Effects of soliton dynamics of acoustic pulses in a paramagnetic crystal

Nonlinear dynamics of longitudinal-transverse acoustic pulses in the deformed cubic crystal containing a paramagnetic impurity with effective spin S = 1 is theoretically investigated. Soliton solutions of systems of equations describing the propagation of extremely short and ultrashort pulses at an arbitrary angle to the direction of external deformation parallel to the crystal symmetry axis are obtained. Classification of longitudinal-transverse soliton types and resonant acoustic transparency regimes is given. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 31–36, August, 2007.     

The behavior of three-dimensional ultimately short optical pulses in a system of carbon nanotubes in the presence of an external magnetic field

The character of the behavior of three-dimensional ultimately short optical pulses propagating in a system of carbon nanotubes in the presence of an external magnetic field perpendicular to both the nanotubes’ axis and the direction of pulse propagation is investigated. Electromagnetic-field evolution is analyzed within the framework of the Maxwell’s equations, while the electronic system of the carbon nanotubes is investigated in the low-temperature approximation.     

Nonlinear acoustic transparency phenomena in strained paramagnetic crystals

Nonlinear dynamics of longitudinal acoustic pulses propagating in a strained paramagnetic cubic crystal at low temperature is analyzed. The direction of constant uniform strain is parallel to one of the fourth-order symmetry axes. Effective-spin 1 ions are considered as paramagnetic impurities with the strongest spin-lattice interaction. In this medium, normally degenerate magnetic sublevels are dynamically shifted by the quadrupole Stark effect, and the frequencies of the transitions induced by an acoustic pulse change accordingly. The self-consistent system of equations derived in this study without using the slowly varying envelope approximation describes pulse propagation at an arbitrary angle to the direction of the static strain. Exponentially and rationally decaying monopolar and breather-like solutions to the system are obtained. An analysis of the solutions reveals an asymmetry of the pulse polarity depending on the type of strain (extension or compression) and the pulse propagation direction. In particular, it is shown that acoustic transparency associated with monopolar strain pulses exhibits threshold behavior. The sign of the time area (zeroth harmonic) of breather-like strain pulses is such that the transition frequency averaged over an oscillation period dynamically decreases. This behavior determines the efficiency of generation of high-order harmonics of acoustic pulses in strained paramagnetic crystals.     

Self-focusing and defocusing of self-similar π pulses in an amplifying two-level medium

The effect of transverse perturbations on the propagation of electromagnetic π pulses in an amplifying two-level medium is studied. The cases of quasi-monochromatic and extremely short pulses are considered. The equations describing the behavior of the transverse size of the pulse during its propagation in the medium are derived. It is shown that, if the ratios of the diffraction length to the length of dispersion spreading are smaller than certain critical values, self-focusing regimes are realized for both types of pulses. Otherwise, at a finite distance, blowup of defocusing occurs, after which the amplified pulse propagates as if it is a one-dimensional pulse, with the velocity equal to the velocity of light in vacuum. Similarities and distinctions in the dynamics of propagation of extremely short and quasi-monochromatic pulses are indicated.     

超短激光脉冲在多能级系统中的传输特性

运用数值方法研究了超短激光脉冲在多能级系统中的传输特性.当激光脉冲能量相对较弱时,适当的脉冲面积可以实现自感应透明;激光脉冲能量逐渐增强,脉冲将产生分裂.脉冲分裂的基本面积（即脉冲实现稳定传播的最小面积）与二能级系统不同,而是A₀=2π/κ,与激发态的能级个数和跃迁偶极矩密切相关.由于分裂和吸收,超短激光脉冲传输了一段距离以后,将演化为一个脉冲宽度更窄、峰值强度更高且面积为A₀的超短激光脉冲. 关键词： 超短激光脉冲 多能级系统 特征时间     

Three-dimensional few-cycle optical pulses in an array of carbon nanotubes inside a magnetic field

The behavior of three-dimensional few-cycle optical pulses, propagating in a system of carbon nanotubes inside an external magnetic field applied parallel to the nanotube axes and perpendicular to the direction of pulse propagation, is studied. The evolution of the electromagnetic field is classically derived using Maxwell’s equations.     

