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.     

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.     

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.     

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.     

Nonlinear acoustic transparency for longitudinal-transverse picosecond pulses in a paramagnetic crystal at low temperatures

Nonlinear propagation of longitudinal-transverse acoustic pulses of duration shorter than one oscillation period (video pulses) is studied theoretically in a system of paramagnetic centers with effective spin S=1. It is shown that, depending on the relationship between the magnitudes of the longitudinal and transverse strain components and on the detuning of their linear velocities, various regimes of propagation corresponding to different dynamics of the field and the medium can occur. In the case where the velocities of longitudinal and transverse hypersonic waves differ only slightly, an effect similar to self-induced transparency is analyzed. For substantial velocity detuning, propagation in the form of rational solitons is possible. If the transverse component is dominant, these solitons can produce full population inversion of Zeeman sublevels. In the opposite limit, the populations remain practically unchanged.     

Acoustic self-induced transparency for transverse waves in a system with resonant and quasi-resonant transitions

A theoretical analysis of acoustic self-induced transparency is presented for transverse elastic waves propagating perpendicular to an applied magnetic field through a crystal with spin-3/2 paramagnetic impurities. The interaction between an acoustic pulse and magnetic field is described by Maxwell-Bloch-type equations for a system with transitions inhomogeneously broadened because of a quadrupole Stark shift. If the pulse carrier frequency is resonant with one transition and quasi-resonant with another transition, then the evolution of a one-dimensional pulse is described by an integrable Konno-Kameyama-Sanuki (KKS) equation. The underlying physics of its soliton solution and the corresponding behavior of the medium are analyzed. Self-focusing and self-trapping conditions are found for a pulse of finite transverse size. In the latter regime, the pulse stretches along the propagation direction, transforming into a “hollow bullet,” while its transverse size remains constant.     

Soliton generation via stimulated Brillouin self-scattering under slow light conditions

Acousto-optic soliton generation via stimulated Brillouin self-scattering is predicted for light propagating at the speed of sound under electromagnetically induced transparency conditions. As in stimulated Raman self-scattering, the frequency of the electromagnetic component is gradually Stokes shifted as its intensity increases; the acoustic component has no carrier frequency. This phenomenon is explained by the possibility of forward stimulated Brillouin scattering, which is forbidden in nondispersive media. In contrast to stimulated Raman self-scattering, the Stokes shift of the electromagnetic component approaches a constant limit after the pulse has propagated to a certain distance. It is shown that the predicted soliton generation does not involve any threshold condition and can occur at extremely low input pulse intensities.     

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.     

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.     

Mode Structure and the Envelope of a Short Pulse in a Graded-Index Optical Fiber with a Longitudinal Inhomogeneity and a Spatial Bending

We consider propagation of a short optical pulse in an optical fiber whose refractive index is strongly dependent on the radial coordinate and is weakly dependent on the longitudinal coordinate with allowance for the possible weak spatial bending of the fiber axis. The three-dimensional nonlinear wave equation modelling the pulse propagation is solved asymptotically with respect to a small parameter specifying the order of magnitude of the pulse amplitude. A relationship between the propagating modes and the eigenvalues and eigenfunctions of the singular Sturm-Liouville problem is established. The pulse propagation is shown to have three scales: the high-frequency carrier is modulated by the envelope which evolves in a two-scale manner and is described by a nonlinear Schrödinger equation whose coefficients depend on the longitudinal coordinate. The transverse distribution of the wave field and the envelope soliton are obtained in terms of elementary functions for several types of transverse and longitudinal inhomogeneities of the fiber. The possibility of controlling the pulse parameters by varying the transverse and longitudinal inhomogeneities of the fiber is pointed out.     

Experimental investigation of ultrasonic velocity anisotropy in magnetic fluids: Influence of grain–grain interaction

Magnetic field-induced dispersion of ultrasonic velocity in a Mn_0.7Zn_0.3Fe₂O₄ fluid (applied magnetic field is perpendicular to the ultrasonic propagation vector) is determined by employing continuous wave method. The magnitude of dispersion initially decreases with increasing field, then increases and reaches a plateau at higher fields. Results indicate that the velocity anisotropy is dominated by grain–grain interactions rather than grain–field interaction. At the critical temperature, the grain–grain interaction becomes weak as the transverse component of the particle/cluster moment is larger than the longitudinal one and the system reaches saturation even at low field. These observed variations in the field-induced anisotropy are analysed by incorporating the moment distribution of particles in Tarapov’s theory (J. Magn. Magn. Mater. 39, 51 (1983)).     

Optoacoustic solitons in Bragg gratings

Optical gap solitons, which exist due to a balance of nonlinearity and dispersion due to a Bragg grating, can couple to acoustic waves through electrostriction. This gives rise to a new species of "gap-acoustic" solitons (GASs), for which we find exact analytic solutions. The GAS consists of an optical pulse similar to the optical gap soliton, dressed by an accompanying phonon pulse. Close to the speed of sound, the phonon component is large. In subsonic (supersonic) solitons, the phonon pulse is a positive (negative) density variation. Coupling to the acoustic field damps the solitons' oscillatory instability, and gives rise to a distinct instability for supersonic solitons, which may make the GAS decelerate and change direction, ultimately making the soliton subsonic.     

