Diffraction of electromagnetic waves by a half-plane which is permeable to a stream of cold plasma

Diffraction of plane electromagnetic waves by a conducting half-plane located in an orthogonal stream of cold plasma is studied. It is assumed that the half-plane has almost no mechanical effect on the particles of the medium. (For example, the half-plane can be a model of a metal grid with fairly small cells.) The general solution of the problem has been obtained by the Wiener-Hopf-Fock technique. The scattering field containing waves of two types is studied analytically and numerically. The behavior of these waves away from the half-plane edge is analyzed. It is shown that the electric field at the edge is finite, and the shadow area is absent under certain conditions. Radiophysical Research Institute of the State University of St. Petersburg., Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40. No. 4, pp. 399–419, April, 1997.     

Diffraction of electromagnetic waves by a nonconducting half-plane in a hot plasma

The diffraction of transverse and longitudinal plane waves by a thin nonconducting perfectly rigid half-plane in a hot plasma is examined. The general solution of the problem and asymptotic formulas for the far zone are found. It is shown that they are significantly simplified for frequencies well above the plasma frequency. The behavior of the field near the edge is analyzed.St. Petersburg State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 37, No. 12, pp. 1503–1511, December, 1994.     

Magnetic line source diffraction by a conductive half-plane in an anisotropic plasma

An integral theory that is associated with the scattered fields is considered for the solution of H-polarized line source diffraction by a conductive half-plane, which is surrounded by an anisotropic plasma. As the anisotropy does not affect an E-polarized incident wave, only one polarization case is considered. The cold plasma medium is characterized by the dielectric tensor. The constant external magnetic field producing the anisotropy in a cold plasma is applied parallel to the edge of the half-plane. The total, scattered, and diffracted waves are derived in terms of the Fresnel functions. Therefore, finite magnitude values at the transition boundaries are obtained. The wave behaviours are investigated numerically for different quantities of the medium.     

Acoustic diffraction by a half-plane in a viscous fluid medium

We consider the diffraction of a time-harmonic acoustic plane wave by a rigid half-plane in a viscous fluid medium. The linearized equations of viscous fluid flow and the no-slip condition on the half-plane are used to derive a pair of disjoint Wiener-Hopf equations for the fluid stresses and velocities. The Wiener-Hopf equations are solved in conjunction with a requirement that the stresses are integrable near the edge of the half-plane. Specific wave components of the scattered velocity field are given analytically. A Padé approximation to the Wiener-Hopf kernel function is used to derive numerical results that show the effect of viscosity on the velocity field in the immediate vicinity of the edge of the half-plane.     

Rayleigh Waves in a Homogeneous Isotropic Half-Plane with a Periodic Edge

Doklady Physics - The existence of Rayleigh waves propagating along the periodic boundary of a homogeneous isotropic half-plane with an arbitrary edge profile is proved. It is shown that a periodic...     

On the possible mechanism of the jet noise intensification near a wing

A qualitative model of the mechanism of intensification of jet noise issuing from a nozzle located near a wing is proposed. A two-dimensional model problem on the diffraction of a plane acoustic wave at the edge of a nozzle nozzle located near a half-plane simulating the wing edge is formulated. It is shown that diffraction on the wing edge of Kelvin-Helmholtz instability waves developing from the edge of the nozzle can lead to the significant intensification of the acoustic energy radiated into the far field.     

SOUND SCATTERING BY A HARD HALF-PLANE: EXPERIMENTAL EVIDENCE OF THE EDGE-DIFFRACTED WAVE

In this short note, some experimental results are presented on the diffraction of a spherical way by a hard half-plane. This study was conducted with the aim to give evidence to the existence of the edge-diffracted wave. The sound source used in this experimental study is a condenser microphone operating in a reverse way. The wave emitted by a sound source propagates in space and hits a thin aluminium sheet with a straight edge, considered as an idealization of the hard half-plane. The resulting impulse response includes among others a wave diffracted by the edge of the half-plane, which is compared to its theoretical prediction. This latter is calculated from the exact Biot and Tolstoy solution to the problem of diffraction of a spherical wave by a hard wedge. Relatively satisfactory agreement is found between theory and experiment.     

