Propagation of a short pulse in a medium with a resonance relaxation: The exact solution

A new analytical representation is obtained for the fundamental solution (Green’s function) to the problem of the propagation of a short pulse in an arbitrary medium with a single resonance relaxation process. The analytical representation is based on the generalized function of the local response of a linear medium [1] and includes the well-known Debye and Lorentz relaxation models as particular cases. The representation is used to determine the complete set of possible types of behavior for a short pulse propagating in the medium.     

Nonlinear processes in media with an acoustic hysteresis and the problems of dynamic interaction between piles and earth foundation

Evolution of a pulsed disturbance in a nonlinear medium whose properties irreversibly vary in the course of wave propagation is studied. Equations describing the propagation process are obtained. It is demonstrated that the waveform distortion and the dynamics of the field and energy characteristics of a signal noticeably differ from those observed in conventional nonlinear media. New nonlinear equations describing a pulse in a medium with relaxation of its nonlinear properties are derived. A finite “delay time” for irreversible processes is introduced in the defining equation. The shape of a pulse reflected from the boundary between an ordinary medium and a nonlinear hereditary medium is calculated. It is demonstrated that, in the case of a fixed relation between the peak pressure in the incident pulse and the ratio of linear impedances of the two media, a total transmission of the trailing edge of the pulse into the compressed medium occurs. Possible applications of the results to topical construction problems are discussed.     

Measurement of the moments of the relaxation time spectrum of a liquid by pulsed acoustic spectroscopy

On the basis of theoretical results describing the propagation of short acoustic pulses in relaxation media, the temporal characteristics of a signal that carry the information on the first five moments of the relaxation time spectrum (RTS) are determined. The measurement of these characteristics forms the basis of the proposed variant of pulsed acoustic spectroscopy of relaxation media. An experimental setup was developed in which short acoustic pulses were excited by a neodymium glass laser. Test measurements of RTS moments for an acetic acid, the liquid with a single relaxation time, are carried out.     

Two-dimensional extremely short optical pulses with a Bessel cross section in inhomogeneous medium of carbon nanotubes

The problem of dynamics of propagation of extremely short optical pulses (light bullets) with a Bessel cross section in inhomogeneous medium of carbon nanotubes has been considered. It is numerically shown that the optical pulse propagation is stable and steady.     

New class of extremely short electromagnetic solitons

A physical realization is presented for the integrable modified sine-Gordon equation. In this case, this equation describes the propagation of an extremely short vector electromagnetic pulse in the system of asymmetric quantum objects that have permanent dipole moments in the self-energy states. Using soliton solutions for ordinary and extraordinary components, new regimes of the dynamics of the pulse and medium that are specific only to asymmetric media have been found.     

On propagation failure in one- and two-dimensional excitable media

We present a nonperturbative technique to study pulse dynamics in excitable media. The method is used to study propagation failure in one-dimensional and two-dimensional excitable media. In one-dimensional media we describe the behavior of pulses and wave trains near the saddle node bifurcation, where propagation fails. The generalization of our method to two dimensions captures the point where a broken front (or finger) starts to retract. We obtain approximate expressions for the pulse shape, pulse velocity, and scaling behavior. The results are compared with numerical simulations and show good agreement.     

Nonlinear Longitudinal Strain Waves in a Solid Exposed to Pulsed Laser Radiation

The propagation of longitudinal strain waves in a solid with quadratic nonlinearity of elastic continuum was studied in the context of a model that takes into account the joint dynamics of elastic displacements in the medium and the concentration of the laser-induced point defects. The input equations of the problem are reformulated in terms of only the total displacements of the medium points. In this case, the presence of structural defects manifests itself in the emergence of a delayed response of the system to the propagation of the strain-related perturbations, which is characteristic of media with relaxation or memory. The model equations describing the nonlinear displacement wave were derived with allowance made for the values of the relaxation parameter. The influence of the generation, relaxation, and the strain-induced drift of defects and the flexoelectricity on the propagation of this wave was analyzed. It is shown that, for short relaxation times of defects, the strain can propagate in the form of both shock fronts and solitary waves (solitons). Exact solutions depending on the type of relation between the coefficients in the equation and describing both the shock-wave structures and the evolution of solitary waves are presented. In the case of longer relaxation times, shock waves do not form and the strain wave propagates only in the form of solitary waves or a train of solitons. The contributions of the finiteness of the defect-recombination rate and the flexoelectricity to linear elastic moduli and spatial dispersion are determined.     

Dynamics of solitons in periodic systems with different nonlinear media

To analyze pulse dynamics in an optical system consisting of a periodic sequence of nonlinear media, a composite model is used. It includes a model of the resonance interaction of an ultrashort light pulse with the energy transition of the medium with allowance made for an upper level pump and an almost integrable model that describes the propagation of the light field in the other medium with a cubic nonlinearity and dispersion. Additional allowance is made for losses and other kinds of interaction by introducing perturbation terms. On the bases of the inverse scattering transform and perturbation theory, a simple method for analyzing specific features of soliton evolution in periodic systems of this kind is developed. It is used to describe various modes of soliton evolution in such a system, including chaotic dynamics.     