Optical-acoustic soliton under the conditions of slow light and stimulated Mandelstam-Brillouin scattering

The possibility of forming a stable optical-acoustic soliton in the regime of electromagnetically induced transparency has been analyzed under the condition that the group velocity of light in a medium with stimulated Mandelstam-Brillouin scattering decreases to the speed of sound. This possibility exists because the forward Mandelstam-Brillouin scattering, which is forbidden in a nondispersive medium, is allowed under this condition. The optical component is an envelope pulse, and the acoustic component has no carrier frequency. It has been shown that such a soliton can be formed for anomalously low input intensities of the optical pulse.     

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.     

Experimental study of nonlinear dust acoustic solitary waves in a dusty plasma

The excitation and propagation of finite-amplitude low-frequency solitary waves are investigated in an argon plasma impregnated with kaolin dust particles. A nonlinear longitudinal dust acoustic solitary wave is excited by pulse modulating the discharge voltage with a negative potential. It is found that the velocity of the solitary wave increases and the width decreases with the increase of the modulating voltage, but the product of the solitary wave amplitude and the square of the width remains nearly constant. The experimental findings are compared with analytic soliton solutions of a model Korteveg-de Vries equation.     

Long-range interaction of picosecond solitons through excitation of acoustic waves in optical fibers

We present the theory of electrostrictional interaction of soliton pulses in optical fibers. Solitons excite acoustic waves propagating in the direction transverse to the fiber axis. Scattering of optical radiation on these waves leads to a timing jitter of the optical pulses arrival time. We consider this effect as nonlinear self-scattering of light on acoustic waves. Because of the fact that a value of acoustic lifetime can reach a value of about 100 ns self-scattering on acoustic waves can be observed for a single optical pulse as well as for an optical pulse sequence as a whole. The value of single soliton self-frequency shift due to excitation of acoustic waves as a function of soliton duration have been obtained. For soliton duration _sol > 14 ps an acoustic wave soliton self-frequency shift is larger than the Raman soliton self-frequency shift.The obtained theoretical results describe well the long-range interaction of soliton pulse trains in an optical fiber. The value of bit error rate due to electrostrictional interaction of optical pulses in high bit rate, ultra long soliton communication systems have been obtained.     

Kinetic study of instability growth rate in a helicon plasma discharge source

In this work, a kinetic model is developed to study the effects of the radio frequency antenna wavenumber, helicon plasma electron density, as well as their drift velocity and temperature on the instability increment rate of the helicon wave in both longitudinal and transverse directions. The ion acoustic (IA) wave frequencies and wavenumbers of the helicon waves are obtained when the maximum wave energy is deposited on the plasma ions. Moreover, it is shown that, at the IA wavenumber and frequencies, while the longitudinal instability increment rates for both the helicon and IA waves are ignorable, the transverse instability increment rate for both the helicon and IA wave increases. Besides, the longitudinal instability increment rate for the helicon or IA wave has non‐zero resonant frequencies. On the other hand, the transverse instability increment rate of helicon or IA wave can be neglected. Furthermore, it is observed that, while both the imaginary part of longitudinal permittivity and longitudinal instability increment rate are not influenced by the electron temperature, their transverse component increases linearly with the electron temperature. In addition, the imaginary part of transverse permittivity increases almost linearly with the drift velocity of the plasma electrons.     

用于储罐底板缺陷检测的超声兰姆波模式研究

从超声兰姆波的声场方程出发,得到板材表面离面位移(法向位移)为零的条件,即当超声兰姆波的相速度等于板材介质的纵波声速时,在板材表面的离面位移为零。在给定适当频厚积的条件下,分别数值模拟了仅有切向位移而无离面位移的A1、S1、A2和S2兰姆波模式在有液体负载的单层钢板中的传播情形。结果表明:离面位移为零的S2模式频散较小且对板中缺陷更为敏感。     

一种基于非线性光纤环镜开关特性的超短光孤子产生方法

提出了一种利用非线性光纤环镜的开关特性将连续波同时转化为亮孤子和暗孤子的新方法 ,即让连续波和另一波长的调制脉冲串共同耦合入光纤环镜 ,交叉相位调制使得一部分连续波被环镜透射 ,其余部分被反射 ;再让透射波和反射波分别在反常色散光纤和正常色散光纤中传输 ,自相位调制和群速度色散之间的相互作用使得透射波和反射波分别演化为亮、暗孤子。数值计算表明 ,该方法不仅可产生脉宽比调制脉冲窄、重复频率比调制脉冲高的亮孤子和暗孤子 ,而且几乎可将全部的连续波能量转化为孤子能量。     

Gravitational Instability of a Two-Component Viscous Plasma with Finite Conductivity Flowing Through a Porous Medium with Fir Corrections

The gravitational instability of a two component plasma is studied to include the simultaneous effects of collisions, gyroviscosity, finite conductivity, viscosity and porosity of the medium within the framework of two-fluid theory. From linearized equations of the system, using normal mode analysis, the dispersion relations for parallel and perpendicular directions to the magnetic field are derived and discussed. For longitudinal wave propagation it is found that the value of critical JEANS' wave number increases with increasing density and decreasing temperature of the neutral component. For transverse wave propagation the value of critical JEANS' wave number depends on gyroviscosity, ALFVÉN number, ratio of sonic speeds and densities of the two component and porosity of the medium. It is observed that the effect of magnetic field and porosity is suppressed by finite condutivity of the plasma and similarly the effect of gyroviscosity is removed by viscosity from JEANS' expression of instability. For both the directions instability is produced when the velocity perturbations are considered parallel to wave vector. The damping effect is produced due to collisional frequency, permeability of the porous medium and viscosity. The density of the neutral component and porosity of the medium tends to destabilize the system while an increased value of FLR corrections leads the system towards stabilization.