Diffraction of a Plane Electromagnetic Wave by an Infinite Dihedral Wedge with a Magnetodielectric-Coated Cylinder at the Apex

We present a technique for obtaining a rigorous solution to the problem of diffraction of a plane electromagnetic wave by an infinite dihedral wedge with a magnetodielectric-coated cylinder at the apex. In the case of an E-polarized incident wave, we obtain a closed-form solution of the problem and present the results of exact calculations of the far-zone diffracted field for wide ranges of the structure parameters. In particular, it is shown that if the wedge apex is loaded with only a magnetodielectric cylinder, then the diffracted field for the very long-wavelength incident wave is not affected by the dielectric permittivity of the cylinder and the wave-incidence angle, but is affected only by the opening angle of the wedge, the diameter of the dielectric coating in terms of the free-space wavelength, the magnetic permeability of the coating, and the electric properties of the surrounding medium. If a half-plane or a wedge-shaped part are added to a single cylinder, then the backscattering coefficient of such a structure decreases, but the discovered resonance variation in the backscattering coefficient of the cylinder in the long-wavelength range becomes more pronounced.     

Diffraction of a Guided Mode of a Dielectric Waveguide

Using the finite-difference time-domain method, we solve the problem of diffraction of a guided mode of a planar dielectric waveguide by an arbitrary-shaped body. Particular results are obtained for the scatterers in the form of isolated circular and elliptic cylinders and metal strips. We calculate the reflection and transmission coefficients of the mode along with the field structure in the near zone. Comparison with the results obtained by expansion in terms of plane waves is performed for a test problem of diffraction of the mode by a circular metal cylinder.     

Electromagnetic analysis of cylindrical invisibility cloaks and the mirage effect

We present a finite-element analysis of a diffraction problem involving a coated cylinder enabling the electromagnetic cloaking of a lossy object with sharp wedges located within its core. The coating consists of a heterogeneous anisotropic material deduced from a geometrical transformation as first proposed by Pendry [Science 312, 1780 (2006)]. We analyze the electromagnetic response of the cloak in the presence of an electric line source in p polarization and a loop of magnetic current in s polarization. We find that the electromagnetic field radiated by such a source located a fraction of a wavelength from the cloak is perturbed by less than 1%. When the source lies in the coating, it seems to radiate from a shifted location.     

Laser Generation of Surface Waves on Cylinder with a Slow Coating

An analytical model of acoustic field excited by a pulsed-laser line source on a coated cylinder is presented. Surface wave dispersive behaviours for a cylinder with a slow coating are analysed and compared with that of a bare cylinder. Based on this analysis, the laser-generated transient response of the perturbed Rayleigh wave and the higher modes of steel cylinder with a zinc coating are calculated from the model using residue theory and FFT technique. The theoretical result from the superposed waveform of the perturbed Rayleigh wave and higher modes agree well with the waveform obtained in experiment. The results show that the model and numerical method provide a useful technique for quantitatively characterizing coating parameters of coated cylinder by the laser generated surface waves.     

Exact diffraction calculation from fields specified over arbitrary curved surfaces

Calculation of the scalar diffraction field over the entire space from a given field over a surface is an important problem in computer generated holography. A straightforward approach to compute the diffraction field from field samples given on a surface is to superpose the emanated fields from each such sample. In this approach, possible mutual interactions between the fields at these samples are omitted and the calculated field may be significantly in error. In the proposed diffraction calculation algorithm, mutual interactions are taken into consideration, and thus the exact diffraction field can be calculated. The algorithm is based on posing the problem as the inverse of a problem whose formulation is straightforward. The problem is then solved by a signal decomposition approach. The computational cost of the proposed method is high, but it yields the exact scalar diffraction field over the entire space from the data on a surface.     

Obtaining of preset electrostatic fields in a quasi-electrode system

A method for obtaining electrostatic fields of a preset form in a quasi-electrode cylindrical system is considered. “Distributed” electrodes (filamentary conductors) make it possible to solve the inverse boundary-value problem, viz., to preset an azimuthal electric potential distribution over the cylinder surface for obtaining the required field in the cylinder, thus ensuring a larger working region as compared to an obviously electrode system.     

A theory of the diffraction of an electromagnetic wave by a plane screen

The problem of the diffraction of an arbitrarily polarized electromagnetic plane wave by a perfectly conducting plane screen of infinitesimal thickness is reduced to scalar problems by the method known from earlier papers. The wave field diffracted either by a screen of infinite extent which is perforated by an aperture of arbitrary size and shape or by a complementary screen is then described by means of the bra-vectors, ket-vectors and linear operators introduced by the present author in one of his preceding papers.     

A finite-element method for solving a scalar problem of diffraction by two-dimensional scatterers of complex structure

A scalar problem of diffraction by two-dimensional domains of complex form is solved by the finite-element method. The good agreement of the numerical results with the exact solution to the problem of plane wave diffraction by an infinite cylinder is demonstrated. In conclusion, examples of the capabilities of the program are demonstrated.     

