Perturbation theory results for the diffuse scattering of light from two-dimensional randomly rough metal surfaces

Abstract

Using the unitarity and reciprocity preserving formulation of Brown et al a perturbation treatment, correct to fourth order in the surface profile function, is given for the scattering of electromagnetic waves from a weakly rough, two-dimensional, random metal surface. In this formulation the boundary conditions on the electromagnetic fields are satisfied using the extinction theorem in conjunction with the Rayleigh hypothesis and the vector equivalent of the Kirchhoff integral. The theory is applied to, and results are presented for, several different types of rough surfaces which are characterized by power spectra that are extensions to two-dimensional random surfaces of the power spectrum of some one-dimensional random surfaces recently fabricated by West and O'Donnell. These surfaces, which can be realized experimentally, favor coherent, interferent, multiple scattering of electromagnetic waves via surface plasmon polaritons in intermediate states, and clearly exhibit enhanced backscattering caused by the surface plasmon polariton mechanism. Theoretical results are presented for silver surfaces at optical wavelengths.     

The chemical nature of electron waves in metals — A basis for the study of heterogeneous catalysis

The tight-binding method is used to describe the electronic waves of metals in the atomic orbital language familiar to chemists. It is shown that (in both fcc and bcc crystals) k vectors with components (0, 0, 1) or (1, 1, 1) carry hybrids between the s waves and Z² waves whose axis Z is parallel to the direction of the wave vector. In particular the higher-energy hybrid waves are strongly pointed along the wave vector direction. Furthermore, using the finite cube model, with excellent analytical approximations to the orbitals, the existence of privileged wave vector directions perpendicular to the surface approached by an incoming substrate is demonstrated. A preliminary discussion of the favorable conditions for catalysis emphasizes the extremely favorable role of such pointed hybrids if their sub-band lies (empty) just above the Fermi level of the metal.     

New phenomena in the propagation of optical waves through random media

Abstract

A review is presented of some new and exciting phenomena regarding the multiple scattering of optical waves in random systems. In particular, the author develops the important role played by the vector nature of the wave on memory effects (the ‘polarization memory effect’), correlations and statistical fluctuations (‘microstatistics’). He also describes the recent progress on the effect of a restricted geometry on correlation phenomena and nonRayleigh statistics.     

On the theory of the diffraction of light by two parallel ultrasonic waves,one being then th harmonic of the other

Assuming the validity ofRaman andNath's preliminary theory, the amplitudes of the light diffracted by two parallel ultrasonic waves consisting of a fundamental tone and its n^th harmonic are compared in the following cases:

1. (1)

   the sound waves are superposed;

2. (2)

   the sound waves are situated side by side.

The diffraction patterns are approximately the same if the condition πnL/λ^*¦sin ?_s¦?1 is fulfilled, where sin?_s=?sλ/μ₀λ^*(s being an integer);λ is the wave-lenght of the incident light in vacuum, λ^* is the wave-lenght of the fundamental tone of the sound waves, μ₀ is the refractive index of the medium andL the width of the sound field. The good agreement between recent experiments ofMurty andRao in the arrangement of case (2) and theoretical results calculated in case (1) is thus justified. The theoretical confirmation of older experiments byPande, Pancholy andParthasarathy is thereby established at the same time.

     

Eigenfunction expansion method to characterize Rayleigh wave propagation in orthotropic medium with phase lags

ABSTRACT

The present paper deals with the propagation of Rayleigh surface waves in homogeneous, orthotropic thermoelastic half space in the context of three-phase lag model of thermoelasticity. A vector matrix differential equation is formed by employing normal mode analysis to the considered equations which is then solved by eigenfunction expansion method. The frequency equations for different cases are derived and the path of surface particles during Rayleigh wave propagation is found elliptical. Effect of phase lags on phase velocity, attenuation coefficient, and specific loss are presented graphically with respect to frequency as well as wave number.     

Traveling Wave Solutions of the Camassa-Holm and Korteweg-de Vries Equations

Abstract

We show that the smooth traveling waves of the Camassa-Holm equation naturally correspond to traveling waves of the Korteweg-de Vries equation.     

Symmetry Properties and Reduction of the Generalized Nonlinear System of Two-Phase Liquid Equations

Abstract

We consider discontinuous flows of relativistic magnetic fluid with a general equation of state that is not supposed to be normal in the sense of Bethe and Weyl. The criteria of admissibility of the shock waves without a supposition of the relativistic version of the convexity condition are obtained. The results are used to analyze the cases of perpendicular and parallel shock waves.     

