Nonlinear three-wave interaction in marine sediments

Nonlinear interaction of three acoustic waves in a sandy sediment is studied in the frequency range where there is a considerable wave velocity dispersion. The possibility of an experimental observation of the generation of a sound wave by two pump waves propagating at an angle to each other is estimated.     

Interaction of strongly nonlinear waves on the free surface of a dielectric liquid in a horizontal electric field

The nonlinear dynamics of the free surface of an ideal dielectric liquid with a large relative permittivity in a strong horizontal electric field has been considered. It has been demonstrated that the interaction between oppositely propagating solitary waves in arbitrary geometry is elastic: they conserve their energy and momentum. The interaction between waves has been numerically simulated with the use of conformal variables. It has been shown that the interaction deforms the waves; this effect is weak for waves with a relatively small amplitude: deformation for oppositely propagating waves with the identical shape is determined by the fourth power of their amplitude. At multiple collisions of strongly nonlinear waves, a tendency to the formation of singularities, i.e., points with a high energy density of the field, is observed.     

Propagation and interaction of nonlinear waves in a liquid with gas bubbles

The propagation and interaction of nonlinear solitonlike waves in a liquid with gas bubbles are considered using the Nakoryakov-Pokusaev-Shreiber two-wave equation. It is shown that these waves exist within the “opacity” window for linear waves. The interaction of such waves propagating in opposite directions may lead to their splitting into secondary localized waves.     

Superheterodyne Amplification of Sub Millimeter Electromagnetic Waves in an n-GaAs Film

The superheterodyne amplification of sub-millimeter electromagnetic waves in GasAs due to negative differential mobility is analyzed. The nonlinearity arises from the current and the magnetic field of the electromagnetic waves. The case of interaction of two traveling counter propagating electromagnetic waves and the following space charge wave in an n-GaAs film, placed onto i-GaAs substrate, is considered, under a 2D electron gas model. The simulation of this nonlinear interaction shows a certain amplification of the sub-millimeter electromagnetic wave.     

Excitation of excitons in semi-infinite solids with a nonrelativistic electron beam

The instability of an infinite thin electron beam propagating in vacuum over the surface of an isotropic nongyrotropic crystal is investigated. The possibilities of exciting additional longitudinal waves and polarization waves are analyzed. The dispersion laws of exciton-beam coupled waves are obtained. It is demonstrated that the interaction of the beam with the additional bulk longitudinal wave and the surface polarization wave leads to the appearance of the absolute instability.     

Wave reflection and transmission in beams

The vibrational behaviour of beam systems can be expressed in terms of waves of both propagating and near field types. A propagating wave incident upon a discontinuity gives rise to reflected and transmitted waves of both kinds whose amplitudes may be found from well-known reflection and transmission coefficients. In this paper the approach is extended to the case of incident near field waves, reflection and transmission matrices being derived for the cases of a point support and a change in section. Reflection at a boundary and the effects of applied excitations are also considered. It is seen that incident near fields can give rise to substantial propagating components. The application of the results to the analysis of free and forced vibration of beams is then demonstrated. By adopting this approach the effects of the interaction of the near fields with neighbouring discontinuities are fully included.     

Nonlinear wave interactions in porous media filled with a quantum fluid

The problem of the nonlinear interaction between the fourth sound and an acoustic wave propagating in a porous medium filled with superfluid helium is solved. Based on the Landau equations of quantum fluid dynamics and on the Biot theory of mechanical waves in a porous medium, nonlinear wave equations are derived for studying the aforementioned interaction. An expression is obtained for the vertex that determines the excitation of an acoustic wave by two waves of the fourth sound. The possibility of an experimental observation of this process is estimated.     

Nonlinear wave processes in media containing cracks partially filled with a viscous liquid

A nonlinear (in the cubic approximation) relaxation equation of state is derived for a rod containing cracks partially filled with an incompressible viscous liquid. The nonlinear effects of the self-action and interaction of low-and high-frequency longitudinal elastic waves propagating in such a rod are studied for the cases of identical and size-varied cracks. Linear and nonlinear acoustic parameters characterizing the self-action and interaction of elastic waves in a cracked rod are determined.     

