Diffraction Of Plane Wave Research Articles

Wiener-Hopf Analysis of the Plane Wave Diffraction by a Thin Material Strip: the Case of E Polarization

The E-polarized plane wave diffraction by a thin material strip is analyzed using the Wiener-Hopf technique together with approximate boundary conditions. An asymptotic solution is obtained under the condition that the thickness and the width of the strip are small and large compared with the wavelength, respectively. The scattered field is evaluated asymptotically based on the saddle point method and a far field expression is derived. Scattering characteristics of the strip are discussed via numerical results of the radar cross section.

Talbot carpet at the transverse plane produced in the diffraction of plane wave from amplitude radial gratings.

We experimentally demonstrate and theoretically predict a new and unprecedented optical carpet that includes all the geometric shadow and far-field and near-field diffraction patterns at the transverse plane in the diffraction from a radial grating illuminated by a plane wavefront. The main feature of using radial grating is the continuous change of the spatial period along the radial direction. Therefore, the geometric shadow, and the near-field and far-field diffraction regimes are mixed at various propagation distances, and the traditional definitions for the different diffraction regimes would not apply here. We show that for a given propagation distance, at a certain radial distance the shadow regime changes to the near-field regime and at another certain radial distance, the diffraction pattern changes from a near-field to a far-field case.

Coupled Plasmon Oscillations in Two Elliptic Silver Nanocylinders

A two-dimensional problem of plane wave diffraction in the optical band by two silver ribbons with elliptical cross-section is considered. The scattering and absorption spectra are calculated by rigorous numerical methods. Two variants of the relative position of the ribbons are considered. The influence of the distance between the ribbons on the form of the resonance response of the system is studied.

Singular integral equations in diffraction problem by an infinite periodic strip grating with one strip removed: E–polarization case

The E- polarized plane wave diffraction by the infinite periodic grating with removed strip is considered. The scattered field is represented as a sum of the field of the infinite periodic grating and the field of the correction currents excited due to extraction of a single strip. The problem is reduced to the dual integral equations relatively unknown spectral function of the correction field. After differentiation of these equations the singular integral equation with additional conditions with respect to the correction current density is obtained. For comparison, the single mode current approximation model is also presented. The currents on the strips and far-field distribution of correction current are analyzed.

Diffraction by a Narrow Cone in a Skew Incidence

The scalar problem of plane wave diffraction by a narrow cone is considered. The angle of the cone α and the angle of incidence are assumed to be small, and the field is studied in a boundary layer near the surface at distances z from the cone tip such that kz ~ α −2. The parabolic equation method is applied, and the leading order approximation is constructed in the form of an integral.

Account for the nonlocal effect in light scattering by plasmonic nanoparticles in the hybrid scheme of the discrete sources method

A three dimensional problem of plane wave diffraction on a plasmonic nanoparticle is considered, with account for the nonlocal effect. A solution is constructed on the basis of a modified computational scheme of the discrete sources method. A numerical study of the nonlocal effect influence on the scattering properties of spherical nanoparticles upon their deformation is conducted.

Solution of the Neumann Problem of Diffraction by a Strip Using the Wiener–Hopf Method: Short-Wave Asymptotic Solutions

Plane wave diffraction by a strip is considered by the Wiener–Hopf method and the simple short-wave asymptotic solutions are obtained. The Neumann boundary value problem is reduced to the solutions of the Fredholm integral equations of the second kind, and the exact solution in the form of the sum of infinite series has been found by the method of successive approximations. With the help of the saddle point method, the integral operators are calculated and the asymptotic solutions of system are found. The outcomes are compared with supra known asymptotic solutions taking into account tertiary diffraction. Quarternary diffraction was solved and the calculation methodology for the subsequent diffractions was shown.

Web-interface for HPC computation of a plane wave diffraction on a periodic layer

This article considers the problem of plane wave diffraction on a cylindrical layer with periodic surface and periodic permittivity distribution. The current work presents the developed web-interface for performing such simulation. Supercomputer computations were implemented using the MPI communication protocol and performed at the Hybri LIT cluster installed at the Laboratory of Information Technologies of the Joint Institute for Nuclear Research, Dubna, Russia. The computations utilized up to 48 computational cores of the cluster.

