable wave equation for strain, which is transformed into the Hirota equation for the envelope of the given strain in the quasi-monochromatic limit. The effect of transverse perturbations on extremely short and quasi-monochromatic solitons is studied in detail. The conditions and features of self-focusing and defocusing of acoustic solitons in the form of extremely short pulses and envelope solitons are revealed. The propagation of an extremely short “half-wave” hypersonic pulse in the “acoustic bullet” regime in the medium with a quasiequilibrium population of quantum sublevels of effective spins is predicted.     

Soliton mechanism of acoustic pulse frequency conversion to the red region

Self-scattering of a transverse acoustic pulse from a longitudinal strain video pulse (induced by an acoustic pulse) in a paramagnetic crystal in a magnetic field is predicted. This effect is accompanied by a continuous frequency shift of the hypersonic pulse to the red region; this shift is proportional to the pulse intensity.     

Self-induced acoustic transparency in the long-short-wave resonance mode

The effect of self-induced acoustic transparency for transverse-longitudinal pulses propagating along an external magnetic field in a system of resonance paramagnetic impurities with the effective spin S=1/2 is theoretically investigated. In this case, the short-wave transverse component of the pulse causes quantum transitions, and the longitudinal long-wave component dynamically shifts the frequency of those transitions. When the speeds of the longitudinal and transverse acoustic waves in the crystal matrix are close to each other, both components interact in the mode of the long-short-wave resonance, which is described by a system of nonlinear integro-differential equations. It is shown that this interaction results, in particular, in the modulation of the carrier frequency of the circular-polarized component of the pulse. More precisely, the frequency in the neighborhood of the signal’s maximum is less than in the vicinity of its edges. Solutions in the form of traveling 2π-pulses are analyzed analytically and numerically. It is shown that there exist solutions that include a longitudinal component and cannot be reduced to well-known transverse solitons of the sinus-Gordon equation.     

The influence of transverse perturbations on the propagation of picosecond acoustic pulses in a paramagnetic crystal

The influence of transverse perturbations on the dynamics of a picosecond soliton-like acoustic pulse in a paramagnetic crystal in an external magnetic field is investigated. The nonlinear and dispersion effects are governed by the intrinsic properties of the crystal and the spin-phonon interaction. The effect of different nonlinear mechanisms and an external magnetic field on the stability against transverse perturbations is analyzed. It is shown that, in the absence of paramagnetic impurities, there can exist only a compression pulse that propagates in a defocusing regime. In the presence of paramagnetic ions in the crystal, there can arise rarefaction pulses that, under specific conditions, can propagate in self-focusing and self-channeling regimes.     

Influence of relaxations on acoustic solitons

The influence of the transverse and longitudinal magnetic relaxations on the propagation of an acoustic resonance soliton is considered. The dynamics of the changes of the width and frequency shift of acoustic pulse in both the Markovian and the non-Markovian cases are compared. It is shown that memory effects do cause a qualitatively change in the nature of the effects of transverse magnetic relaxations on an acoustic soliton, in comparison to that of the Markovian case. The pulse width in both the Markovian and the non-Markovian cases for experimentally realized parameters are presented.     

Enhanced electron trapping by a static longitudinal magnetic field in laser wakefield acceleration

An externally applied longitudinal magnetic field was found to enhance the particle trapping in the laser wakefield acceleration. When a static magnetic field of a few tens of tesla is applied in parallel with the propagation direction of a driving laser pulse, it is shown from two-dimensional particle-in-cell simulations that total charge of the trapped beam and its maximum energy increase. The analysis of electron trajectories strongly suggests that the enhanced trapping originates from the suppression of the transverse motion by the magnetic field. The enhanced trapping by the magnetic field was observed consistently for various values of the plasma density, the amplitude of the laser pulse and pulse spot size.     

Integrable models for the dynamics of a longitudinal-transverse acoustic wave in a crystal with paramagnetic impurities

We theoretically study the evolution of longitudinal-transverse acoustic pulses propagating parallel to an external magnetic field in a system of resonant paramagnetic impurities with an effective spin S=1/2. For equal group velocities of the longitudinal and transverse waves, the pulse dynamics is shown to be described by evolution equations. In limiting cases, these equations reduce to equations integrable in terms of the inverse scattering transform method (ISTM). For the most general integrable system of equations that describes the dynamics of acoustic pulses outside the scope of the slow-envelope approximation, we derive the corresponding ISTM equations. These equations are used to find a soliton solution and a self-similar solution. The latter describes the leading edge of the packet of acoustic pulses generated when the initial unstable state of a spin system decays. Analysis of our solutions and models indicates that the presence of a longitudinal acoustic wave leads not only to a change in the amplitude and phase of the transverse wave but also to a qualitatively new dynamics of sound in such a medium.     

