Randomly layered active medium as a broadband amplifier

A flat-layered active medium in which two types of layers with different refractive indices alternate is considered. The thickness of a layer is assumed to be random and large as compared to the wavelength of propagating radiation. A wave propagating along the normal to the layers in such a medium is exponentially enhanced over lengths of the order of many layer thicknesses. In contrast to the familiar case of a periodic flat-layered active medium, waves with any (not necessarily definite resonant) frequency are amplified identically in a wide frequency range. By way of an example, convective instability of space-charge waves in a flow of charged particles moving through a randomly layered medium is considered. The predicted effect can be regarded as an analogue of Anderson’s localization, when increasing solutions rather than exponentially ecreasing ones are selected in view of the activity of the medium.     

Phase velocities of plane waves in a pipe with a flow whose velocity varies along the radius

The phase velocities of plane waves in a pipe filled with a moving acoustic medium are studied for different laws of flow velocity variation along the pipe radius. The wave equation is solved by the discretization method, which breaks the entire pipe volume into individual cylinders under the assumption that, within each of the cylinders, the flow velocity of the medium is constant. This approach makes it possible to reduce the solution to the wave problem to solving Helmholtz equations for individual cylinders. Based on boundary conditions satisfied at the boundaries between neighboring cylinders, a homogeneous system of linear algebraic equations is obtained. From this system, with the use of the scattering matrices, a simple dispersion equation is derived for determining the phase velocities of plane waves. The stability of the numerical solution to the dispersion equation with respect to the number of cylinders is investigated. The phase velocities of quasi-homogeneous and inhomogeneous waves in a pipe are numerically calculated and analyzed for different velocities of a moving medium and different laws of flow velocity variation along the radius. It is shown that the variation that occurs in the phase velocity of a homogeneous plane wave in a pipe due to the motion of the medium is identical to the mean flow velocity for different laws of flow velocity variation along the radius. For inhomogeneous plane waves, the phase velocity increment exceeds the mean flow velocity several times and depends on both the law of wave amplitude distribution along the radius and the law of the flow velocity variation along the radius.     

Distortion of waves with profile discontinuities in the medium with a periodic transverse inhomogeneity distribution

For the purpose of describing the joint influence of nonlinear effects and refractive inhomogeneities on the evolution of intense acoustic waves, a model of the medium the local velocity of sound of which is periodic in the transverse direction and decreases in the propagation direction, which generalizes the known models of the layered medium and of the infinitesimally thin phase screen, is proposed. An exact solution is found for the wave with arbitrary initial conditions: time profile and transverse profile. The spatial wave structure in the inhomogeneous medium is calculated; it is shown that narrow high-amplitude regions are formed and the rate of nonlinear effect accumulation changes. It is shown that the amplitude of the wave at long distances from the source may differ little from its initial value due to compensation for the effects of nonlinear attenuation and of focusing by inhomogeneities. Possibilities of amplification of intense waves depending on the proportion between parameters of the wave and those of the inhomogeneous medium are studied.     

Intensity fluctuations in a moving random medium

We consider the intensity fluctuations arising when a point source of radiation moves in a randomly inhomogeneous scattering medium. The medium itself can also move with a velocity whose component normal to the direction of propagation can have an arbitrary distribution. We derive an expression for the space-time autocorrelation function of the intensity fluctuations transverse to the direction of propagation. The result is analysed for some particular cases and it is shown how the resulting information can be useful in examining the behaviour of random media in situations of practical interest.     

Guided waves in a stratified half-space

The dispersion and excitation mechanisms and the energy distribution of guided waves in a stratified half-space are studied. All possible guided waves excited by a symmetric point source in two or three-layer medium models and their relation to the medium parameters are analyzed in detail. The excitation and propagation characteristics, as well as the energy distribution along the depth direction, of all modes of the surface waves and trapped waves are numerically investigated and analyzed thoroughly not only in the case when the shear wave velocity increases from up to down layers but also when a low-velocity layer is contained in halfspace, especially when the shear wave velocity decreases from up to down layers. It is found that there exist many guided wave modes in the case where the shear wave velocity of each layer increases from up to down layers. However, there is less than one guided wave mode in the case where the shear wave velocity of each layer decreases from up to down layers. The trapped waves exist and propagate along the low-velocity structure in the stratified half-space. It is also found that the characteristic of a mode is related to the source frequency. It is possible that a surface wave at one value of frequency is like a trapped wave at another value of frequency. Finally, the relation of the characteristics of all guided waves (surface waves and trapped waves) to the parameters of media is studied.     

Intensity fluctuations in a moving random medium

We consider the intensity fluctuations arising when a point source of radiation moves in a randomly inhomogeneous scattering medium. The medium itself can also move with a velocity whose component normal to the direction of propagation can have an arbitrary distribution. We derive an expression for the space–time autocorrelation function of the intensity fluctuations transverse to the direction of propagation. The result is analysed for some particular cases and it is shown how the resulting information can be useful in examining the behaviour of random media in situations of practical interest.     

