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.     

Effect of the field of a nonlinear electromagnetic wave on the shape of a soliton in a semiconductor superlattice

The effect of the electric component of the field of a high-frequency (HF) nonlinear electromagnetic (EM) wave on the propagation of a solitary EM wave (soliton) in a quantum semiconductor superlattice is studied. It is noted that in the collisionless approximation, the solution of the modified sine-Gordon equation corresponding to the amplification of an EM pulse that, with allowance made for interminiband electron transitions, transforms into a dissipative soliton is possible. The effect of electron collisions with irregularities of the crystal lattice on the soliton dynamics under the action of the field of a HF nonlinear wave is considered. The condition for an increase in the traveling time of the solitary wave is found.     

Quasi-static electromagnetic pulse generated by ultra-intense laser pulses

A solitary structure of quasi-static electromagnetic pulse is formed in moderate density plasmas by a propagation of ultra-intense and ultra-short laser pulse, which is formed after the laser pulse is depleted and slowly propagates in the laser propagation direction. The structure is sustained by huge magnetic pressure and compensating electric field which are in an electromagnetic equilibrium together with the plasma motion. The solitary structure is formed when the resonance condition is satisfied and laser intensity is high enough to induce huge magnetic field pressure.     

Extremely short electromagnetic pulses in a resonant medium with a permanent dipole moment

The propagation of an extremely short (one cycle long) pulse of an electromagnetic field in a medium whose resonant transition is characterized by both diagonal and off-diagonal matrix elements of the dipole-moment operator is considered theoretically. The set of Maxwell-Bloch equations without the approximation of the slowly varying envelopes is used. Two types of solutions of this set, which are found describing the steady-state propagation of an electromagnetic pulse in such a medium.     

Light bullet passing an array of carbon nanotubes with metallic mesh irregularities

We consider the propagation of 2D solitary electromagnetic waves and their scattering on a lattice of metallic inhomogeneities in the system of carbon nanotubes (CNTs). The electromagnetic field is considered on the basis of Maxwell equations, and the electronic system of carbon nanotubes is treated by the Boltzmann equation in relaxation time approximation. We numerically analyze the derived effective equation and reveal an increase of spectral composition of the last electromagnetic wave. Some possible practical applications of the discovered effect are discussed.     

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.     

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 reconstructing photon statistics by on/off detectors: Toward the multi-partite case

The propagation of pulses of the pump and its second harmonic in a quadratically nonlinear medium whose linear properties are characterized by a negative refractive index at the pump frequency and by a positive refractive index at the harmonic frequency is considered theoretically. In the case of a low intensity of the interacting waves, the pump and second-harmonic pulses propagate in the opposite directions, but sufficiently powerful pulses can form a simulton—a solitary two-frequency wave propagating in a certain direction as a single whole. Solutions to a set of equations are found which describe the steady-state propagation of a solitary wave and of a nonlinear periodic (cnoidal) wave.     

Solitary Surface Waves in Plasmas Interacting with a High-Frequency Electric Field

We show that a solitary surface wave can exist at the boundary between a plasma and a dielectric, due to a balance between the nonlinear surface charge terms and the dispersive terms which here are caused by the presence of a high-frequency incident electromagnetic wave. The solitary wave propagation velocity, which depends on the intensity of the incident field, is also calculated.     

Kerr类非线性介质周期结构中的慢Bragg孤子

在耦合模理论的基础上,给出了一维无限大Kerr类非线性介质周期结构中的孤波解,并且指出,孤波的振幅依赖于入射频率以及脉宽两个参量.同时也证明,在布拉格共振极限条件下,孤波解可以简化成所谓的“隙孤子”解或是“慢布拉格孤子”解 关键词： 孤波 慢布拉格孤子 隙孤子 耦合模理论     

Propagation of an ultimately short electromagnetic pulse in a nonlinear medium described by the fifth-order Duffing model

We discuss propagation of an ultimately short (single-cycle) pulse of an electromagnetic field in a medium whose dispersion and nonlinear properties can be described by the cubic-quintic Duffing model, i.e., by an oscillator with third-and fifth-order anharmonicity. A system of equations governing the evolution of a unidirectional electromagnetic wave is analyzed without using the approximation of slowly varying envelopes. Three types of solutions of this system describing stationary propagation of a pulse in such a medium are found. When the signs of the anharmonicity constants are different, then the amplitude of a steady-state pulse is limited, but its energy may grow on account of an increase in its duration. The characteristics of such a pulse, referred to as an electromagnetic domain, are discussed.     

Two-dimensional electromagnetic breathers in an array of nanotubes with multilevel impurities

The propagation of a two-dimensional bipolar electromagnetic pulse in an array of semiconductor carbon nanotubes with multilevel impurities is studied. The electromagnetic field in the array of nanotubes is described by Maxwell’s equations reduced to a non-one-dimensional wave equation. The numerical solution to the wave equation demonstrates the possibility of the propagation of a two-dimensional electromagnetic breather in the array of nanotubes. The character of the evolution of the shape of the breather is elucidated, and the time dependence of the maximum intensity of its field is obtained. It is demonstrated that the introduction of multilevel impurities causes a significant change in the parameters, thereby providing an additional possibility for the stabilization of a laser pulse propagating in an array of semiconducting carbon nanotubes.     

Two-frequency mutual coherence function for electromagnetic pulse propagation over rough surfaces

The propagation of a transient electromagnetic pulse over irregular terrain is considered. We model the wave propagation using the parabolic wave equation, which is valid for near-horizontal propagation. We model the effect of scattering from the rough terrain by introducing a surface-flattening coordinate transform. This coordinate transform simplifies the boundary condition of our problem, and introduces an effective refractive index into our wave equation. As a result, the problem of propagation over an irregular surface becomes equivalent to the problem of propagation through random media. The parabolic equation is solved analytically using the path integral method. Both vertically polarized and horizontally polarized signals are treated. Cumulant expansion is introduced to obtain an approximate expression for the two-frequency mutual coherence function. From the mutual coherence function, spatial and temporal dependence of the propagating signal can be determined. It can be shown that scattering from the irregular surface can cause broadening of the transient signal. This can have a significant impact on the performance of radio communication systems.     

