Total internal reflection at a boundary between vacuum and an optical medium with quasi-zero refractive index

It is shown that, on a surface of optical transparency of a medium with quasi-zero refractive index, surface optical waves traveling along the surface can be excited for different angles of incidence of external radiation. Expressions for the amplitudes of nonspecular reflection and transmission of light waves at an inhomogeneous boundary between two media are derived. Using these expressions, the boundary reflectance and transmittance for different angles of incidence and refraction can be calculated.     

Trapping of an electromagnetic wave by the boundary of created plasma

We discuss a new phenomenon of the electrodynamics of transient media, the trapping of electromagnetic radiation by the boundary of a transient plasma due to the conversion of the radiation into surface waves localized at the boundary. Calculations are done for an initial plane wave and for a beam of finite width in conditions where the boundary of the suddenly created (because of ionization) plasma half-space is perpendicular to the initial wavefront. Two frequency down-shifted surface waves traveling along the boundary in opposite directions are shown to be excited, as well as frequency up-shifted outgoing radiation and a time-independent mode in the form of a spatially inhomogeneous structure of dc currents and a magnetic field within the plasma half-space. We study the associated kinematic, amplitude, and energy relations. Finally, we establish that the most efficient trapping (up to 40% in energy) can be achieved with the forward (with respect to the direction of the initial wave propagation) surface mode and that the trapping is accompanied by concentration of electromagnetic energy at the plasma boundary. Zh. éksp. Teor. Fiz. 113, 1277–1288 (April 1998)     

Excitation of surface electrostatic waves in semibounded layered superconductors by a nonrelativistic electron beam

Excitation of potential surface waves by a nonrelativistic electron beam traveling in a vacuum space near the boundary of a layered superconductor is studied theoretically. Dispersion relations for surface waves at an arbitrary angle between superconductor layers and interface are obtained. Allowance is made for an arbitrary direction of wave propagation in the interfacial plane. Increments of kinetic and hydrodynamic instabilities are found. It is shown that absolute instability may occur.     

Nonlinear effects in trapped modes of standing waves on the surface of shallow water

It was shown that traveling waves may coexist with standing waves in a planar infinitely long channel filled by ideal liquid with a free surface. The standing waves are localized near a dynamic inclusion—a massive die on an elastic base. The amplitude of the traveling waves may be turned to zero by appropriately selecting the vibration frequency of the die. The standing waves arise because the vibration eigenfrequencies have a mixed spectrum; that is, the discrete and continuous spectra superpose. Nonlinear effects were observed for the first time when standing waves form in shallow water. In particular, a relationship between the die weight necessary to excite trapped modes, die dimensions, and vibration frequency was derived. It was shown that the nonlinear effects cause double-frequency traveling waves with amplitudes of the next order of smallness. These traveling waves vanish if the die geometry is properly chosen, as for the waves of the zeroth order.     

A distributed model for continuous-wave erbium-doped fiber laser

A distributed model of a continuous-wave erbium-doped fiber laser is discussed. The model is based on two contra-propagated traveling laser waves, and includes inhomogeneous pumping, excited state absorption at the pump and the laser wavelengths, amplified spontaneous emission and radial distribution of populations of erbium levels. It is shown that excited state absorption is a main limiting factor to the laser's efficiency. Moreover, consideration of radial distributions of erbium levels' populations in the model reduces laser efficiency and decreases optimal reflection of the laser output coupler. The modeling results are in excellent agreement with the experimental study on the EDFL efficiency.     

Nonlinear electrostatic surface waves in a semi-infinite plasma

The nonlinear equations which govern the filamentation of a large-amplitude high-frequency electrostatic surface wave are studied considering solutions in the form of stationary traveling waves. It is shown that solitary surface waves exist at certain amplitude and phase conditions.     

STEADY INTERNAL WATER WAVES WITH A CRITICAL LAYER BOUNDED BY THE WAVE SURFACE

In this paper we construct small amplitude periodic internal waves traveling at the boundary region between two rotational and homogeneous fluids with different densities. Within a period, the waves we obtain have the property that the gradient of the stream function associated to the fluid beneath the interface vanishes, on the wave surface, at exactly two points. Furthermore, there exists a critical layer which is bounded from above by the wave profile. Besides, we prove, without excluding the presence of stagnation points, that if the vorticity function associated to each fluid in part is real-analytic, bounded, and non-increasing, then capillary-gravity steady internal waves are a priori real-analytic. Our new method provides the real-analyticity of capillary and capillary-gravity waves with stagnation points traveling over a homogeneous rotational fluid under the same restrictions on the vorticity function.     