Eigenwaves in an inhomogeneous azimuthally bigyrotropic medium

The problem of natural electromagnetic waves in an azimuthally magnetized bigyrotropic medium which is inhomogeneous in the radial direction is solved analytically. A system of generalized wave equations is obtained in the longitudinal components of the electrical and magnetic fields. Particular solutions of the system are represented in the form of generalized power series. The series exponents are determined and recursion formulas are built up for calculating their coefficients. The passage to particular cases of a homogeneous gyrotropic and inhomogeneous isotropic medium is realized, and the results are compared with known data from the literature.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 46–49, November, 1982.     

Acoustic waves in random fields

The effect of space- and time-dependent random mass density, velocity, and pressure fields on frequencies and amplitudes of acoustic waves is considered by means of the analytical perturbative method. The analytical results, which are valid for weak fluctuations and long wavelength sound waves, reveal frequency and amplitude alteration, the effect of which depends on the type of random field. In particular, the effect of a random mass density field is to increase wave frequencies. Space-dependent random velocity and pressure fields reduce wave frequencies. While space-dependent random fields attenuate wave amplitudes, their time-dependent counterparts lead to wave amplification. In another example, sound waves that are trapped in the vertical direction but are free to propagate horizontally are affected by a space-dependent random mass density field. This effect depends on the direction along which the field is varying. A random field, which varies along the horizontal direction, does not couple vertically standing modes but increases their frequencies and attenuates amplitudes. These modes are coupled by a random field which depends on the vertical coordinate, but the dispersion relation remains the same as in the case of the deterministic medium.     

Gouy wave modes: undistorted pulse focalization in a dispersive medium

Gouy wave modes are linear waves with finite energy that propagate without distortion at any phase and group velocity through a focal region in a dispersive medium. These features make them potentially useful for the onset and control of nonlinear interactions.     

On the third harmonic generation in a medium with negative pump wave refraction

The propagation of the pump and its third harmonic pulses in a cubically nonlinear medium is considered theoretically, provided that the linear properties of the medium are characterized by a negative refractive index at the pump frequency and a positive refractive index at the harmonic frequency. For low-intensity interacting waves, the pump and third harmonic pulses propagate in opposite directions, but sufficiently intense pulses can produce a simulton—a solitary two-frequency wave that propagates in a certain direction as a single whole. The system of equations is investigated numerically for a model that, apart from the harmonic generation, includes the second-order group velocity dispersion and the nonlinear self- and cross-phase modulations of the interacting waves. The separation of the pump and harmonic pulses due to the difference in the directions of their group velocities and peculiarities of the Manley-Rowe relation for parametric processes in metamedia are discussed.     

Sound propagation and scattering in media with random inhomogeneities of sound speed, density and medium velocity

This review presents both classical and new results of the theory of sound propagation in media with random inhomogeneities of sound speed, density and medium velocity (mainly in the atmosphere and ocean). An equation for a sound wave in a moving inhomogeneous medium is presented, which has a wider range of applicability than those used before. Starting from this equation, the statistical characteristics of the sound field in a moving random medium are calculated using Born-approximation, ray, Rytov and parabolic-equation methods, and the theory of multiple scattering. The results obtained show, in particular, that certain equations previously widely used in the theory of sound propagation in moving random media must now be revised. The theory presented can be used not only to calculate the statistical characteristics of sound waves in the turbulent atmosphere or ocean but also to solve inverse problems and develop new remote-sensing methods. A number of practical problems of sound propagation in moving random media are listed and the further development of this field of acoustics is considered.     

Scattering of phase-conjugate ultrasonic waves by microinclusions in a liquid flow

The paper presents the results of experimental and theoretical studies of processes of phase-conjugate ultrasonic wave propagation in a liquid flow containing gas microbubbles. It is shown that a signal from a phase-conjugate wave, which is recorded by a transceiving transducer, contains information on the flow velocity of scatterers and their concentration. In this case, the flow velocity is determined both in the presence and absence of moving scattering objects. A theory developed on the basis of the generalized reciprocity principle for a moving inhomogeneous medium represents the main experimentally observed features of the formation of signals from a phase-conjugate wave scattered by a disperse liquid flow.     

Non-linear peristaltic transport of a Newtonian fluid in an inclined asymmetric channel through a porous medium

Peristaltic transport of an incompressible viscous fluid in an inclined asymmetric channel through a porous medium is studied under long-wavelength and low-Reynolds number assumptions. The flow is examined in a wave frame of reference moving with the velocity of the wave. The analytical solution has been obtained in the form of a stream function from which the axial velocity and pressure gradient have been derived. The results for the pressure drop and shear stress have also been computed numerically. The effects of various physical parameters are discussed through graphs and the phenomenon of trapping is also discussed. Comparison of various wave forms (namely sinusoidal, triangular, square and trapezoidal) on the flow is discussed.     