Nichtlineare Wechselwirkung elektromagnetischer Wellen im Plasma mit konstantem Magnetfeld

The nonlinear interaction of waves in anisotropic plasmas is considered. Solving the hydrodynamics equations with a n-th order perturbation procedure, an equation for the nonlinear electric field is derived. The n-th order current produced by interaction of waves with lower order is represented by means of a nonlinear tensor of conductivity, which is calculated for n = 2. It is shown, that a miced plasma wave with combination frequencies is excited as the result of interaction of two transverse (ordinary) waves propagating perpendicular to the magnetic field.     

Near-field distributions of resonant modes in small dielectric objects on flat surfaces

We report numerical simulations of the coupling of waves, either propagating or evanescent, with the eigenmodes of dielectric nanocylinders and nanospheres upon substrates. The multiple interaction of light between these objects and the dielectric surface at which the evanescent waves are created is taken into account. In this way, we present an accurate procedure for predicting and controlling the creation of large field enhancements concentrated both within and near the nanoparticle compared with the angle of incidence and the state of polarization.     

Wave propagation phenomena from a spatiotemporal viewpoint: Resonances and bifurcations

By using biorthogonal decompositions, we show how uniformly propagating waves, togehter with their velocity, shape, and amplitude, can be extracted from a spatiotemporal signal consisting of the superposition of various traveling waves. The interaction between the different waves manifests itself in space-time resonances in case of a discrete biorthogonal spectrum and in resonant wavepackets in case of a continuous biorthogonal spectrum. Resonances appear as invariant subspaces under the biorthogonal operator, which leads to closed sets of algebraic equations. The analysis is then extended to superpositions of dispersive waves for which the (Fourier) dispersion relation is no longer linear. We then show how a space-time bifurcation, namely a qualitative change in the spatiotemporal nature of the solution, occurs when the biorthogonal operator is a nonholomorphic function of a parameter. This takes place when two eigenvalues are degenerate in the biorthogonal spectrum and when the spatial and temporal eigenvectors rotate within each eigenspace. Such a scenario applied to the superposition of traveling waves leads to the generation of additional waves propagating at new velocities, which can be computed from the spatial and temporal eigenmodes involved in the process (namely the shape of the propagating waves slightly before the bifurcation). An eigenvalue degeneracy, however, does not necessarily lead to a bifurcation, a situation we refer to as being self-avoiding. We illustrate our theoretical predictions by giving examples of bifurcating and self-avoiding events in propagating phenomena.     

Obliquely propagating dust-density plasma waves in the presence of an ion beam

Self-excited dust-density waves are experimentally studied in a dusty plasma under microgravity. Two types of waves are observed: a mode inside the dust volume propagating in the direction of the ion flow and a new mode propagating obliquely at the boundary between the dusty plasma and the space-charge sheath. A model for dust-density waves propagating at an arbitrary angle with respect to the ion-flow direction is presented, which explains the preference for oblique or parallel modes as a function of ion velocity.     

Nonlinear waves in porous media saturated with live oil

A nonlinear equation is obtained for waves propagating in porous media of arbitrary consolidation (relative rigidity) saturated with live (i.e., air-bearing) oil. The equation describes the evolution of fast and slow Biot-Frenkel longitudinal acoustic waves propagating in both directions and allows one to analyze the reflected waves and their interaction. For a wave of the second kind, the diffusion coefficient is determined. The dependences of the dispersion and dissipation parameters on the rigidity of the oil pool structure and on the depth of the oil pool occurrence are analyzed.     