Reflection and refraction of light by a system of interfering atomic states

The boundary problem of nonlinear optics was investigated for a trial wave reflected (refracted) by an excited region of a nonlinear medium considered as a system of multilevel atoms in the spectrum of which there are two closely-spaced energy levels excited by a powerful quasi-resonant radiation. It is shown that under interference conditions of the atomic states in the field of the trial and resonance waves there exist three types of waves: an inverse wave and two polarization waves. By way of extension of the Ewald-Oseen procedure to this case a formula for the complex refractive index of a nonlinear medium for the three types of waves as well as a generalized extinction theorem have been obtained. It is shown that the trial wave can be amplified without inversion of the interfering atomic states and that the refractive index can be markedly changed at certain concentrations of atoms in the medium. General formulas for the amplitudes of the reflected and refracted waves have been obtained. Ul’yanovsk State University, 42, Tolstoi Str., Ul’yanovsk, 432700, Russia. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 65, No. 4, pp. 568–575, July–August, 1998.     

Evanescent Plane Waves in Multilayer Structures

We have considered evanescent plane waves in structures with a layer of a substance with ε, μ < 0 and with a layer of a well-reflecting metal, ε < 0, μ ≥ 1. Waves with increased amplitude as compared with the initial wave have been found to occur, due to which evanescent waves with wave number as in the initial wave but with increased amplitude arise behind these layers. A composite material with ε, μ < 0 at optical frequencies are proposed. Surface waves on a metal layer are considered in detail. It is shown that surface waves with a sufficiently arbitrary wave number can be excited. It is also shown that, on very thin layers, surface waves with wave number exceeding ten times that of a homogeneous plane wave in vacuum can be excited. Propagation losses are calculated. For a silver layer, the wave path can be from 30 up to 100 wavelengths. Practical use in developing techniques for optical transformations of short-wave surface waves in 2D space, similar to those in 3D space, are pointed out.     

Effect of surface electron scattering on the excitation of cyclotron waves in metals

Exact numerical calculations of the change in the surface impedance of a metal due to the excitation of cyclotron waves have been carried out for substantially different electron boundary conditions. It is shown that cyclotron waves can be used as a sensitive probe of the electron scattering at the surface of a metal.     

Reflection of retrograde waves within the cochlea and at the stapes

A number of authors [de Boer and Viergever, Hear. Res. 13, 101-112 (1984); de Boer et al., in Peripheral Auditory Mechanisms (Springer-Verlag, Berlin, 1986); Hear. Res. 23, 1-7 (1986); Viergever, in Auditory Frequency Selectivity (Plenum, New York, 1986), pp. 31-38; Kaernbach et al., J. Acoust. Soc. Am. 81, 408-411 (1987)] have argued that backward-traveling waves, in striking contrast to waves traveling forward towards the helicotrema, suffer appreciable reflection as they move through the basal turns of the cochlea. Such reflection, if present, would have important consequences for understanding the nature and strength of otoacoustic emissions. The apparent asymmetry in reflection of cochlear waves is shown, however, to be an artifact of the boundary condition those authors impose at the stapes: conventional cochlear models are found not to generate reflections of waves traveling in either direction even when the wavelength changes rapidly and the WKB approximation breaks down. Although backward-traveling waves are not reflected by the secular variation of the geometrical and mechanical characteristics of the cochlea, they are reflected when they reach the stapes. The magnitude of that boundary reflection is computed for the cat and shown to be a large, rapidly varying function of frequency.     

Excitation of surface elasticity waves in piezoelectric media by ion beams∗

Kinetically it has been shown that by considering a semi-bounded piezoelectric medium with hexagonal symmetry with an ion beam flowing on its free surface, the surface elasticity waves can be excited on their surface-vacuum interface as a result of the piezoelectric effect.     