Sound propagation and scattering in media with random inhomogeneities of sound speed,density and medium velocity

Abstract

This review presents both classical and new results of the theory of sound propagation in media with random inhomogeneities of sound speed, density and medium velocity (mainly in the atmosphere and ocean). An equation for a sound wave in a moving inhomogeneous medium is presented, which has a wider range of applicability than those used before. Starting from this equation, the statistical characteristics of the sound field in a moving random medium are calculated using Born-approximation, ray, Rytov and parabolic-equation methods, and the theory of multiple scattering. The results obtained show, in particular, that certain equations previously widely used in the theory of sound propagation in moving random media must now be revised. The theory presented can be used not only to calculate the statistical characteristics of sound waves in the turbulent atmosphere or ocean but also to solve inverse problems and develop new remote-sensing methods. A number of practical problems of sound propagation in moving random media are listed and the further development of this field of acoustics is considered.     

Reflection–refraction of attenuated waves at the interface between a thermo-poroelastic medium and a thermoelastic medium

Phenomenon of reflection and refraction is considered at the plane interface between a thermoelastic medium and thermo-poroelastic medium. Both the media are isotropic and behave dissipative to wave propagation. Incident wave in thermo-poroelastic medium is considered inhomogeneous with deviation allowed between the directions of propagation and maximum attenuation. For this incidence, four attenuated waves reflect back in thermo-poroelastic medium and three waves refract to the continuing thermoelastic medium. Each of these reflected/refracted waves is inhomogeneous and propagates with a phase shift. The propagation characteristics (velocity, attenuation, inhomogeneity, phase shift, amplitude, energy) of reflected and refracted waves are calculated as functions of propagation direction and inhomogeneity of the incident wave. Variations in these propagation characteristics with the incident direction are illustrated through a numerical example.     

Wave scattering in a multiscale random inhomogeneous medium

In this paper, using the Fock method of the fifth parameter and weighted Fourier-transform with respect to the coordinates of the source and observer, an integral representation is obtained for the wave field in a randomly inhomogeneous medium without invoking the assumption about small-angle propagation. Random trajectory variations to a first approximation are taken into account in calculating the partial wave phase (the expression under the integral sign). The expressions for the field in a medium with different-scale irregularities and for the scintillation index, obtained using this integral representation, are compared with known results. The good agreement with results from the theory of single scattering in a medium with background irregularities, and with investigations of the scintillation index made in terms of Rytov's method and path integrals, indicates that it is possible to use the approach developed in this study to describe the effects of simultaneous influence of different-scale irregularities.     

非均匀可激介质中的螺旋波

以Barkley模型为对象,研究了可激介质的非均匀性对螺旋波斑图形成的影响.该模型中各参数与可激介质的属性密切相关,通过参数涨落的正态分布来刻画非均匀性,数值研究了单参数以及多参数涨落的正态分布情形下螺旋波斑图的形成.研究表明,可激介质的非均匀性对于螺旋波波纹的粗细及疏密程度有较大影响.参数涨落分布的方差越大,形成的螺旋波波纹越粗糙.对于两参数均匀分布的极端情形,当参数分布大于某一范围,无法形成螺旋波.这些都与螺旋波旋转的角频率密切相关.螺旋波旋转的角频率越大,螺旋波波纹越粗,同时波纹越密集;反之,螺旋波 关键词： 螺旋波 非均匀介质 Barkley模型     

Moving near-gap solitons in the nonlinear optical medium

For a one-dimensional nonlinear optical medium with a periodic refraction index, new two-parameter soliton solutions of electrodynamics equations have been found. These solutions represent two interacting waves that propagate in two opposite directions. The oscillation frequency of each wave may fall either into the forbidden gap in the linear spectrum or outside it, and the group velocity may vary from zero to a maximal value that is determined by the parameters of the medium. Algebraic soliton solutions have been found as the limit of the nonlinear solutions, when the nonlinear wave frequency tends to the frequency of one of the linear-spectrum branches.     

Evolution of acoustic waves in channels with permeable-wall regions in an inhomogeneous porous medium

The evolution of acoustic waves that propagate in cylindrical channels containing permeable regions and surrounded with a porous medium is studied. The quantitative and qualitative features of the wave dynamics are determined in relation to the condition of the inhomogeneous porous medium. In particular, cases when the channel is surrounded with radial fractures or with a low-permeability mudcake are considered.     

Positive-, negative-, and orthogonal-phase-velocity propagation of electromagnetic plane waves in a simply moving medium: Reformulation and reappraisal

Reformulating the issue of planewave propagation in a simply moving, dielectric-magnetic medium that is isotropic in the co-moving reference frame, using the Lorentz transformations of electric and magnetic fields and not the Minkowski constitutive relations-we reaffirm that plane waves which have positive phase velocity in the co-moving frame of reference can have negative phase velocity in certain non-co-moving frames of reference. Furthermore, this phenomenon occurs whether the medium is dissipative or not. For a fixed propagation direction, orthogonal phase velocity arises only at a unique velocity of the non-co-moving frame.