Locally nonequilibrium magnetic excitations in insulators

The equation of motion for the magnetic moment vector M in a locally nonequilibrium medium is derived. The dispersion and attenuation of the coupled modes of the magnetic vector potential and magnetization are determined. It is shown that the continuous spectrum contains frequencies corresponding to undamped waves or constant-phase damped waves.     

Reflection and transmission of plane waves at the interface of pyroelectric bi-materials

A simple reflection and transmission theory of plane waves at the interface of pyroelectric media is studied in this paper. In an infinite homogeneous pyroelectric medium, there are four bulk wave modes: quasi-longitudinal (QL), two quasi-transversal (QT) and one temperature (T) waves, whose velocities depend on the frequency and incident angle. Simultaneously, a quasi-surface (QS) wave on each side of the interface of pyroelectric bi-materials will appear in the general reflection and transmission problem. The quasi-surface wave has the same wave vector component with the incident waves along the interface plane. So, the reflection and transmission problem is different with the propagation wave in the infinite homogeneous space, but it is still solvable. In the reflection and transmission problem, there are ten complex continuous conditions on the interface, which are satisfied by the bulk and quasi-surface waves together. Numerical calculations are performed for bi-material PZT-6B/BaTiO₃. Incidences of the quasi-longitudinal and quasi-transversal waves from the side of PZT-6B or BaTiO₃ medium are discussed. The reflection and transmission amplitude coefficients and energy flow ratios varying with the incident angle are examined.     

Resonances of intensities and oscillation frequencies in ring gas lasers. I

Narrow resonances of the intensities and oscillation frequencies of counterpropagating waves in the vicinity of the center of the quantum transition in a pure-isotope ring gas laser have been studied. It is shown that the origin of resonances is related to the presence of sources causing unequal losses and/or frequencies of the counterpropagating waves in the laser cavity. The resonance change of intensities, which is accompanied by the resonance behavior of the medium dispersion for each of the waves, is not related to resonance changes of the saturated gain coefficients of the nonlinear medium. The resonances are caused by the redistribution of energy between the waves. The character of resonance changes of frequencies and intensities depends on the nature of nonreciprocity present in the cavity.

     

A two-scale model from the point of view of the small-slope approximation

Abstract

General results for the scattering cross section following from the small-slope approximation (SSA) are applied to the case of two-scale surface roughness which can be represented as a superposition of small-scale and large-scale components. The purpose of the paper is to obtain analytically tractable results with obvious physical meaning which can be used for estimates prior to undertaking extensive numerical calculations according to exact unambiguous expressions of the SSA. The general case of vector (electromagnetic) or scalar (sound) waves is considered. The statistics of small-scale roughness is not assumed to be Gaussian (in any sense) or space-homogeneous, and the possible dependence of the statistics of small-scale roughness on a large-scale undulating surface is taken into account. As a result, a modified local spectrum of small-scale components of roughness enters into corresponding expressions for the scattering cross section. It is demonstrated that under appropriate conditions, the resulting formulae for the scattering cross section reduce to the conventional two-scale model.     

Reflection of spin and spin-elastic waves at the interface of a ferromagnetic half-space

This paper considers the reflection of pure spin and spin-elastic (or magneto-elastic) waves at the interface of a ferromagnetic half-space and a vacuum. For pure spin waves two cases are considered, with exchange effects, and without. It is shown that when exchange effects are taken into account, volume spin waves in the ferromagnetic half space incident at the boundary with the vacuum generate a reflected volume spin wave, and an accompanying compound surface wave propagating along the boundary and consisting of two partial inhomogeneous spin waves in the ferromagnetic half-space and a partial magneto-static inhomogeneous surface wave in the vacuum. When exchange effects are neglected the incident wave generates only a reflected volume wave in the ferromagnetic half-space.

Reflection and transmission of spin-elastic (or magneto-elastic) waves has been considered only in the case of the absence of exchange effects. An incident volume wave generates a volume spin-elastic reflected wave and one inhomogeneous magneto-static accompanying surface wave.

Excitations of the magnetic field are not transmitted into the vacuum in both cases when the exchange effect is neglected. In all cases the reflection of a spin wave has the character of a full internal reflection.     

Refraction and reflection of sound at the boundary of a bubbly liquid

Reflection and refraction of acoustic waves at the interface between pure water and bubbly water are investigated for the case of oblique incidence. From an analysis of analytic solutions, it is concluded that, for a wave incident on the interface from the side of a bubbly liquid, a critical angle of incidence, which depends on the frequency and the parameters of the disperse system, exists, so that, at angles of incidence exceeding the critical one, the wave is totally reflected from the interface.

