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We consider scattering of a scalar complex source beam (CSB) by wide-angle cones. We derive an asymptotic solution that consists of a complex geometrical optics term augmented by complex tip diffraction, expressed as a local spectral integral. The results are compared to the exact solution, expressed as a complex conical-harmonics expansion. It is shown that unlike the narrow-cone case, considered...
The exact and asymptotic solutions to the scattering of a complex-source beam (CSB) by an acoustically soft or hard semi-infinite circular cone are explored. The exact solution, expressed as a spherical-harmonics expansion, is compared with the complex geometrical optics (CGO) solution augmented by a complex ray diffraction at the tip.
The spherical-multipole expansion of an inhomogeneous electromagnetic plane wave is derived by extending the spherical source coordinates v to a complex number. The analytical results are successfully validated by comparing the numerical evaluation of the multipole expansion with the corresponding closed-form results. The paper also contains a first result for an inhomogeneous plane electromagnetic...
The spherical-multipole analysis in sphero-conal coordinates in combination with a complex-source beam as the incident field has been utilized to derive the scattered electromagnetic far-field of a PEC plane angular sector. That canonical problem is of particular practical interest as many structures contain edge-like elements which cannot be treated by common asymptotic high-frequency techniques...
The spherical-multipole analysis is used to describe the statistics of an electromagnetic field in a shielding enclosure whose geometry is known by its statistic moments only. All of the statistical information is contained in a few scalar spherical-multipole amplitudes. Numerical results prove the correctness and usefulness of the approach. Moreover, the statistical spherical-multipole expansion...
The problem of an arbitrarily directed Gaussian beam (GB) illuminating an acoustically soft or hard semi-infinite circular cone is solved by using a complex source beam (CSB) whose waist and direction are defined by the real and imaginary parts of the source coordinate, respectively. The corresponding scalar boundary-value problem is solved by assigning a complex-valued source coordinate into the...
The paper deals with the scalar (acoustic) diffraction of a uniform complex-source beam (Uniform CSB) by an acoustically soft or hard semi-infinite circular cone. The diffracted field is found by evaluating the bilinear modal form of the cone's Green's function and by assigning suitable complex-valued source coordinates. The field expansion is valid everywhere in space including the waist of the beam...
The paper deals with the electromagnetic scattering and diffraction of a complex-source beam by a perfectly electrically conducting (PEC) semi-infinite circular cone. Particularly, we are interested in the diffraction by the tip of the circular cone as a function of various parameters (opening angle of the cone, angle of incidence, polarization). The results are important in the context of the application...
A particular goal of ultrasonic nondestructive testing comprises the identification of cracks, for instance, in welds. Set as an inverse scattering problem for elastic waves in solids it is essentially the crack tip scattering that delivers information about the crack size, which, on the other hand, is the crucial input for fracture mechanical life time estimation of the part under concern. Unfortunately,...
An analytical approach is presented to analyze the diffraction of a scalar complex-source beam (CSB) by an acoustically soft or hard semi-infinite circular cone. The beam is described by a spherical-multipole expansion and impinges exactly on the tip of the cone from an arbitrary direction. The numerical results include an investigation of the total field and of the convergence properties of the method.
The transient shielding effectiveness (SE) which originally has been defined for incident plane waves is investigated for the case of canonical near-field sources. For elementary sources (Hertzian and Fitzgerald dipoles, Huygens source) normalization factors are introduced such that the transient SE can be calculated from measured values of the standard electric and magnetic SE for any arbitrary form...
The paper describes the influence of small statistical variations in the physical parameters on the shielding behavior of an enclosure. The varying parameters are given in terms of the first few statistical moments of their distributions. From these the amplitudes of a spherical-multipole expansion are derived analytically. These multipole amplitudes contain the statistical properties of the electromagnetic...
A recently introduced theorem which states that the electromagnetic field in any homogeneous domain is uniquely determined by the knowledge of the electric or the magnetic field at one single point and a small neighborhood about that point can be used to investigate several possible applications in inverse-scattering theory and practice. In particular, the phenomenon of ldquonon-radiating sourcesrdquo...
A new systematic approach is described which can be used to efficiently obtain the frequency- and time-domain multipole amplitudes of the electromagnetic field due to an arbitrary linear antenna. In particular, the method is perfectly fitted for the finite-difference time-domain (FDTD) method, which is first used to obtain the time-domain multipole amplitudes of the antenna driven by a wide-band signal...
We introduce an efficient t-recursive algorithm to compute Legendre polynomials Pn(t) and their derivatives Pn(t) on the interval (0, 1) with fixed order nisinN. The numerical properties are discussed and related examples in Computational Electromagnetics are given. In particular, this method is well suited to enhance a recently proposed spherical-multipole based time-domain near-to-far-field transformation...
The contribution deals with a brief survey on selected parts of the theory and applications of multipole analysis in Electromagnetics. The theory will be explained exemplarily on the basis of the spherical-multipole analysis, including some remarks on the bilinear form of the dyadic Green's function and the addition theorems of the vector multipole functions. In addition to some well-known examples...
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