Resonant transparency effects in an anisotropic medium with a permanent dipole moment

The propagation of a two-component laser pulse in an optically uniaxial medium is investigated under the conditions of the Zakharov-Benney resonance (viz., resonance of long and short waves). The short-wave ordinary component of the pulse, which is in resonance with the atomic subsystem, effectively generates a video pulse of the extraordinary wave (long-wave component). The latter dynamically detunes the ordinary pulse from the resonance and causes its phase modulation due to nonzero diagonal matrix elements of the dipole moment. An approximate operator approach is proposed for solving constitutive equations for the density matrix, which is equivalent to the asymptotic WKB method and makes it possible to reduce the analysis to solving a system of nonlinear wave equations for both components of the pulse. The possibility an extraordinary wave video pulse being generated with the help of a quasimonochromatic ordinary pulse with a longer wave-length. It is shown that, when the ordinary component dominates, the self-induced transparency mode is realized; in the opposite limit, the effect known as extraordinary transparency takes place. Solitary pulses corresponding to the latter case experience a decrease in the velocity of propagation, which is similar to that observed for self-induced transparency and practically do not change the population of quantum levels. Physical situations reducing the initial system of constituent and wave equations to familiar integrable models are analyzed.     

Dynamics of an extremely short pulse in a Stark medium

Effects of propagation of an extremely short (of one or several oscillation periods) electromagnetic pulse in a medium whose resonance transition is characterized by diagonal as well as nondiagonal matrix elements of the dipole moment operator have been studied numerically. The Maxwell-Bloch system of equations is employed without using the approximation of slowly varying envelopes. An analog of the McCall and Hahn area theorem is discussed as applied to the division of the initial extremely short pulse into subpulses. The solution is obtained in the form of a solitary stable bipolar signal with a nonzero pulse area (nonzero breather).     

Allowable propagation of short pulse laser beam in a plasma channel and electromagnetic solitary waves

Nonparaxial and nonlinear propagation of a short intense laser beam in a parabolic plasma channel is analyzed by means of the variational method and nonlinear dynamics. The beam propagation properties are classified by five kinds of behaviors. In particularly, the electromagnetic solitary wave for finite pulse laser is found beside the other four propagation cases including beam periodically oscillating with defocussing and focusing amplitude, constant spot size, beam catastrophic focusing. It is also found that the laser pulse can be allowed to propagate in the plasma channel only when a certain relation for laser parameters and plasma channel parameters is satisfied. For the solitary wave, it may provide an effective way to obtain ultra-short laser pulse.     

高峰值光场的定点产生

 用有限差分方法联立求解 Maxwell-Bloch方程时,发现2p光脉冲通过1维共振介质时的两个现象：当共振介质的偶极矩较大或共振粒子数密度较大时,2p脉冲波形会发生分裂,不再以孤子形式传播;峰面积符号相同、脉宽不同的两个2p脉冲传播时,脉宽小的脉冲将赶上脉宽大的脉冲,赶超过程中光电场大小的变化不明显,而峰面积符号相反、脉宽不同的脉冲在赶超过程中会引起光场的叠加而形成光电场峰值高、脉宽小的脉冲,因而可以通过控制两脉冲的相对脉宽或相对距离,在介质的指定位置产生高峰值的光场。     

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.     

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.     

Instability control in microwave-frequency microplasma

This paper introduces comprehensive large-signal analyses of modulation dynamics and noise of a chaotic semiconductor laser. The chaos is induced by operating the laser under optical feedback (OFB). Control of the chaotic dynamics and possibility of suppressing the associated noise by sinusoidal modulation are investigated. The studies are based on numerical solutions of a time-delay rate equation model. The deterministic modulation dynamics of the laser are classified into seven regular and irregular dynamic types. Variations of chaotic dynamics and noise with sinusoidal modulation are examined in both time and frequency domains over wide ranges of the modulation depth and frequency. The results showed that chaotic dynamics can be converted into five distinct dynamic types; namely, continuous periodic signal (CPS), continuous periodic signal with relaxation oscillations (CPSRO), periodic pulse (PP), periodic pulse with relaxation oscillations (PPRO) and periodic pulse with period doubling (PPPD). The relative intensity noise (RIN) of these types is characterized when the modulation frequencies are much lower, comparable to, and higher than the resonance frequency. Suppression of RIN to a level 8 dB/Hz higher than the quantum limit was predicted under the CPS type when the modulation frequency is 0.9 times the resonance frequency and the modulation depth is 0.14.     

Nonstationary theory of polarized light pulse propagation through a four-level resonant medium with allowance for nonlinear complex refractive index of medium

Nonstationary theory of polarized light pulse propagation through the medium with resonant transition 1/2 -1/2 is developed with taking into account complexity of the medium nonlinear refractive index. The theory is developed based on the irreducible tensor formalism which allows diagonalizing relaxations matrix and introducing effective decay times associated with the population relaxation, as well as relaxation of coherence between magnetic sublevels of the resonant system. It is shown that as a result of interference of magnetic sublevels in the polarized radiation field the inversionless amplification of radiation occurs due to optical pumping process. The dependence of inversionless amplification on the line broadening and resonance detuning is studied.     

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.     

Area of ultimately short light pulses

The evolution of the area of a pulse of optical radiation propagating in a nonlinear medium is analyzed. The role played by the medium relaxation and the correctness of the formulation of the problem on the propagation of short pulses are discussed.     

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.     

Capture into resonance: a method for efficient control

To achieve large changes in adiabatic invariants using small control input, a conservative dynamical system must possess an internal resonance. Capture into resonance is an inherently probabilistic process. We propose a control method to make it more structured. We study the motion of charged particles in an electromagnetic field as an example of such a system. When the nominal dynamics brings particles close to a resonance surface, a short control pulse forces the capture of a particle into the resonance with the wave. A captured particle is transported by the wave across the energy levels. The second pulse releases a particle from the resonance when the desired energy level is achieved. We discuss the distribution of energy achieved by the method.