Propagation dynamics of relativistic electromagnetic solitary wave as well as modulational instability in plasmas

By one-dimensional particle-in-cell(PIC) simulations, the propagation and stability of relativistic electromagnetic(EM) solitary waves as well as modulational instability of plane EM waves are studied in uniform cold electron-ion plasmas.The investigation not only confirms the solitary wave motion characteristics and modulational instability theory, but more importantly, gives the following findings. For a simulation with the plasma density 10²³ m^-3 and the dimensionless vector potential amplitude 0.18, it is found that the EM solitary wave can stably propagate when the carrier wave frequency is smaller than 3.83 times of the plasma frequency. While for the carrier wave frequency larger than that, it can excite a very weak Langmuir oscillation, which is an order of magnitude smaller than the transverse electron momentum and may in turn modulate the EM solitary wave and cause the modulational instability, so that the solitary wave begins to deform after a long enough distance propagation. The stable propagation distance before an obvious observation of instability increases(decreases) with the increase of the carrier wave frequency(vector potential amplitude). The study on the plane EM wave shows that a modulational instability may occur and its wavenumber is approximately equal to the modulational wavenumber by Langmuir oscillation and is independent of the carrier wave frequency and the vector potential amplitude.This reveals the role of the Langmuir oscillation excitation in the inducement of modulational instability and also proves the modulational instability of EM solitary wave.     

Modulation instability for a relaxational Kerr medium

We investigated on the influence of a temporally dispersive Kerr effect on the modulation instability and the propagation of solitary wave pulse. The modulation instability gain is derived and compared with numerical calculations. The role of nonlinear response time on reshaping the solitary pulse is examined.     

Time-dependent electromagnetic perturbations in a magnetized plasma with relaxing conductivity

The problem of one-dimensional propagation of a time-dependent electromagnetic perturbation in a homogeneous ionospheric plasma with relaxing conductivity in the presence of a horizontal geomagnetic field is considered. The approximate Green's function is constructed assuming that the dynamics of electromagnetic perturbations is determined by the diffusion mechanism if the diffusion is due to the sound wave motion. It is found that the relaxation of plasma conductivity may result in a solitary perturbation precursor preceding the arrival of the sound wave front.State University, St. Petersburg. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, No. 7, pp. 668–677, July, 1995.     

Propagation dynamics on the Fermi-Pasta-Ulam lattices

The spatiotemporal propagation of a momentum excitation on the finite Fermi-Pasta-Ulam lattices is investigated. The competition between the solitary wave and phonons gives rise to interesting propagation behaviors. For a moderate nonlinearity, the initially excited pulse may propagate coherently along the lattice for a long time in a solitary wave manner accompanied by phonon tails. The lifetime of the long-transient propagation state exhibits a sensitivity to the nonlinear parameter. The solitary wave decays exponentially during the final loss of stability, and the decay rate varying with the nonlinear parameter exhibits two different scaling laws. This decay is found to be related to the largest Lyapunov exponent of the corresponding Hamiltonian system, which manifests a transition from weak to strong chaos. The mean-free-path of the solitary waves is estimated in the strong chaos regime, which may be helpful to understand the origin of anomalous conductivity in the Fermi-Pasta-Ulam lattice.     

Two-frequency mutual coherence function for electromagnetic pulse propagation over rough surfaces

The propagation of a transient electromagnetic pulse over irregular terrain is considered. We model the wave propagation using the parabolic wave equation, which is valid for near-horizontal propagation. We model the effect of scattering from the rough terrain by introducing a surface-flattening coordinate transform. This coordinate transform simplifies the boundary condition of our problem, and introduces an effective refractive index into our wave equation. As a result, the problem of propagation over an irregular surface becomes equivalent to the problem of propagation through random media. The parabolic equation is solved analytically using the path integral method. Both vertically polarized and horizontally polarized signals are treated. Cumulant expansion is introduced to obtain an approximate expression for the two-frequency mutual coherence function. From the mutual coherence function, spatial and temporal dependence of the propagating signal can be determined. It can be shown that scattering from the irregular surface can cause broadening of the transient signal. This can have a significant impact on the performance of radio communication systems.     

Inelastic interaction of ultrashort pulses of polarized light with an ensemble of isolated quantum dots

A system of equations is formulated describing the evolution of a slowly varying envelope of an arbitrarily polarized ultrashort pulse of electromagnetic radiation in a medium with its resonant properties determined by an ensemble of isolated quantum dots. It is assumed that the concentration of quantum dots is small and that the whole system is equivalent to a gas of resonant four-level atoms. Particular solutions are found that correspond to the propagation of a stationary optical pulse. It is shown by numerical solution of the generalized truncated Maxwell-Bloch equations that steady-state propagation is possible only for circularly polarized light pulses, whereas the pulses of arbitrary polarization either decay and experience the dispersion-related broadening or are converted into circularly polarized solitary waves.     

Nonlinear short-wave propagation in ferrites

In this paper we discuss the propagation of nonlinear electromagnetic short waves in ferromagnetic insulators. We show that such propagation is perpendicular to an externally applied field. In the nonlinear regime we determine various possible propagation patterns: an isolated pulse, a modulated sinusoidal wave, and an asymptotic two-peak wave. The mathematical structure underlying the existence of these solutions is that of the integrable sine-Gordon equation.