Diffraction of cylindrical waves by an ideally conducting wedge in an anisotropic plasma

The problem of diffraction of cylindrical waves by an ideally conducting wedge in an anisotropic plasma is formulated and solved. The integral equations for the field are reduced to function equations, which are solved with the aid of a special function that is introduced. The properties of this function are studied. The general solution is represented as a double contour integral in the plane of a complex variable. The radiation field and surface waves for a number of special cases are analyzed: a source of cylindrical waves on an edge; at infinity; etc. Diffraction in a half-plane is studied separately.     

Dynamic stress around a cylindrical nano-inhomogeneity with an interface in a half-plane under anti-plane shear waves

Taking into account the size of the nanostructure, the effect of surface/interface stiffness on the dynamic stress around a cylindrical nano-inhomogeneity embedded in an elastic half-plane subjected to anti-plane shear waves is investigated. The boundary condition at the straight edge of the half-plane is traction free, which is satisfied by the image method. The analytical solutions of displacement fields are expressed by employing a wave function expansion method. The addition theorem for a cylindrical wave function is applied to accomplish the superposition of wave fields in the two half-planes. Analyses show that the effect of the interface properties on the dynamic stress is significantly related to the nano-scale distance between the straight edge and the center of the cylindrical nano-inhomogeneity. The frequency and incident angle of incident waves and the shear modulus ratio of the nano-inhomogeneity to matrix also show different effect on the dynamic stress distribution when the inhomogeneity shrinks to nano-scale. Comparison with the existing results is also given.     

The distribution of equilibrium magnetization currents in systems with dimensional quantization in a finite magnetic field

The distribution of equilibrium magnetization currents in two-dimensional bounded systems placed in an external magnetic field is studied. A half-plane, a quantum disk, and a wide quantum ring are considered. The passage from classical to quantizing magnetic fields is investigated. The edge currents near the boundary of the half-plane are shown to experience damped (far from the boundaries) spatial oscillations related to the Fermi electron wavelength. The region occupied by currents was found to narrow with increasing field. Apart from these oscillations, the current contains a component that smoothly changes with distance but oscillationally depends on the position of the Fermi level relative to the Landau levels. The suppression of the oscillations by temperature is studied. The spatial distribution of the current in a circular disk and a ring is shown to significantly depend on the position of the Fermi level.     

Study of the Radiation Capability of a Perfectly Conducting Half-Plane Excited by a Slot Perpendicular to the Conductor Edge

Radiophysics and Quantum Electronics - We solve the problem of excitation of an infinite, perfectly conducting half-plane by an external field in the slot line, which is perpendicular to the edge...     

Scattering and diffraction of a plane wave by a randomly rough half-plane*

Abstract

The scattering and diffraction of a TE (transverse electric) plane wave by a randomly rough half-plane are studied by a combination of three techniques: the Wiener-Hopf technique, the small perturbation method and a probabilistic method based on the shift-invariance of a homogeneous random function. By use of the D^a-Fourier transformation based on the shift-invariance, it is shown that the scattered wave is written by an inverse Fourier transformation of a homogeneous random function with a complex parameter. For a small rough case, such a random function with a complex parameter is expanded in a perturbation series and then the first-order solution is obtained exactly in an integral form. The first-order solution involves two physical processes such that the edge-diffracted wave is scattered by the randomly rough plane and the scattered wave, due to roughness, is diffracted by the half-plane. The solution is transformed into a sum of the Fresnel integrals with complex arguments, an integral along the steepest descent path and a branch-cut integral, which are evaluated numerically. Then, intensities of the coherently scattered wave and incoherent wave are calculated in the region near the edge and illustrated in figures.     

A theoretical study of the efficiency of instability wave excitation in a two-dimensional nozzle edge model

The paper considers a model problem of instability wave generation that occurs at a tangential discontinuity leaving the edge of a half-plane because of a specially adjusted external action, which models the basic characteristics of an active action on a jet by means of small-size actuators. The dependence of the instability wave amplitude on both the degree of spatial boundedness of the external action and its position with respect to the edge is investigated.     

Magnetic Edge States in Transition Metal Dichalcogenide Monolayers

JETP Letters - We developed theory of the magnetic edge states in a half-plane of transition metal dichalcogenide monolayer. The main qualitative feature of such system that distinguishes it from...     

