Radiophysics and Quantum Electronics最新文献

We present a brief overview of the theory of high-intensity nonlinear diffracting beams. Characteristic distortions of the profiles of acoustic waves, which are observed during the wave propagation, are described. The following features are pointed out. First, the positive and negative half periods of the original harmonic signal are differently distorted. The positive-pressure phase duration is shortened and its “amplitude” is increased. On the contrary, the region of negative pressure is somewhat extended and reduced in “amplitude.” Second, the profiles are shifted to the region of negative values of the “accompanying” time, i.e., the diffraction of a convex beam leads to a slight increase in its propagation velocity. In addition, the positive pressure in some range of distances may exceed the initial value. Low-frequency geometric dispersion leads to differentiation of the weak signal profile in the focal region and in the far zone, which leads to the disappearance of unipolar video pulses. A stationary wave composed of sections of a parabolic shape can be formed in the waist. The limiting values of acoustic pressure and wave intensity in the focus are estimated. Approximate mathematical methods and the models used in the calculation of the wave profiles are described.

We have found a new class of three-dimensional vector laser solitons within the framework of the quasi-optical approximation (parabolic equation) for a medium with a fast response of nonlinear amplification and absorption by numerical modeling. These solitons have different polarization singularities. The range of parameters in which solitons are stable is studied, and scenarios of destabilization when leaving this range are indicated.

We discuss the common properties of and the differences between the exact solution of the Burgers equation (the Cole–Hopf solution) and the asymptotic solution of the parabolic equation of quasioptics (the geometrical-optics approximation). It is shown how the application of the modified lens transformation (Talanov transformation) allows one to consider several problems of the nonlinear interaction of intense acoustic waves having essentially different time scales.

We review modern studies of the self-action of laser radiation in discrete systems using the example of multicore fibers. The critical power is shown to exist, at which the self-trapping (the discrete analog of collapse) of radiation occurs even in a one-dimensional lattice of weakly coupled cores. The transition of nonlinear dynamics to the stochastic regime in discrete systems is studied, and the threshold amplitude for this transition is determined. It is shown that the use of a special configuration with a dedicated core in the center of a ring of identical cores makes it possible to control the self-trapping process and apply it for nonlinear radiation filtering and self-compression of laser pulses. It is established that arbitrarily powerful coherent radiation can be handled using stable out-of-phase supermodes, which are wave-field distributions over all fiber cores with a maximum propagation constant. Such out-of-phase supermodes are demonstrated for core configurations shaped as a ring, a line, a square matrix, and a hexagonal structure. The first experiments have already shown the feasibility and stability of the found out-of-phase supermodes, in both fibers with a ring configuration and fibers having a square matrix of cores.

The paper presents a brief review of the quasiclassical wave dynamics for the nonlinear Schrödinger equation (NLSE) as applied to focusing and defocusing media. The NLSE depends significantly on the space dimension d. The two-dimensional NLSE has an additional symmetry of the conformal type with respect to the Talanov transformations (Talanov in JETP Lett. 11:199–201, 1970), which were initially found for the stationary self-focusing in a medium with the Kerr nonlinearity. A consequence of this symmetry is the Vlasov–Petrishchev–Talanov theorem (Vlasov et al. in Radiophys. Quantum Electron. 14:1062–1070, 1971) that relates the mean of the squared distribution and the Hamiltonian of the system. This theorem is valid for both focusing and defocusing media. In the quasiclassical limit, this makes it possible to construct anisotropic solutions which describe beam compression during self-focusing and quantum-gas expansion into vacuum within the so-called critical nonlinear Schrödinger equations, in particular, for the Gross–Pitaevskii equation with a chemical potential having a power-law dependence on density with the exponent ν = 2/d. For the Gross–Pitaevskii equation, the case d = 2 corresponds to a condensate of a weakly nonideal Bose gas, and the case d = 3 describe condensate of a Fermi gas in the unitary limit. For d = 3, the Gross–Pitaevskii equation in the quasiclassical limit transforms into equations of the gas dynamics with the adiabatic exponent γ = 5/3. The self-similar solutions in this approximation describe the angular deformations of a gas cloud against the background of an expanding gas. Angular deformations of such type are observed in both the expansion of quantum gases and the action of high-power laser radiation on matter. For three-dimensional supercritical focusing NLSE, the quasiclassical solutions of the collapsing type are presented, including the exact semiclassical solution described by the strong collapse regime. It is found that all such quasiclassical collapses are found to be unstable, except for the collapse that is simultaneously the weakest and the fastest collapse corresponding to the self-similar NLSE solution. The problem of post-collapse is also considered as the continuation of a weak collapse, which results in the formation of a quasistationary singularity in the form of a black hole into which energy is drawn from the surrounding collapsing region. For the NLSE with d ≥ 4, the formation of a black hole can be described in the quasiclassical approximation. It is shown that the anisotropy caused by the magnetic field significantly alters the structure of the Langmuir collapse, in particular, leads to the formation of strongly anisotropic black holes described quasiclassically.

