On-axis Gaussian beam scattering by an eccentrically coated conducting cylinder

Based on the generalized Lorenz–Mie theory (GLMT) framework, an exact analytic solution to electromagnetic scattering by an eccentrically coated conducting cylinder is constructed, for oblique incidence of an on-axis Gaussian beam described by a localized beam model. The solution is found by the classical separation of variables technique and the translational addition theorem. For a tightly focused Gaussian beam propagating perpendicularly to the cylinder axis, numerical results of the normalized differential scattering cross section are presented, and the scattering characteristics are discussed concisely.     

Scattering of a Gaussian electromagnetic beam by a thin semiconducting cylinder

The scattering of a three-dimensional Gaussian electromagnetic beam by a thin (compared to the wavelength) semiconducting cylinder of infinite length is considered. Expressions for the scattered field and for the current induced in the cylinder are obtained. A numerical analysis of the distribution of the secondary current along the cylinder axis was made. It is shown that the dependence of the induced current on the distance along the cylinder axis becomes Gaussian as the aperture of the incident beam is increased.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 78–80, January, 1991.     

Scattering from a coated nihility circular cylinder placed in chiral metamaterial

The scattering of electromagnetic plane wave from a coated nihility circular cylinder placed in chiral metamaterial is investigated. The nihility cylinder is coated with chiral or chiral-nihility metamaterial and the medium hosting the coated cylinder is also considered as chiral or chiral-nihility metamaterial. The vector wave equation is used to find out the solution for the fields scattered from the concentric chiral ciruclar cylinders immersed in chiral metamaterial. Inner chiral cylinder is reduced to nihility cylinder taking permittivity and permeability approaching to zero with chirality parameter equal to zero. Coated perfect electric conductor (PEC)/perfect magnetic conductor (PMC) are obtained by taking very large value of permittivity/permeability of the inner cylinder. Numerical results for fields reflected from coated nihility cylinder are compared with those obtained for coated PEC/PMC cylinder. Our results for the special case of dielectric coated nihility/PEC cylinders in free space are shown to be in agreement with already published results thus validating the scheme of analysis.     

Scattering of a plane electromagnetic wave by an infinite wedge with a truncated circular cylinder coated coaxially with a magnetodielectric layer

We formulate and solve the problem of scattering of a plane electromagnetic wave by an infinite, perfectly conducting wedge with a truncated, perfectly conducting circular cylinder which is coated coaxially with a magnetodielectric layer and located along the wedge edge. The rigorous solution is obtained and reduced to a system of linear algebraic equations of the second kind for unknown coefficients of Fourier expansions of the scattered field. The results of calculating the scattered field in the far zone with a specified accuracy are presented for the case of an H-polarized wave. It is shown that for certain values of the electric radius of the cylinder, the backscattering cross section of such a structure has pronounced maxima.     

Scattering of gaussian beam by a ferrite cylinder

The scattering of a Gaussian beam by a ferrite cylinder is analyzed using two methods. The spatial pictures in the amplitude of the total Gaussian beam near the cylinder resulting from the two methods are both clarified and compared. The scattering by a ferrite cylinder coating a dielectric sleeve is also presented.     

Scattering of Lamb waves by a circular cylinder.

Following our previous attempt at the scattering from a cylinder in a slab to the incidence of a guided shear wave, we hereby discuss the scattering by an elastic cylinder embedded in an isotropic plate for a variety of bonding states to incidence of the fundamental Lamb wave modes S0 and A0 at the low-frequency regime. The plate is divided up into three regions by introducing two imaginary planes located symmetrically some distance from the cylinder and perpendicular to surfaces of the plate. The wave fields in various regions are expanded either into cylinder wave modes or into Lamb wave modes. A system of equations determining the coefficients of expansion is obtained according to the traction-free boundary conditions on the plate walls and the displacement and stress continuity conditions across the virtual planes. By taking an appropriate finite number of terms of the infinite expansion series and some selected points on the two properly chosen imaginary planes and the surfaces of the plate through convergence and precision tests, a matrix equation to numerically evaluate the expansion coefficients is found. Coefficients of the reflection and transmission versus the normalized radius of the cylinder in welded, slip, and cracked interfacial conditions are numerically computed. In the low-frequency range, the relative errors are found to be less than 1%. Contrast curves of the reflection coefficient for the cylinder of nearly all permissible size in perfect and imperfect interfacial bonding are shown and prominent differences are noted.     