On the physical reality of edge sources

In the celebrated Sommerfeld's rigorous solution to the half-plane problem, a condition fully demonstrated states that the edge neither radiates nor absorb energy. So, the well known Grimaldi's phenomenon, the shining of the edge, is claimed as an “optical illusion” (literally optische Täuschung) in his original paper. This paper deals with an apparent contradiction about this matter showing experimentally that the edge acts as a real source.     

Control over the instability wave in terms of the two-dimensional model of a nozzle edge

The problem of generation of an instability wave leaving the edge of a half-plane that separates an immobile medium from a moving medium is considered. It is assumed that the instability wave is initiated by an acoustic wave arriving from the moving medium. The possibility of suppressing the instability wave by another acoustic wave incident from the nonflowing medium is considered. It is shown that the suppression is always possible by adjusting the amplitude and phase of the control perturbation to the parameters of the instability wave.     

Trajectory-Based Interpretation of Laser Light Diffraction by a Sharp Edge

In the diffraction pattern produced by a half-plane sharp edge when it obstructs the passage of a laser beam, two characteristic regions are noticeable. There is a central region, where the diffraction of laser light appears in the region of geometric shadow, while intensity oscillations are observed in the non-obstructed area. On both sides of the edge, there are also very long light traces along the normal to the edge of the obstacle. The theoretical explanation of this phenomenon is based on the Fresnel–Kirchhoff diffraction theory applied to the Gaussian beam propagation behind the obstacle. In this paper, we supplement this explanation by considering electromagnetic flow lines, which provide a more complete interpretation of the phenomenon in terms of electric and magnetic fields and flux lines; at the same time, that can be related to average photon paths.     

Cylindrical wave diffraction at a half-plane in an anisotropic plasma

The problem of cylindrical wave diffraction at a half-plane located in a cold anisotropic plasma is considered. The exact solution is shown to be expressible in terms of Fresnel integrals.The author thanks M. S. Bobrovnikov for suggesting the problem and his interest.     

Scattering and diffraction of a plane wave by a randomly rough half-plane

The scattering and diffraction of a TE (transverse electric) plane wave by a randomly rough half-plane are studied by a combination of three techniques: the Wiener-Hopf technique, the small perturbation method and a probabilistic method based on the shift-invariance of a homogeneous random function. By use of the D^a-Fourier transformation based on the shift-invariance, it is shown that the scattered wave is written by an inverse Fourier transformation of a homogeneous random function with a complex parameter. For a small rough case, such a random function with a complex parameter is expanded in a perturbation series and then the first-order solution is obtained exactly in an integral form. The first-order solution involves two physical processes such that the edge-diffracted wave is scattered by the randomly rough plane and the scattered wave, due to roughness, is diffracted by the half-plane. The solution is transformed into a sum of the Fresnel integrals with complex arguments, an integral along the steepest descent path and a branch-cut integral, which are evaluated numerically. Then, intensities of the coherently scattered wave and incoherent wave are calculated in the region near the edge and illustrated in figures.     

TM plane wave scattering and diffraction from a randomly rough half-plane: (part II) An evaluation of the diffraction kernel

In a previous paper (part I), it has been shown that a random wavefield from a randomly rough half-plane for a TM plane wave incidence is written in terms of a Wiener-Hermite expansion with three types of Fourier integrals. This paper studies a concrete representation of the random wavefield by an approximate evaluation of such Fourier integrals, and statistical properties of scattering and diffraction. For a Gaussian roughness spectrum, intensities of the coherent wavefield and the first-order incoherent wavefield are calculated and shown in figures. It is then found that the coherent scattering intensity decreases in the illumination side, but is almost invariant in the shadow side. The incoherent scattering intensity spreads widely in the illumination side, and have ripples at near the grazing angle. Moreover, a major peak at near the antispecular direction, and associated ripples appear in the shadow side. The incoherent scattering intensity increases rapidly at near the random half-plane. These new phenomena for the incoherent scattering are caused by couplings between TM guided waves supported by a slightly random surface and edge diffracted waves excited by a plane wave incidence or by free guided waves on a flat plane without any roughness.