Abstract
The extended boundary condition method (EBCM) was formulated for the perturbation of a source electric potential by a 3D object composed of a homogeneous anisotropic dielectric medium whose relative permittivity dyadic is positive definite. The formulation required the application of Green’s second identity to the exterior region to deduce the electrostatic counterpart of the Ewald–Oseen extinction theorem. The electric potential inside the object was represented using a basis obtained by implementing an affine bijective transformation of space to the Gauss equation for the electric field. The EBCM yields a transition matrix that depends on the geometry and the composition of the 3D object, but not on the source potential.
Highlights
Dating back more than a hundred years, the Ewald–Oseen extinction theorem [1, 2] states that when a 3D object is illuminated by an incident timeharmonic electromagnetic field, the electric and magnetic surface current densities induced on the exterior side of its surface produce an electromagnetic field that cancels the incident field throughout the interior region of the object
Green’s second identity yields an expression [13, 14] that was used by Farafonov [15] in 2014 to formulate the extended boundary condition method (EBCM) for the perturbation (i.e., “scattering”) of a source electric potential by a 3D object composed of a homogeneous isotropic medium
Our objective in this paper is to generalize the EBCM for electrostatic problems in which the perturbing 3D object is composed of a homogeneous anisotropic dielectric medium whose permittivity dyadic is positive definite
Summary
Dating back more than a hundred years, the Ewald–Oseen extinction theorem [1, 2] states that when a 3D object is illuminated by an incident timeharmonic electromagnetic field, the electric and magnetic surface current densities induced on the exterior side of its surface produce an electromagnetic field that cancels the incident field throughout the interior region of the object. Since a bilinear expansion of the free-space dyadic Green function is known [4, 5], the EBCM can be used to investigate scattering by an object composed of any linear homogeneous medium for which a basis exists to represent the electromagnetic field therein. Green’s second identity yields an expression [13, 14] that was used by Farafonov [15] in 2014 to formulate the EBCM for the perturbation (i.e., “scattering”) of a source electric potential (the electrostatic counterpart of an incident time-harmonic electromagnetic field) by a 3D object composed of a homogeneous isotropic medium. Our objective in this paper is to generalize the EBCM for electrostatic problems in which the perturbing 3D object is composed of a homogeneous anisotropic dielectric medium whose permittivity dyadic is positive definite.
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