Diffraction of a plane electromagnetic wave by a two-layer finite array of small bodies of revolution

A three-dimensional vector problem of plane-wave diffraction by a two-layer finite array of perfectly conducting bodies of revolution is considered. The problem is solved under the assumption that the sizes of the elements of the array are small as compared to the wavelength. The approach proposed was tested by comparing the far-field patterns of an array with a small number of elements, calculated by two different methods. Angular dependences of the far-field patterns of arrays of elements in the form of spheres, oblate spheroids, and superellipsoids of revolution are constructed. Dependences of the plane-wave reflection and transmission coefficients on the angle of incidence for single-row finite and infinite arrays are presented.

Acoustic plane wave diffraction from a truncated semi-infinite cone in axial irradiation

The diffraction problem of the plane acoustic wave on the semi-infinite truncated soft and rigid cones in the case of axial incidence is solved. The problem is formulated as a boundary-value problem in terms of Helmholtz equation, with Dirichlet and Neumann boundary conditions, for scattered velocity potential. The incident field is taken to be the total field of semi-infinite cone, the expression of which is obtained by solving the auxiliary diffraction problem by the use of Kontorovich-Lebedev integral transformation. The diffracted field is sought via the expansion in series of the eigenfunctions for subdomains of the Helmholtz equation taking into account the edge condition. The corresponding diffraction problem is reduced to infinite system of linear algebraic equations (ISLAE) making use of mode matching technique and orthogonality properties of the Legendre functions. The method of analytical regularization is applied in order to extract the singular part in ISLAE, invert it exactly and reduce the problem to ISLAE of the second kind, which is readily amenable to calculation. The numerical solution of this system relies on the reduction method; and its accuracy depends on the truncation order. The case of degeneration of the truncated semi-infinite cone into an aperture in infinite plane is considered. Characteristic features of diffracted field in near and far fields as functions of cone's parameters are examined.

Heart diffraction.

A theoretical study of the plane-wave diffraction by a heart-like sharp-edge aperture corresponding to the involute of a circle is proposed here. Through the recently developed paraxial boundary diffraction wave theory, expressed via the language of catastrophe optics, the presence of pseudo-nondiffracting regions within the three-dimensional spatial intensity distribution of the diffracted wavefield is intuitively explained and quantitatively characterized. The results of some old, beautiful, but nearly forgotten, diffraction experiments have also been reconsidered from such a peculiar and rather unorthodox perspective.

Scattering of Plane and Cylindrical SH Waves by a Horseshoe Shaped Cavity

An analytical solution for diffraction of both plane and cylindrical SH waves induced by a horseshoe shaped cavity with an inverted arch is presented in this paper. The geometry of the cavity is assumed to be composed of two circular arcs. By introducing an auxiliary boundary, the whole physical region is divided into two computational regions. The scattered wavefield in the open region and the standing wavefield in the enclosed region are presented by means of the wave function expansion method. Both of the wavefields are given in terms of the wave function series with unknown coefficients. By applying the Graf’s addition formula, two systems of equations for seeking the unknowns are derived by taking advantage of the boundary conditions based on the region-matching strategy. The problem of wave scattering is finally solved after seeking the solutions of the two systems of equations through standard matrix techniques. Then the effects of the excitation frequency, the cavity embedment depth and cavity geometry are discussed. The differences in terms of ground motions under different excitations and the influence of source location under cylindrical waves are also examined.

Reflection coefficient of a dominant mode in a pentafurcated duct

This paper presents the diffraction of acoustic plane wave through a semi-infinite soft duct. The soft plates are enclosed symmetrically inside an infinite duct with hard boundary conditions. We fully emphasize the analysis of the behavior of the reflected field amplitude for the pentafurcated duct by applying the straightforward mode-matching technique. We also depict some graphical representations by determining the reflected field amplitude for various dimensions of the pentafurcated duct. We also present comparisons of results with the existing results of a hard pentafurcated duct problem. This research work will assist the future researchers in reducing noise effects in complicated devices and exhaust systems.