Dynamics of ultrashort pulse focusing

The method for studying the transformation of an ultrashort pulse of a spherical wave in the vicinity of the focus was developed. It was shown that the impulse response of the circular aperture contains two components: the transmitted one “cut” by the aperture from the incident wave and the toroidal edge one. Simple algebraic relations describing the propagation process were derived and corresponding software was developed. An example of a change in the pulse shape with Gaussian envelope is given. It was shown that pulses propagating with velocity ν > c, one of which overtakes the primary wave, are formed on the system axis.     

Ultrasonic pulse waves in cancellous bone analyzed by finite-difference time-domain methods

The trabecular frame of cancellous bone has a high degree of porosity, anisotropy and inhomogeneity. The propagation of ultrasonic waves in cancellous bone is significantly affected by the trabecular structure. In this paper, two two-dimensional finite-difference time-domain (FDTD) methods, which were the popular viscoelastic FDTD method for a viscoelastic medium and Biot's FDTD method for a fluid-saturated porous medium, have been applied to numerically analyze the ultrasonic pulse waves propagating through bovine cancellous bone in the directions parallel and perpendicular to the trabecular alignment. The Biot's fast and slow longitudinal waves, which were identified in previous experiments for the propagation parallel to the trabecular orientation, could be analyzed using Biot's FDTD method rather than the viscoelastic FDTD method. For the single wave propagation in the perpendicular direction, on the other hand, the viscoelastic FDTD result was found to be in more good agreement with the experimental result.     

Dynamics of the parameters of pulses in uniaxial crystals

A set of equations describing the dynamics of the parameters of an electromagnetic pulse is derived using the Ritz-Whitham variational principle. An ordinary pulse component is a quasi-monochromatic pulse, and its extraordinary component is a videopulse. The transverse dynamics of pulses having the super-Gaussian shape is considered for propagation along an optical crystal axis.     

On the nonlinear propagation of few-cycle pulses in a uniaxial crystal

The soliton-like dynamics of few-cycle optical pulses propagating in a uniaxial crystal at an arbitrary angle to the optic axis is analytically studied. Solutions describing the one-dimensional dynamics of pulses representing coupled states of the ordinary and extraordinary field components are analyzed. The ordinary component can contain an arbitrary number (down to one period) of optical oscillations, whereas the extraordinary component is a unipolar video pulse. The effect of small-scale transverse perturbations on the propagation of such pulses is considered. Regions of values of parameters of the medium and the pulse in which the propagation is stable are found. The spectrum of the ordinary component is shown to substantially depend on the sign of the birefringence of the crystal as well as on the angle at which the pulse propagates with respect to the optic axis.     

On nonlinear propagation of extremely short pulses in optically uniaxial media

Nonlinear wave equations describing the propagation of optical pulses of duration up to a period of electromagnetic oscillations in transparent media with uniaxial optical anisotropy are derived on the basis of a quantum-mechanical model of material response. The electron and electron-vibrational nonlinearities, electron and ion dispersion, and diffraction are taken into account. It is shown that the inclusion of the electron response alone leads to a system of two constitutive equations for the ordinary and extraordinary polarization components. When a pulse propagates across the optical axis, this system is reduced to an inhomogeneous model of the Henon-Heiles type and, hence, generalizes the Lorentz classical electron model. In order to take into account stimulated Raman scattering (SRS) processes, an anisotropic analog of the Bloembergen-Shen quantum-mechanical model taking into account the population dynamics of SRS sublevels is obtained. The generation of an extraordinary wave video pulse with the help of the high-frequency ordinary component in the Zakharov-Benney resonance mode is investigated. Some analytic soliton-like solutions in the form of propagating bound states of ordinary and extraordinary video pulses corresponding to different birefringence modes are considered and their stability to self-focusing is analyzed.     

Formation of ultrashort pulses in the process of the propagation of tightly focused femtosecond light packets in a transparent condensed medium

The evolution of the space-time structure of tightly focused femtosecond light packets in a transparent condensed medium (fused silica) is analyzed by means of numerical simulation. The nonlinear self-action of light packets leads to the formation of ultrashort pulses (duration of about 10 fs) propagating in various directions. The spectral composition, time structure, and position of ultrashort pulses at the time axis depend on their propagation direction.     

