The direct scattering problem of obliquely incident electromagnetic waves by a penetrable homogeneous cylinder

Abstract

In this paper we consider the direct scattering problem of obliquely incident time-harmonic electromagnetic plane waves by an infinitely long dielectric cylinder. We assume that the cylinder and the outer medium are homogeneous and isotropic. From the symmetry of the problem, Maxwell's equations are reduced to a system of two 2D Helmholtz equations in the cylinder and two Helmholtz equations in the exterior domain coupled on the boundary. We prove uniqueness and existence of this differential system by formulating an equivalent system of integral equations using the direct method. We transform this system into a Fredholm type system of boundary integral equations taking advantage of Maue's formula for hypersingular operators. Applying a collocation method we derive an efficient numerical scheme and provide accurate numerical results using as test cases transmission problems corresponding to analytic fields derived from fundamental solutions.

The electromagnetic scattering problem by a cylindrical doubly connected domain at oblique incidence: the direct problem

“…The scatterer is illuminated by a time-harmonic transverse magnetic polarized electromagnetic plane wave, the so-called oblique incident wave. The cylindrical symmetry and the homogeneity of the medium reduces the three-dimensional scattering problem (1) -(3) to a two-dimensional problem only for the z−components of the fields, see for instance [11,21,26].…”

“…For the convergence and error analysis, see [16]. We do not present here the parametrized forms of the integral operators (16) since they can be found in many works, we refer the reader to the books [8,17] and to [11,Section 4] for a complete list of all forms and special decompositions.…”

“…From a mathematical point of view, this scattering problem has also attracted considerable attention. Many methods have been considered for the numerical solution of this problem, see [4,24,25,27], but only recently the well-posedness of the direct problem has been addressed [11,21,26].…”

Body Shape and Complex Permittivity Determination Using the Method of Auxiliary Sources

“…In article [5], the author used the double Fourier transform for the inverse problem solution. Furthermore, there are some other analytical and numerical works related to this topic [6][7][8][9][10][11][12][13][14]. There are also other authors who used the Method of Auxiliary Sources to solve direct scattering problem [15][16][17].…”

The inverse electromagnetic scattering problem by a penetrable cylinder at oblique incidence

“…The transmission conditions now contain also the tangential derivatives of the electric and magnetic fields. In [10] we showed that the corresponding direct problem is well-posed and we constructed a unique solution using the direct integral equation method. A similar problem has been considered for an impedance cylinder embedded in a homogeneous [24], and in an inhomogeneous medium [22].…”