Spatiotemporal Evolution of Intense Short Gaussian Laser Pulses in Weakly Relativistic Magnetized Plasma

The weakly relativistic regime of propagation of a short and intense laser pulse in the magnetized plasma is investigated. By considering relativistic nonlinearity and using non‐linear Schrödinger equation with paraxial approximation, two second‐order coupled differential equations are obtained for the longitudinal pulse width parameter (in time) and for the transverse pulse width parameter (in space). The simultaneous evolution of spot size and length of a relativistic Gaussian laser pulse in a magnetized plasma can be calculated by the numerical solution of the equations. The effect of magnetic field is investigated. It is observed that in the presence of magnetic field both the self‐compression and the self‐focusing can be enhanced. Furthermore, the interplay between the longitudinal self‐compression and the transverse self‐focusing in a magnetized plasma is investigated. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Acoustic activity effect for picosecond soliton-like pulses

A theoretical analysis is made of the acoustic activity for interfering picosecond acoustic soliton-like pulses of down to a single oscillation period. An analysis is made of the case where these pulses propagate parallel to an external magnetic field and one of the acoustic axes in a cubic crystal containing paramagnetic impurities having effective spin S = 1. Allowance is made for natural, magnetic (Faraday), and cross acoustic activity. This cross activity is caused by the significant spatial nonlocality of the spin-phonon interaction for such short pulses in crystals having no center of inversion in the presence of paramagnetic impurities. A system of nonlinear equations is obtained for the transverse and longitudinal components of the strain in the form of a coupling between the “differentiated” nonlinear Schrödinger equation (with nonlinearity after the derivative sign) and the Korteweg-de Vries equation which generalizes the known systems of long-short-wavelength resonance to the case where the slowly varying envelope approximation is not valid. An approximate solution of this system is used to study the structure of an elastic soliton-like pulse whose transverse component has a rotating plane of polarization, which propagates under conditions of nonlinear coupling with the longitudinal strain.     

The evolution of longitudinal and transverse acoustic waves in a medium with paramagnetic impurities

We study the bipartial interaction of longitudinal and transverse acoustic pulses with a system of paramagnetic impurities with an effective spin S=1/2 in a crystalline layer or on a surface in the presence of an arbitrarily directed external constant magnetic field. We derive a new system of evolution equations that describes this interaction and show that, in the absence of losses, for equal phase velocities of these acoustic components, and under the condition of their unidirectional propagation, the original system reduces to a new integrable system of equations. The derived integrable system describes the pulse dynamics outside the scope of the slow-envelope approximation. For one of the reductions of the general model that corresponds to the new integrable model, we give the corresponding equations of the inverse scattering transform method and find soliton solutions. We investigate the dynamics and formation conditions of the phonon avalanche that arises when the initial completely or incompletely inverted state of the spin system decays. We discuss the application of our results to describing the interaction dynamics of spins and acoustic pulses in various systems with an external magnetic field.     

Transverse relaxation rate enhancement caused by magnetic particulates

Magnetic particulates have been shown to be powerful transverse relaxation enhancers and are under consideration as an MR contrast agent for the detection of liver and spleen lesions. This work describes the magnetic properties of a commercially available magnetic particulate and a Monte Carlo simulation of the effect of these particles on the transverse relaxation rates of water protons for spin-echo experiments. From the simultations, empirical relations were developed to describe the dependence of the enhancement of particle size, and concentration as well as the diffusion constant of water and the pulse spacing of a Carr-Purcell-Meiboom-Gill pulse sequence used to measure the transverse relaxation time. The simulations are shown to agree with measurements of relaxation rates in agar samples containing the magnetic particulates.     

Parametric excitation of hybrid mode in magnetised piezoelectric semiconductors

Using the hydrodynamic model of homogeneous plasma, the parametric decay of a laser beam into an acoustic wave and another electromagnetic wave has been studied in heavily dopedn-type piezoelectric semiconductors in the presence of a transverse magnetostatic field. This decay process results in the parametric excitation of the hybrid mode. The threshold electric field necessary for the onset of instability equals to zero. The magnetostatic field couples the acoustic and the electromagnetic waves and in its absence the instability disappears. The growth rate increases with the square of the magnetic field.     

Auxiliary phase encoding in multi spin-echo sequences: application to rapid current density imaging

Multi spin-echo sequences such as single-shot RARE are very sensitive to the initial phase of the transverse magnetization, and they can preserve only the transverse magnetization component which is aligned with the axis of the refocusing pulse rotation. Therefore, two separate single-shot RARE experiments with phases of refocusing pulses 90 degrees apart have to be run and their complex images summed to obtain an error-free phase map of the initial transverse magnetization. This is particularly useful when auxiliary phase encoding is integrated in the preparation period of the RARE sequence, such as when encoding flow, displacement, susceptibility, pH or temperature. In this paper, the two-shot RARE approach is verified first theoretically and then experimentally by demonstrating its application to rapid current density imaging (CDI). The sequence consists of the preparation period which triggers electric pulses in the sample followed by the RARE acquisition period. Electric currents through the sample induce a magnetic field change in the direction of the static magnetic field and a phase change of the initial magnetization proportional to it. To calculate one component of current density two orthogonal components of magnetic field change must be measured. In general, for 2D non-symmetrical samples, this can be done by rotating the sample to a perpendicular orientation. The proposed CDI method allows much for faster magnetic field change mapping than the standard spin-echo based CDI.     