Resonant transparency regimes under conditions of long/short-wave coupling

Nonlinear two-component electromagnetic pulse propagation through a resonant axially symmetric anisotropic medium having a permanent dipole moment is analyzed under conditions of strong coupling between the ordinary (short-wavelength) and extraordinary (long-wavelength) pulse components. It is shown that a pulse can propagate through the medium in regimes different from self-induced transparency if its ordinary component is detuned off resonance. In particular, a pulse propagating in the regime of self-induced super-transparency substantially changes quantum-level populations, but its group velocity remains almost equal to the linear velocity. If a pulse propagates in the extraordinary transparency regime and the carrier-frequency detuning from resonance is small, then its group velocity is substantially lower, while the level populations remain virtually invariant. Regimes of propagation through weakly excited media under quasi-resonance conditions are also identified.     

Photoluminescence Properties of Thin-Film Nanohybrid Material Based on Quantum Dots and Gold Nanorods

The dynamics of coherent propagation of a unipolar subcycle pulse of a large electric-field area (the integral of the electric-field strength with respect to time) in a nonlinear two-level resonant medium is studied theoretically. The propagating pulse is shown to be capable of splitting into a pair of individual components, each of which behaves like a pulse of self-induced transparency. This phenomenon is similar to the well-known phenomenon of splitting of a 4π or 6π pulse into a pair of 2π pulses of self-induced transparency, which occurs in the case of propagation of long pulses, when the notion of the pulse area is applicable and the area theorem holds.     

On the soliton-like dynamics of ultrashort acoustic pulses in a paramagnetic crystal

A system of nonlinear equations describing the dynamics of the longitudinal and transverse components of an acoustic pulse in a cubic crystal containing paramagnetic impurities has been obtained. On the basis of this system, the dynamics of a two-component ultrashort acoustic pulse propagating under the Zakharov-Benney resonance conditions has been analytically investigated.     

Propagation of the ultrashort laser pulses through the quantum nonlinear medium with resonant properties

The propagation of ultrashort few-cycle laser pulses through a quantum nonlinear medium with resonant properties is studied using the method of slowly varying amplitudes with allowance for dispersion effects. A self-consistent system of nonlinear wave equation for the evolution of laser field and the nonstationary Schrödinger equation that determines the material polarization response is numerically solved. Specific features of the propagation of laser pulse caused by a relatively large spectral width and the nonadiabatic character of the laser pulse are established. The rise of the slowly dumping polarization at the eigenfrequency of the medium and the consequent stretching of the laser pulse are observed. The role of the resonant absorption of the laser energy in the medium is analyzed. The nonlinear spectral broadening is demonstrated for the laser pulse propagating through the medium.     

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.     

Dynamics and control of few-cycle ultrashort pulse propagation in an asymmetric coupled-quantum-well nanostructure

The nonlinear propagation of few-cycle ultrashort pulse in an asymmetric coupled-quantum-well (CQW) nanostructure is simulated by solving numerically the full Maxwell-Bloch equations with an iterative predictor-corrector finite-difference time-domain method. The behaviors of electric field profiles for 2π and 4π ultrashort pulses in different propagating zones are predicted in details beyond the slowly varying envelope and rotating-wave approximations. This investigation may provide a guideline for optimizing and controlling ultrashort pulses in solid-state media, which are promising for practical applications in high-speed optical communications.     

Polarization dynamics of unidirectional optical pulse evolution in a laser amplifier

Polarization dynamics of optical pulses in an isotropic two-level medium is analyzed by solving an integrable system of evolution equations without using the slowly varying envelope approximation. The analysis is focused on the regime of unidirectional pulse generation in an initially inverted medium. Qualitative difference in polarization dynamics is revealed between few-cycle and quasi-monochromatic pulse propagation     

Soliton regimes of ultrashort pulse propagation through an array of asymmetric quantum objects

Nonlinear regimes of two-component ultrashort pulse propagation through an array of anisotropic quantum systems are analyzed theoretically under conditions when the slowly varying envelope approximation is inapplicable. It is shown that if the spectral width of the pulse is much larger than the quantum transition frequency, then the dynamics of its ordinary component can be described by a modified sine-Gordon equation that belongs to the class of integrable models but has never been used in physical applications. It is shown that the extraordinary pulse component responsible for the dynamic Stark shift of the transition frequency is coupled to its ordinary component by an algebraic relation. The soliton solutions to the derived equation are classified. Depending on the pulse duration, the solutions have the form of 2π pulses (kinks and antikinks) or steady traveling 0π pulses having no counterparts in isotropic models (neutral kinks). Interactions between the medium and solitons of different types and soliton collisions are analyzed.