Nonlinear modes and traveling waves of parametrically excited cylindrical shells

Donnel's equations are used to predict nonlinear vibrations of cylindrical shells, which are excited by parametric dynamical load. A multi-degree-of-freedom dynamical system of cylindrical shells is derived. The nonlinear modes of the parametrically excited system are treated. The analyses have been carried out both with and without dissipation, using the Harmonic Balance Method. These nonlinear modes correspond to the standing waves in the shell. Traveling waves are also analyzed in detail. We come to the conclusion that the behavior of the nonlinear modes and the traveling waves are similar.     

Large-time behavior of solutions of initial and initial-boundary value problems of a general system of hyperbolic conservation laws

We study the asymptotic behavior of the solution of the initial and initial-boundary value problem of hyperbolic conservation laws when the initial and boundary data have bounded total variation. It is shown that the solution converges to the linear superposition of traveling waves, shock waves and rarefaction waves. The strength and speed of these waves depend only on the values of the data at infinity.Results obtained at the Courant Institute of Mathematical Sciences, New York University while the author was a Visiting Member at the Institute; this work was supported by the National Science Foundation, Grant NSF-MCS 76-07039On leave from the University of Maryland, College Park, USA     

Formation of plasmon pulses in the cooperative decay of excitons of quantum dots near a metal surface

The formation of pulses of surface electromagnetic waves at a metal–dielectric boundary is considered in the process of cooperative decay of excitons of quantum dots distributed near a metal surface in a dielectric layer. It is shown that the efficiency of exciton energy transfer to excited plasmons can, in principle, be increased by selecting the dielectric material with specified values of the complex permittivity. It is found that in the mean field approximation, the semiclassical model of formation of plasmon pulses in the system under study is reduced to the pendulum equation with the additional term of nonlinear losses.     

Laboratory experiment on kinetic Alfven waves in connection withphenomena in space plasmas

A laboratory experiment has been performed in connection with interesting phenomena in space plasmas such as geomagnetic pulsations in the magnetosphere or particle acceleration by the kinetic Alfven wave in field-aligned currents of the auroral circuit. Fast waves or MHD surface waves in a cylindrical finite-β plasma have been observed to be mode converted into kinetic Alfven waves at the Alfven resonance layer. The surface waves were excited using small loop antennas located at the edge of the inhomogeneous plasma to simulate those on the magnetosphere or plasmapause     

Chaotic particle motion under linear surface waves

We investigate the motion of infinitesimal particles in the flow field inside the fluid under a traveling surface wave. It is shown that, even for two-dimensional waves, a superposition of two or more traveling harmonic waves is enough to generate chaotic particle motion, i.e., Lagrangian chaos. (c) 1996 American Institute of Physics.     

Bulk Nonlinear Elastic Strain Waves in a Bilayer Coaxial Cylindrical Rod

The problem of the propagation of long nonlinear elastic strain waves in a bilayer coaxial cylindrical rod with an ideal contact between the layers has been considered. Expressions for transverse displacements through longitudinal displacements have been derived. The former satisfies free boundary conditions and continuity conditions for displacements and stresses at the interlayer interface with the desired accuracy. It has been shown how these expressions generalize the well-known plane-section and Love hypotheses for an isotropic homogeneous rod. An equation for the propagation of a nonlinearly elastic strain longitudinal wave has been derived, and its particular solution in the form of a solitary traveling wave has been studied.     

On the Existence of Traveling Waves in the 3D Boussinesq System

We extend earlier work on traveling waves in premixed flames in a gravitationally stratified medium, subject to the Boussinesq approximation. For three-dimensional channels not aligned with the gravity direction and under the Dirichlet boundary conditions in the fluid velocity, it is shown that a non-planar traveling wave, corresponding to a non-zero reaction, exists, under an explicit condition relating the geometry of the crossection of the channel to the magnitude of the Prandtl and Rayleigh numbers, or when the advection term in the flow equations is neglected.     

Rayleigh’s flow near a boundary between two liquids

The problem of a stationary acoustic flow that occurs in a standing wave field formed by two traveling monochromatic plane waves incident on a plane boundary between two liquids is solved theoretically. It is shown that the flow formed in such conditions noticeably differs from the known Rayleigh’s flow that occurs near a rigid plane.