Simulation of a bubble chain in a container of high aspect ratio exposed to a magnetic field

The influence of a homogeneous magnetic field acting in the direction of gravity on a bubble chain is studied with phase-resolving numerical simulations. The bubbles rise in a narrow container filled with liquid metal. Individual bubbles are represented by an immersed boundary method with the bubble shape being described by spherical harmonics and deformed by the surrounding liquid metal. A Gaussian bubble size distribution is realized as suggested by corresponding experiments. Bubble-bubble and bubble-wall interactions are modelled based on a repelling potential. With a magnetic field, the averaged trajectory of the bubble chain becomes more rectilinear, and the transverse dispersion is reduced. The average rise velocity decreases under the impact of the field.     

Picosecond acoustic solitons anisotropically coupled to a spin system

An integrable model developed by the author is used to analyze the evolution of longitudinal-transverse acoustic pulses propagating parallel to an external magnetic field in a paramagnetic crystal with spin-1/2 impurities. Acoustic pulse propagation in a medium with orthorhombic spin-phonon coupling symmetry is described without invoking the slowly varying envelope approximation. A solution to the model is found by a modified inverse scattering method based on an analysis of the Riemann-Hilbert problem taking into account the problem symmetry.     

Generalized Susceptibilities for a Wall-Stabilized Electric Are Displacement

Complex susceptibilities for are displacement produced by an intermittent HF irradiation or by a time-dependent transverse magnetic field, are defined. The analytical character of these susceptibilities is established from the development of its Kramers-Kronig relations. Some experimental results for an are in a transverse magnetic field are shown.     

Propagation of vector solitons in a quasi-resonant medium with stark deformation of quantum states

The nonlinear dynamics of a vector two-component optical pulse propagating in quasi-resonance conditions in a medium of nonsymmetric quantum objects is investigated for Stark splitting of quantum energy levels by an external electric field. We consider the case when the ordinary component of the optical pulse induces ?? transitions, while the extraordinary component induces the ?? transition and shifts the frequencies of the allowed transitions due to the dynamic Stark effect. It is found that under Zakharov-Benney resonance conditions, the propagation of the optical pulse is accompanied by generation of an electromagnetic pulse in the terahertz band and is described by the vector generalization of the nonlinear Yajima-Oikawa system. It is shown that this system (as well as its formal generalization with an arbitrary number of optical components) is integrable by the inverse scattering transformation method. The corresponding Darboux transformations are found for obtaining multisoliton solutions. The influence of transverse effects on the propagation of vector solitons is investigated. The conditions under which transverse dynamics leads to self-focusing (defocusing) of solitons are determined.     

Excitation of narrow frequency bands with reduced relaxation-related signal losses: methodology and preliminary applications

Selective excitation of a narrow frequency band is usually obtained by a long-duration, symmetrical-shaped RF pulse or by a series of short pulses with a symmetrical envelope. In species with fast transverse relaxation, both approaches lead to marked signal losses. Asymmetrical excitations applying truncated shaped pulses or half-Gaussian envelopes for trains of equidistant hard pulses were reported to provide higher signal intensity, but the frequency response is clearly inferior to the corresponding symmetrical excitations. Methods allowing asymmetrical excitation, but excellent frequency response are described in the present work. An additional 90 degree pulse is applied after a train of equidistant hard pulses with a half-Gaussian envelope. Suitable timing in the entire sequence of pulses and a phase cycle with length 2 only for the additional 90 degree pulse combined with an even number of scans allow the removal of undesired transverse magnetization outside narrow frequency bands. Thus, a periodical excitation with a very small bandwidth is obtained. In imaging sequences with standard 2D Fourier reconstruction the new excitation strategies can be included to generate a normal image representing morphology beside a band pattern with chemical information, if an odd number of scans is used. The separation of both parts in the final image is based on the principle of alternated line scanning. Macroscopic and microscopic field inhomogeneities in tissue are assessable in a single experiment. Preliminary applications on specimens with limited homogeneity of the magnetic field and on human tissue are demonstrated.     

Faraday and Cotton-Mouton effects for acoustic phonons in paramagnetic Rare Earth compounds

A theory is developed for the Faraday effect and Cotton-Mouton effect of acoustic phonons in paramagnetic Rare Earth systems. The effects occur if degenerate transverse acoustic phonons are propagating in the direction of an applied magnetic field and perpendicular to it. The theory is formulated for cubic crystals but a generalization to other crystal symmetries is straightforward. The theoretical findings are applied to TmTe and it is demonstrated that both effects are large enough to be observable.