Tunneling of evanescent waves into propagating waves

The tunneling of evanescent waves into propagating waves is related to the convolution of the high spatial frequencies of the source with those of the detectors. Such an approach is demonstrated by treating the evanescent waves which are diffracted from very narrow apertures in a plane screen (with dimensions much smaller than the wavelength) and are converted to propagating waves by tip detectors. The mechanism responsible for the conversion of evanescent waves into propagating waves is explained and a general formula for the conversion of evanescent waves into propagating waves is derived. PACS 42.25.Fx; 42.30.Kq; 42.25.Bs     

Coupling interaction between a single emitter and the propagating surface plasmon polaritons in a graphene microribbon waveguide

The coupling interaction between an individual optical emitter and the propagating surface plasmon polaritons in a graphene microribbon （GMR） waveguide is investigated by numerical calculations, where the emitter is situated above the GMR or in the same plane of the GMR, The results reveal a multimode coupling mechanism for the strong interaction between the emitter and the propagating plasmonic waves in graphene. When the emitter is situated in the same plane of the GMR, the decay rate from the emitter to the surface plasmon polaritons increases more than 10 times compared with that in the case with the emitter above the GMR.     

Cumulative second-harmonic generation of Lamb waves propagating in a two-layered solid plate

The physical process of cumulative second-harmonic generation of Lamb waves propagating in a two-layered solid plate is presented by using the second-order perturbation and the technique of nonlinear reflection of acoustic waves at an interface. In general, the cumulative second-harmonic generation of a dispersive guided wave propagation does not occur. However, the present paper shows that the second-harmonic of Lamb wave propagation arising from the nonlinear interaction of the partial bulk acoustic waves and the restriction of the three boundaries of the solid plates does have a cumulative growth effect if some conditions are satisfied. Through boundary condition and initial condition of excitation, the analytical expression of cumulative second-harmonic of Lamb waves propagation is determined. Numerical results show the cumulative effect of Lamb waves on second-harmonic field patterns.     

Three-wave Interactions in Magnetized Plasmas

This paper considers the nonlinear interaction between three waves in a warm magnetized twocomponent plasma. A general formalism is developed within a simple macroscopic theory in order to treat waves propagating in arbitrary directions. Some results of previous papers are generalized and discussed.     

Nonlinear TE-polarized quasi-surface waves in a symmetric optical waveguide with a nonlinear core

A theory of nonlinear polarized symmetric quasi-surface waves in a symmetric planar structure with a nonlinear core and linear coatings has been proposed. The nonlinearity of the core is caused by exciton-photon interaction and optical exciton-biexciton conversion. The dispersion laws for propagating waves have been obtained and studied.     

Visual characteristics of inhomogeneous acoustic waves

Experimentally obtained visualizations of propagating inhomogeneous acoustic waves driven by zero-order antisymmetric Lamb waves (flexural waves) in water are presented. The inhomogeneous waves are visualized by optical holographic interferometry. A series of photographs show the evolution in time of instantaneous acoustic pressure distributions associated with propagating inhomogeneous waves. The photographs reveal characteristic features of flexurally driven inhomogeneous waves such as transversely attenuated wavefronts oriented perpendicularly to the plate boundary and a phase propagation velocity along the boundary approximately equal to the plate wave velocity (250 meters/second). Effects due to the dispersive nature of the flexural plate waves are also noted in the photographic series. Features distinguishing these subsonic, inhomogeneous surface waves (also called trapped or evanescent waves) from the leaky, lateral or head wave and also from incompressible fluid motions associated with low frequency vibrations of fluid loaded plates are identified. The relevance of inhomogeneous acoustic waves driven by subsonic flexural waves to practical sound-structure interaction problems is discussed.     

Propagation of electromagnetic waves in periodic structures with superconducting layers having electrodynamic parameters in the nonlinearity range of the dynamic mixed state

The propagation of electromagnetic waves in type-II superconductor-insulator periodic structures is studied for the case when the superconductor falls into the nonlinearity range of the dynamic mixed state described in the framework of the Larkin-Ovchinnikov theory. A dispersion relation for waves propagating in different directions is derived. It is shown that the electromagnetic waves can be amplified via interaction with a moving lattice of Abrikosov vortexes.