     

Entanglement of the l- and the r-photons in an anisotropic crystal

Light incident onto an anisotropic crystal is divided into the ordinary and the extraordinary waves which vibrate in two perpendicular directions. Because of the tensor property of the dielectric constant, the direction of the electric displacement is not parallel to the vector of the incident electric field. An optical torque is induced by incidence of the linearly polarized light and propagating through the crystal. The optical torque tends to rotate the directions of eigenvibration which results in self-modulation of the ordinary and the extraordinary waves, and causes an energy splitting of the left (l)-, and the right (r)-handed circularly polarized waves in the crystal. The l- and the r-photons are correlated through the optical torque, which are found to be in an entanglement state.     

Anisotropy of electrooptical interaction in LiNbO3 crystals

Results of studying the conditions for optimum electrooptical (EO) interaction in lithium niobate crystals are presented. Analytical formulas are obtained for calculating refractive indices of natural waves and their polarizations for basis X-, Y-, and Z-cuts of crystals for arbitrary orientations of the wave vector of an optical wave. Conditions are found for the appearance of intermode EO interaction causing the orientation of polarization plane of natural waves to become a function of the external electric field.     

Localized waves of the coupled cubic–quintic nonlinear Schrdinger equations in nonlinear optics

We investigate some novel localized waves on the plane wave background in the coupled cubic–quintic nonlinear Schr o¨dinger(CCQNLS) equations through the generalized Darboux transformation(DT). A special vector solution of the Lax pair of the CCQNLS system is elaborately constructed, based on the vector solution, various types of higherorder localized wave solutions of the CCQNLS system are constructed via the generalized DT. These abundant and novel localized waves constructed in the CCQNLS system include higher-order rogue waves, higher-order rogues interacting with multi-soliton or multi-breather separately. The first-and second-order semi-rational localized waves including several free parameters are mainly discussed:(i) the semi-rational solutions degenerate to the first-and second-order vector rogue wave solutions;(ii) hybrid solutions between a first-order rogue wave and a dark or bright soliton, a second-order rogue wave and two dark or bright solitons;(iii) hybrid solutions between a first-order rogue wave and a breather, a second-order rogue wave and two breathers. Some interesting and appealing dynamic properties of these types of localized waves are demonstrated, for example, these nonlinear waves merge with each other markedly by increasing the absolute value of α.These results further uncover some striking dynamic structures in the CCQNLS system.     

Analysis and Calculations of Forbidden Regions for Transverse-Electric-Guided Waves in the Three-Layer Planar Waveguide with Photonic Metamaterial

Abstract

In this article, the modal theory was used to analyze transverse electric waves in the three-layer planar waveguide with photonic metamaterial. The formulas for the electric fields of transverse electric modes in this structure have been proposed. There always exist two forbidden regions for transverse electric waves in the three-layer planar waveguide with photonic metamaterial. The complete set of modes of all possible solutions for the transverse electric waves in the three-layer planar waveguide with photonic metamaterial had been analyzed and discussed. Similar processes can be extensively used to predict the propagation characteristics of TM waves in the three-layer planar waveguide with photonic metamaterial. The analytical and numerical results show excellent agreement.     

Coupling of counterpropagating light waves in low-symmetry photorefractive crystals

Coupling of two counterpropagating coherent light waves in tin hypothiodiphosphate (Sn₂P₂S₆, SPS) is usually strongly inhibited because of severe space charge limitations. Analysis of two-beam coupling gain is performed for different orientations of the grating vector in this monoclinic crystal that takes into account the anisotropy of dielectric permittivity. Gain enhancements are predicted and demonstrated experimentally for several nontraditional orientations of counterpropagating waves.     

Surface-type waves on the boundary of a metal with a plasma-molecular medium

The influence of the molecular subsystem on the properties of surface-type waves (STW’s) propagating along a plasma-metal boundary is examined with consideration of the thermal motion of the electrons. The dynamics of the molecular subsystem is described using the equation for the polarization vector, which is equivalent to a quantum-mechanical treatment of a rarefied gas with phenomenological consideration of the dissipation. A dispersion equation for surface-type waves is obtained. The molecular subsystem influences both the phase velocity of the waves and the penetration depth. In the case of a weakly ionized medium there is a forbidden frequency band for surface-type waves. Zh. Tekh. Fiz. 67, 47–49 (December 1997)     

On the theory of the radiation of an electron moving in the field of two plane waves and a magnetic field

The motion and radiation of electrons in a homogeneous magnetic field and the field of two plane waves propagating along the vector of the magnetic field intensity are considered. The law of motion and expressions for the total power, frequencies, and angular spectral distribution of the electron radiation intensity are obtained. An analysis is carried out of the results obtained in the case of small intensities of the plane waves. It is shown that the presence of the plane waves has a considerable effect on the characteristics of synchroton radiation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 105–110, August, 1977.