Scattering of ultrarelativistic electrons in ultrathin crystals

Quantum theory is proposed of high energy electrons scattering in ultrathin crystals. This theory is based upon a special representation of the scattering amplitude in the form of an integral over the surface surrounding the crystal, and on the spectral method of determination of the wave function. The comparison is performed of quantum and classical differential scattering cross-sections in the transitional range of crystal thicknesses, from those at which the channeling phenomenon is not developed up to those at which it is established. It is shown that in this thickness range the quantum scattering cross-section, unlike the classical one, contains sharp peaks corresponding to some specific scattering angles, that is connected with the diffraction of the incident plane wave onto the periodically distributed crystal atomic strings. It is shown that the value of the scattering cross-section in the peaks varies periodically with the change of the target thickness. We note that this must lead to a new interference effect in radiation that is connected with the rearrangement of incident wave packet in transitional area of crystal thicknesses.

Very compact focal spot in the near-field of the fractional axicon

Theoretical and numerical analysis of the plane wave diffraction by a fractional axicon with less than one degree is performed in the near-field considering the evanescent waves. The first type of Rayleigh-Sommerfeld integral transformation is used in the calculations. It is shown that the stationary phase method application is not sufficiently precise to obtain analytical estimates in the near-field diffraction. Additional corrections have been introduced to clarify the solution. They have provided qualitative agreement of theoretical and numerical results. It is shown that by using a fractional axicon, which degree is significantly less than one, in the area of the evanescent waves the light spot with both longitudinal and transverse sizes of one tenth of wavelength is formed.

Дифракция плоской волны на золотом наноцилиндре конечных размеров

Дифракция плоской волны на золотом наноцилиндре конечных размеров

Wiener-Hopf Analysis of the Plane Wave Diffraction by a Thin Material Strip

Wiener-Hopf Analysis of the Plane Wave Diffraction by a Thin Material Strip

X-ray plane-wave diffraction effects in a crystal with third-order nonlinearity

The two-wave dynamical diffraction in the Laue geometry has been theoretically considered for a plane X-ray wave in a crystal with a third-order nonlinear response to the external field. An analytical solution to the problem stated is found for certain diffraction conditions. A nonlinear pendulum effect is analyzed. The nonlinear extinction length is found to depend on the incident-wave intensity. A pendulum effect of a new type is revealed: the intensities of the transmitted and diffracted waves periodically depend on the incidentwave intensity at a fixed crystal thickness. The rocking curves and Borrmann nonlinear effect are numerically calculated.

Analytical investigation of microwave resonances of a curling probe for low and high-pressure plasma diagnostics

The concept of ‘active plasma resonance spectroscopy’ (APRS) has attracted greater interest in recent years as an established plasma diagnostic technique. The APRS describes a class of related methods utilizing the intrinsic ability of plasma to resonate at or near the electron plasma frequency . The Curling probe (CP) as a novel realization of the APRS idea, is a miniaturized spiral slot embedded flatly in the chamber wall. Consequently, a plasma diagnostic technique with minimum disturbance and without metal contamination can be developed. To measure the plasma parameters the CP is fed with a weak frequency-swept signal from the exterior of the plasma chamber by a network analyzer which also records the response of the plasma versus the frequency. The resonance behavior is strongly dependent on the electron density and the gas pressure. The CP has also the advantage of resonating at a frequency greater than which is dependent on the spiral’s length. The double resonance characteristic gives the CP the ability to be applied in varying plasma regimes. Assuming that the spiralization does not have a considerable effect on the resonances, a ‘straightened’ infinite length CP has recently been investigated (Arshadi and Brinkmann 2016 Plasma Sources Sci. Technol. 25 045014) to obtain the surface wave resonances. This work generalizes the approach and models the CP by a rectangular slot-type resonator located between plasma and quartz. Cold plasma theory and Maxwell’s equations are utilized to compute the electromagnetic fields propagating into the plasma by the diffraction of an incident plane wave at the slot. A mathematical model is employed and both kinds of resonances are derived. The analytical study of this paper shows good agreement with the numerical results of the probe inventors.

Singular integral equations in diffraction problem by an infinite periodic strip grating with one strip removed

The H-polarized plane wave diffraction by the infinite periodic grating with removed strip is considered. In the formulation, the current induced on each strip is divided into two currents, the current on the infinite periodic strip grating and the correction current induced by the removal of a strip. The scattered field is inducted by these currents. The problem is reduced to the dual integral equations with respect to the unknown spectral function of the correction field, and then to the singular integral equation with additional conditions. The singular integral equation of infinite periodic grating is also presented. The near and far fields scattered by the grating are analyzed.