Electromagnetic Excitation of a Spherical Medium by an Arbitrary Dipole and Related Inverse Problems

Abstract

A piecewise homogeneous spherical medium is excited by an external or internal electric dipole with arbitrary location and polarization. The dyadic Green's function of the medium is determined analytically. Then, the vector electric fields and far‐field patterns are obtained. Low‐frequency approximations of the far‐field patterns are subsequently derived, which encode the dipole's locations coordinates and polarization components in the different orders of the associated expansions. This fact enables the establishment of far‐field inverse scattering algorithms referring to the electromagnetic interior or exterior excitation of a small sphere by an arbitrary dipole. Inverse medium and inverse source problems are considered concerning, respectively, the determination of the scatterer's material parameters and the dipole's characteristics. The developed inverse algorithms determine exactly the unknown parameters of problems fulfilling the low‐frequency assumption, which is indeed the case in most relevant applications, like, e.g., in biomedical imaging.

Analysis of Interaction Scattering Cross Sections and Their Physical Bounds for Multiple-Dipole Stimulation of a Three-Dimensional Layered Medium

“…10, we depict the overall cross section σ and total ISCS ratio σ T /σ versus the radius k 0 a 1 in case of a sphere with dielectric core of different radii a 2 excited by N = 4 internal sources in shell V 1 . For all the examined core's radii, the values of σ remain fairly the same and oscillate rapidly (after k 0 a 1 > 1.2); the latter is expected from the discussions of [21], [26]. The ratios σ T /σ descent smoothly for k 0 a 1 < 5, oscillate rapidly for k 0 a 1 > 5, and are not significantly affected by changes in the core's radii.…”

“…The associated boundary-value problems are solved by employing the methodology developed in [24]- [26], which combines the Sommerfeld's and T-matrix methods in conjunction with suitable eigenfunction expansions. This methodology is entirely analytical and does not require any restrictions on the problem's parameters.…”

Particle Swarm Optimization Algorithms with Applications to Wave Scattering Problems

“…The exact solution of the considered scattering problem was determined in [24][25][26] by means of a combined Sommerfeld and T-matrix methodology in conjunction with suitable eigenfunctions expansions. Specifically, the electric fields in each spherical shell are decomposed into primary and secondary components, which are then expressed as series of the spherical vector wave functions.…”

Particle Swarm Optimization of Layered Media Cloaking Performance

“…The exact solution of the scattering problem is determined analytically by applying a combined Sommerfeld T-matrix methodology, which is developed and analyzed in [11,12]. More precisely, the electric fields in each region of the problem are decomposed into primary and secondary components, which are then expressed as series of the spherical vector wave functions [13,14].…”