柱状导体衍射级数

本文对于任意形状的光滑柱状理想导体的衍射提出一种级数解法。方法的原理与层变媒质的Bremmer级数相似:先以内接多面稜柱代替上述光滑柱体;将此稜柱产生的衍射场展为一个级数。级数之首项为几何光学场;级数之第二项为稜柱的所有各稜产生的元衍射场之和,其中每个元衍射场皆取Sommerfeld问题的解,即将该稜之两侧面视为半无限大的平面。上述每一元衍射场皆投射在其相邻稜上,并在相邻稜上发生衍射;这一衍射场随之又投射在下一个相邻稜上而发生衍射;依此类推。按此方式依次被各稜所衍射的场称为“主掠射元场”。级数之第三项即为这些主掠射元场之和。被某一稜A衍射而后又在相邻的稜B上衍射的某一元场,同样会回射到A上;然后以上述“主掠射”方式传递下去,这样的场称为“一次反射元场”。级数的第四项即为这些一次反射元场之和。依此类推。一般说来,级数之第m项(m>3)为m-3次反射元场之和。元场在任何一稜上的衍射皆取Sommerfeld解。当内接多面稜柱之面数趋向无穷,且每面之宽度趋向零时,多面稜柱即趋于光滑柱体,且级数每一项的求和变为一个积分。这时该级数总和之极限即为原问题之解。对级数之前三项单独进行了推导。对于一般的第m项(m>3),导出了一个递推公式。最后,对该级数之收敛条件进行了探讨。     

Wave diffraction by a concave statistically rough surface

We consider a statistically rough impedance surface that is concave on average in contrast to a plane. Backscattering from such a surface is considered based on the small perturbation theory method. The diffraction problem is divided into two parts which are considered separately: the problem of scattering by small roughness (assumed to be local) and the propagation of incident and scattered fields over a smooth large-scale concave surface. In contrast to the 'two-scale' scattering model, the zero-order unperturbed wavefield is not assumed to be specularly reflected from the local tangent plane to the smooth surface, but it is a solution of a corresponding diffraction problem. Two particular cases of smooth surfaces are considered: first, the inner surface of a concave cylinder with a constant radius and finite angular pattern, and second, a compound surface that consists of a coupled half-plane and the cylindrical surface mentioned above. In a geometrical optics limit and with propagation at low grazing angles, the analytical results for a zero-order (unperturbed) field are obtained for these two cases in the form of a series over multiple specular reflected fields. It is shown that these non-local processes lead to the essential increase in the backscattering cross section in comparison with the two-scale model and tangent-plane approach.     

Scattering by random rough surfaces: Study of direct and inverse problem

In order to study the problems of scattering by rough metallic surfaces, we have used Maxwell’s equations in covariant form within the framework of a non-orthogonal coordinates system adapted to the geometry of the problem. Electromagnetic fields are written in Fourier’s integral form. The solution is found by using a perturbation method applied to the smooth surface problem; this is fully justified when the defects are of small magnitude.For the direct problem, the mean value of diffraction intensity is obtained for random rough surfaces of finite conductivity by computer simulation.In the case of the inverse problem, the reconstruction of the profile of the metal surface from values of the diffraction intensity, obtained by simulation, is found using an iterative algorithm.     

Scattering of electromagnetic waves by a chiral cylinder

We consider the problem of three-dimensional diffraction of electromagnetic waves excited by an elementary source on a chiral infinite cylinder of arbitrary radius. Effective scattering cross sections of a chiral cylinder in the case of two-dimensional diffraction are numerically analyzed. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 10, pp. 872–883, October 2008.     

Shortwave asymptotic behavior of the solution of the problem of diffraction by a convex body. III

Based on an integral representation found previously for the shortwave asymptotic behavior of the solution of the problem of diffraction by a smooth convex cylinder, the author derives asymptotic estimates for the diffraction field in the illuminated region and in a shadow region.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 15, No. 1, pp. 98–111, January, 1972.     

Temperature field dynamics inside a blood vessel subjected to the action of laser radiation

The dynamics of the temperature field in a subcutaneous blood vessel subjected to laser radiation is calculated by a method similar to that used previously but taking into account the heat exchange at the interface between the bloodstream and surrounding tissues. The distribution function of heat sources is determined based on the solution of the problem of diffraction of electromagnetic radiation from a circular cylinder. Regimes of irradiation of skin required for blocking the bloodstream under corresponding medical indications are modeled. In this case, the optimal exposure times depend on the vessel diameters and, for radiation at a wavelength of 530 nm, vary from tens to hundreds of microseconds.     