Scattering of an arbitrarily oriented dipole field by an infinite and a finite length PEMC circular cylinder

Electromagnetic scattering from an infinite and a finite length PEMC circular cylinder, illuminated by an arbitrarily oriented dipole, is investigated theoretically. An electric dipole as a source of excitation is considered first, and then a magnetic dipole as a source of excitation is treated. In contrast to the case of an axially directed dipole, it is shown that no additional terms are needed to incorporate the cross-polarized component of the field for the case of radial and circumferential dipoles. Numerical verifications are presented to verify the validity of derived results and numerical code by comparing results with the published literature.      

Scattering of a First-Order Gaussian Beam by an infinite cylinder with arbitrary location and arbitrary orientation

The theory of scattering of a first-order Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation is presented. A component of the theory is the use of the theory of distributions.     

Scattering of Gaussian beam by a spherical particle with a spheroidal inclusion

A generalized Lorenz-Mie theory framework (GLMT) is applied to the study of Gaussian beam scattering by a spherical particle with an embedded spheroid at the center. By virtue of a transformation between the spherical and spheroidal vector wave functions, a theoretical procedure is developed to deal with the boundary conditions. Numerical results of the normalized differential scattering cross section are presented.     

Scattering of Gaussian beam by arbitrarily shaped inhomogeneous particles

A hybrid finite element-boundary integral method is applied to characterize the scattering of an arbitrarily incident-focused Gaussian beam by arbitrarily shaped inhomogeneous particles. Specifically, the Davis–Barton fifth-order approximation in combination with rotation Euler angles is used to represent the arbitrarily incident Gaussian beams. The finite element method is employed to formulate the fields in the interior region of the inhomogeneous particle, while the boundary integral equation is applied to represent the fields in the exterior region. The interior and exterior fields are coupled by means of the field continuity conditions. To reduce the computational burden, the frontal method and the multilevel fast multipole algorithm are adopted to solve the resultant matrix equation. Numerical results for differential scattering cross sections of several selected inhomogeneous particles are presented and can be served as further study on this subject.     

Scattering of antiplane shear waves by layered circular elastic cylinder

An exact analytical solution for the scattering of antiplane elastic waves by a layered elastic circular cylinder is obtained. The solution and its degenerate cases are compared with other simpler models of circular cylindrical scatterers. The effects of the geometrical and physical properties of the interphase are studied. Numerical results confirm the existence of a resonance mode in which the scatterer's core undergoes a rigid-body motion when the outer layer of the scatterer is very compliant. This resonance mode has been attributed [Liu et al., Science 289, 1734 (2000)] to a new mechanism for the band gap formed in the extremely low frequency range for phononic crystals made of layered spherical scatterers. Numerical results also show the existence of a similar resonance mode when the outer layer of the scatterer has very high mass density.     

Matching of a Gaussian beam into hollow oversized circular waveguides

A Gaussian beam entering an hollow oversized circular waveguide of dielectric or low-conductivity wall material is considered: a simple formula giving the optimal beam charac-teristics for the lowest losses in the guide is derived from an optical theory. This optimization depends on the geometry and the wall material of the guide. The formula is valid for small beam diameters at the guide entrance and for low losses inside the guide, which are conditions corresponding to usual cases. Physical interpretations are given. Comparisons with some experimental results show a good agreement with the theory. These results are of interest for waveguides lasers and waveguide transmission lines.     

Polarization singularities in near-field of Gaussian vortex beam diffracted by a circular aperture

Polarization singularities in the near-field of Gaussian vortex beams diffracted by a circular aperture are studied by a rigorous electromagnetic theory.It is shown that there exist C-points and L-lines,which depend on off-axis displacement parameters along the x and y directions,waist width,wavelength,and topological charge of the diffracted Gaussian vortex beam,as well as on propagation distance.The results are illustrated by numerical calculations.     