We study the possibilities of using the eikonal equation to construct theoretical models of objects that become invisible under certain illumination conditions. The characteristics of the cloaking coating, which performs its functions for a given direction of wave incidence on the cloaked volume of space, are calculated. A method for constructing models of cylindrical objects that are invisible at arbitrary azimuthal and given zenith angles of illumination is proposed. It is shown that by employing the eikonal equation, it is possible to design invisible objects from materials with refractive indices of different signs.

We present an analytical solution to the problem of determining a complex dielectric permittivity of ground based on bistatic Moon location results for the case where the measured values are the moduli of reflection coefficients of radio waves for vertical and horizontal polarizations and the difference in their phases.

We develop differential equations for the probability density of the phase coordinates of the dynamic systems with parametric fluctuations in the form of the non-Markovian dichotomic noise, which has arbitrary lifetime distribution functions in the states ±1. As an example, we calculate the first moment of the phase coordinate of the linear oscillator, whose perturbed motion is described by the stochastic analogue of the Mathieu—Hill equation. These calculations aim at demonstrating the fact that in the case of linear dynamic systems, the non-Markovian parametric fluctuations having hidden periodicity are capable of inducing the states absent in the deterministic regime without periodic coefficients. The problem is solved by the method of supplementary variables, which transforms the non-Markovian dichotomic noise to the Markovian noise. It is shown that the amplitude oscillations, which are typical of the parametric resonance are present, when the structure of the dichotomic noise is described by the lifetime distribution function in the states ±1 in the form of the sum of weighted Erlang distribution exponents of the various order and a constant value of +1. The delta-correlated and Gaussian properties of the studied processes are not used. The calculations are performed within the framework of simple differential equations without involving integral operators and the Novikov—Furutsu—Donsker theorem.

We study theoretically the propagation of longitudinal acoustic waves in structurally inhomogeneous viscoelastic solids with a quadratic–bimodular nonlinearity decreasing with increasing frequency. Exact solutions for stationary waves propagating without changing their shape are obtained. Analytical and numerical solutions for the evolution of an initially harmonic wave are presented, and the amplitude–frequency dependences of nonlinear effects in such media are revealed.

In recent years, significant progress has been made in generating ultrashort electromagnetic pulses of single-cycle and subcycle duration. Unipolar pulses contain one half-cycle of the field and have a nonzero electric area. The conventional concepts of interaction of electromagnetic radiation with matter (in particular, interference) used in the case of multicycle pulses are not applicable to unipolar ones. This minireview discusses the latest results on the effects of extremely short low-amplitude pulses (when the perturbation theory is valid) on resonant media and individual quantum systems (atoms, molecules, and nanostructures) from the viewpoint of the recently introduced concept of “interference” of the areas of short light pulses (electric and envelope areas). We provide a simple relation showing that in order to compare the effects of multicycle bipolar and subcycle unipolar pulses on micro-objects, one should compare their areas, not energies. By numerically solving the Maxwell–Bloch equations, we study the features of area interference are studied beyond the limits of perturbation theory. It is shown that, after the collision of a pair of π-like ultrashort pulses, polarization structures and population difference gratings with nonharmonic multipeak structures are formed inside the medium. The possibility of experimentally determining the electric area of unipolar pulses through interference of their areas is discussed for the first time.