Scalar Field in Cosmology: Potential for Isotropization and Inflation

The important role of scalar field in cosmology was noticed by a number of authors. Due to the fact that the scalar field possesses zero spin, it was basically considered in isotropic cosmological models. If considered in an anisotropic model, the linear scalar field does not lead to isotropization of expansion process. One needs to introduce scalar field with nonlinear potential for the isotropization process to take place. In this paper the general form of scalar field potentials leading to the asymptotic isotropization in case of Bianchi type-I cosmological model, and inflationary regime in case of isotropic space-time is obtained. In doing so we solved both direct and inverse problem, where by direct problem we mean to find metric functions and scalar field for the given potential, whereas, the inverse problem means to find the potential and scalar field for the given metric function. The scalar field potentials leading to the inflation and isotropization were found both for harmonic and proper synchronic time.     

Wave diffraction by a concave statistically rough surface

Abstract

We consider a statistically rough impedance surface that is concave on average in contrast to a plane. Backscattering from such a surface is considered based on the small perturbation theory method. The diffraction problem is divided into two parts which are considered separately: the problem of scattering by small roughness (assumed to be local) and the propagation of incident and scattered fields over a smooth large-scale concave surface. In contrast to the ‘two-scale’ scattering model, the zero-order unperturbed wavefield is not assumed to be specularly reflected from the local tangent plane to the smooth surface, but it is a solution of a corresponding diffraction problem. Two particular cases of smooth surfaces are considered: first, the inner surface of a concave cylinder with a constant radius and finite angular pattern, and second, a compound surface that consists of a coupled half-plane and the cylindrical surface mentioned above. In a geometrical optics limit and with propagation at low grazing angles, the analytical results for a zero-order (unperturbed) field are obtained for these two cases in the form of a series over multiple specular reflected fields. It is shown that these non-local processes lead to the essential increase in the backscattering cross section in comparison with the two-scale model and tangent-plane approach.     

Regularization of boundary integral equations in the problems of wave field diffraction by curved boundaries

A regularization of the exact Fredholm integral equations for the field or its derivative on a scattering surface is proposed. This approach allows one to calculate the scattering or diffraction of pulsed wave fields by curved surfaces of arbitrary geometry. Mathematically, the method is based on the replacement of the exact Fredholm integral equations by their truncated analogs, in which the contributions of the geometrically shadowed regions are cancelled. This approach has a clear physical meaning and provides stable solutions even when the direct numerical solution of mathematically exact initial integral equations leads to unstable results. The method is mathematically substantiated and tested using the problem of plane-wave scattering by a cylinder as an example.     

Inverse faraday effect in plasmonic films

It is shown that the inverse Faraday effect appears in the case of surface plasmon polariton propagation near a metal/paramagnetic interface. The inverse Faraday effect in nanostructured periodically perforated metal-dielectric films increases because of the excitation of surface plasmon polaritons. In this case, a stationary magnetic field is amplified by more than an order of magnitude compared to the case of a smooth paramagnetic film. The distribution of an electromagnetic field is sensitive to the wavelength and the angle of incidence, which allows one to effectively control the local magnetization that arises due to the inverse Faraday effect.     

Damped waves in a cylinder shadow

The sound field in the region of a deep shadow behind an impedance cylinder is analyzed for the case of plane wave diffraction by the cylinder surface. The main part of the field is represented by a cylindrical wave that has a complex index determined from the boundary conditions and decays with the angular coordinate. An expression for the amplitude of this wave is determined by extracting it from the total field formed in the shadow region. It is demonstrated that this wave approximates more closely the total field behind the cylinder, as compared to the least damped wave in the field representation obtained on the basis of the Watson transform. A way to improve the sound barriers is indicated.     

Extraction of the acoustic component of a turbulent flow exciting a plate by inverting the vibration problem

An improvement of the Force Analysis Technique (FAT), an inverse method of vibration, is proposed to identify the low wavenumbers including the acoustic component of a turbulent flow that excites a plate. This method is a significant progress since the usual techniques of measurements with flush-mounted sensors are not able to separate the acoustic and the aerodynamic energies of the excitation because the aerodynamic component is too high. Moreover, the main cause of vibration or acoustic radiation of the structure might be due to the acoustic part by a phenomenon of spatial coincidence between the acoustic wavelengths and those of the plate. This underlines the need to extract the acoustic part. In this work, numerical experiments are performed to solve both the direct and inverse problems of vibration. The excitation is a turbulent boundary layer and combines the pressure field of the Corcos model and a diffuse acoustic field. These pressures are obtained by a synthesis method based on the Cholesky decomposition of the cross-spectra matrices and are used to excite a plate. Thus, the application of the inverse problem FAT that requires only the vibration data shows that the method is able to identify and to isolate the acoustic part of the excitation. Indeed, the discretization of the inverse operator (motion equation of the plate) acts as a low-pass wavenumber filter. In addition, this method is simple to implement because it can be applied locally (no need to know the boundary conditions), and measurements can be carried out on the opposite side of the plate without affecting the flow. Finally, an improvement of FAT is proposed. It regularizes optimally and automatically the inverse problem by analyzing the mean quadratic pressure of the reconstructed force distribution. This optimized FAT, in the case of the turbulent flow, has the advantage of measuring the acoustic component up to higher frequencies even in the presence of noise.