弹性波由吸收圆柱的散射

研究了弹性纵波照射粘弹圆柱产生的稳态散射,导出了简洁的散射场解析表达式,数值计算了吸收和非吸收圆柱散射作的散射截面。结果表明,对高速圆柱散射体,散射截面随Ka增加是光滑振荡变化的,吸收圆柱和非吸收圆柱散射截面特征类似。对低速圆柱散射体,振荡变化的散射截面上叠加有一系列狭窄峰,散射圆柱和周围介质的对应速度差别越大,这种狭窄峰也越多,越靠近极值附近,这些狭窄峰越密,圆柱存在吸收衰减时将降低这些狭窄峰。当散射圆柱和周围介质对应的纵波速度和横波速度差别很小时,散射截面为非规则的小幅度的谐振。     

Analysis of electromagnetic field due to a buried coated PEMC circular cylinder

An analytical solution for the scattering of an electromagnetic plane wave from a coated perfect electromagnetic conducting (PEMC) circular cylinder, buried in the dielectric half space, is presented. Scattering characteristics of a buried PEMC cylinder when coated by double-positive (DPS) or double-negative (DNG) materials is investigated. The cylinder as well as coating layer is of infinite length (2-D problem). Plane wave spectral representations of the fields have been used to solve the problem. Saddle point method is used to solve the integral arising in the analysis. All the multiple interactions between the buried geometry and the dielectric interface separating the two half spaces have been considered in the analysis. The derivation includes both TM and TE polarization cases. It is observed that the response of the coated PEMC cylinder can be used to detect the underground pipes and other buried objects having a cylindrical shape.     

Scattering of Gaussian beam by a spheroidal particle with a spherical inclusion at the center

An analytic solution to electromagnetic scattering by a spheroidal particle having a spherical inclusion at the center, for oblique incidence of a Gaussian beam, is obtained within the framework of the generalized Lorenz–Mie theory (GLMT). By virtue of a transformation between the spheroidal and spherical vector wave functions, a theoretical procedure is developed to deal with the boundary conditions. Numerical results of the normalized differential scattering cross section are evaluated.     

Scattering characteristics of conducting cylinder coated with nonuniform magnetized ferrite

An analytical technique, referred to as the scattering matrix method （SMM）, is developed to analyse the scattering of a planar wave from a conductolution for the nonuniform fering cylinder coated with nonuniform magnetized ferrite. The SMM srite coating can be reduced to the expressions for the scattering and penetrated coefficients in four particular cases： nonuniform magnetized ferrite cylinder, uniform magnetized ferrite-coated conducting cylinder, uniform ferrite cylinder as well as homogeneous dielectric-coated conducting cylinder. The resonant condition for the nonuniform ferrite coating is obtained. The distinctive differences in scattering between the nonuniform ferrite coating and the nonuniform dielectric coating are demonstrated. The effects of applied magnetic fields and wave frequencies on the scattering characteristics for two types of the linear profiles are revealed.     

Induced focusing and conversion of a Gaussian beam into an elliptic Gaussian beam

We have presented an investigation of the induced focusing in Kerr media of two laser beams, the pump beam and the probe beam, which could be either Gaussian or elliptic Gaussian or a combination of the two. We have used variational formalism to derive relevant beam-width equations. Among several important findings, the finding that a very week probe beam can be guided and focused when power of both beams are well below their individual threshold for self-focusing, is a noteworthy one. It has been found that induced focusing is not possible for laser beams of any wavelength and beam radius. In case both beams are elliptic Gaussian, we have shown that when power of both beams is above a certain threshold value then the effective radius of both beams collapses and collapse distance depends on power. Moreover, it has been found that induced focusing can be employed to convert a circular Gaussian beam into an elliptic Gaussian beam.     

Transient scattering by a circular cylinder

The scattering of transient plane waves by a circular cylinder is studied by using the Kirchhoff time-retarded potential boundary integral equation method. Two distinct problems are solved: (i) surface velocity potentials (or pressures) are found for rigid cylinders scattering ramp, ramp-step and Gaussian incident potential (or pressure) waves and (ii) surface velocities are found for free boundary (pressure release) cylinders scattering ramp, ramp-step and Gaussian incident velocity waves. The numerical schemes for both boundary conditions are very similar; since the same influence coefficients are used they differ only by a sign in the final formulation. Numerical results are readily obtained for the first few transit times. This approach is complementary to the usual modal approach in that it is best suited to early time values where the modal solutions converge most slowly.