On the scattering of point‐generated electromagnetic waves by a perfectly conducting sphere, and related near‐field inverse problems

Abstract. The problem of scattering of elastic waves by a bounded obstacle in twodimensional linear elasticity is considered. The scattering problems are presented in a dyadic form. An incident dyadic field generated by a point source is disturbed by a rigid body, a cavity, or a penetrable obstacle. General scattering theorems are proved, relating the far-field patterns due to scattering of waves from a point source set up in either of two different locations. The most general reciprocity theorem is established, and mixed scattering relations are also proved. Finally, a relation between the incident and the scattered wave which refers to the mechanism of energy transfer of the scatterer, the so-called optical theorem, is established.

show abstract

“…For the case of electromagnetic scattering, similar problems regarding point-source excitation have been studied in [5], [6], [7].…”

mentioning

confidence: 99%

Scattering relations for point-generated dyadic fields in two-dimensional linear elasticity

2006

Self Cite

View full text Add to dashboard Cite

show abstract

“…For acoustic scattering, results on incident waves generated by a point source appear in [8][9][10] (see also the references therein, and, in particular, the related work by Dassios [17] and his co-workers).…”

Section: Introductionmentioning

confidence: 99%

“…For electromagnetic scattering, similar problems regarding point-source excitation have been studied in [7,8,10].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the scattering of two-dimensional elastic point sources and related near-field inverse problems for small discs

Athanasiadis

Pelekanos

Sevroglou

et al. 2009

Proceedings of the Royal Society of Edinburgh: Section A Mathem

View full text Add to dashboard Cite

The problem of scattering of a point-generated elastic dyadic field by a bounded obstacle or a penetrable body in two dimensions is considered. The direct scattering problem for each case is formulated in a dyadic form. For two point sources, dyadic far-field pattern generators are defined and general scattering theorems and mixed scattering relations are presented. The direct scattering problem for a rigid circular disc is considered, and the exact Green function and the elastic far-field patterns of the radiating solution in the form of infinite series are obtained. Under the low-frequency assumption, approximations for the longitudinal and transverse far-field patterns of the scattered field are obtained, in addition to an asymptotic expansion for the corresponding scattering cross-section. A simple inversion scheme that locates the radius and the position of a rigid circular disc, which is based on a closed-form approximation of the scattered field at the location of the incident point source, is proposed.

show abstract

“…The benefits of using the near-field quantity of the scattered field at the dipole point, in the development of inverse scattering algorithms for a perfectly conducting sphere excited by an exterior dipole have been pointed in [23]. Other implementations of near-field inverse problems are treated in [24] and [25, p. 133].…”

mentioning

confidence: 99%

A Low-Frequency Electromagnetic Near-Field Inverse Problem for a Spherical Scatterer

Tsitsas¹

2013

JCM

View full text Add to dashboard Cite

The interior low-frequency electromagnetic dipole excitation of a dielectric sphere is utilized as a simplified but realistic model in various biomedical applications. Motivated by these considerations, in this paper, we investigate analytically a near-field inverse scattering problem for the electromagnetic interior dipole excitation of a dielectric sphere. First, we obtain, under the low-frequency assumption, a closed-form approximation of the series of the secondary electric field at the dipole's location. Then, we utilize this derived approximation in the development of a simple inverse medium scattering algorithm determining the sphere's dielectric permittivity. Finally, we present numerical results for a human head model, which demonstrate the accurate determination of the complex permittivity by the developed algorithm. Mathematics subject classification: 34L25, 78A46, 78A40, 41A60, 33C05. / 440 N.L. TSITSAS(e.g., according to [8], k 0 a ≃ 1.3 × 10 −7 for f = 60 Hz and head's radius a = 10 cm). Besides, magnetic resonance imaging low-frequency applications are discussed in [9] for a spherical head with k 0 a ≃ 2 × 10 −6 . A brain electrical impedance tomography low-frequency model with k 0 a ≃ 1.9 × 10 −4 is investigated in [10]. Other applications stem from antennas implanted inside the head for hyperthermia or biotelemetry [11,12]. For extensive reviews on using dipoles inside spheres for brain imaging applications see [13] and [14].Far-field inverse scattering algorithms in the low-frequency region were established in [15] for acoustic scattering by a homogeneous sphere, due to an exterior point-source incident field, by utilizing essentially the distance of the source from the scatterer. Besides, for the pointsource or point-dipole excitation of a layered sphere the exact Green's function, the far-field low-frequency approximations, and related far-field inverse scattering algorithms were given in [16] for acoustic and in [17] for electromagnetic waves. Far-field inverse problems, using low-frequency plane waves impinging on a soft sphere, were analyzed in [18]. The identification of small dielectric inhomogeneities from scattering amplitude measurements was investigated in [19]- [22].The inverse problems, investigated in [15]- [19], are based on far-field measurements. The benefits of using the near-field quantity of the scattered field at the dipole point, in the development of inverse scattering algorithms for a perfectly conducting sphere excited by an exterior dipole have been pointed in [23]. Other implementations of near-field inverse problems are treated in [24] and [25, p. 133]. On the other hand, in [26] near-field inverse problems are analyzed concerning the determination of static point-sources and point-dipoles as well as acoustic point-sources located inside a homogeneous sphere. The inversion algorithms established in [26] use the moments obtained by integrating the product of the total field on the sphere's surface with spherical harmonic functions. Moreover, currents inside three-shell...

show abstract

On the scattering of point‐generated electromagnetic waves by a perfectly conducting sphere, and related near‐field inverse problems

Cited by 19 publications

References 10 publications

Scattering relations for point-generated dyadic fields in two-dimensional linear elasticity

Scattering relations for point-generated dyadic fields in two-dimensional linear elasticity

On the scattering of two-dimensional elastic point sources and related near-field inverse problems for small discs

A Low-Frequency Electromagnetic Near-Field Inverse Problem for a Spherical Scatterer

Contact Info

Product

Resources

About