Transfer and approximation of the impedance for time-harmonic Maxwell’s system in a planar domain with thin contrasted multi-layers

Article type: Research Article

Authors: Goffi, F.Z.^{; *} | Lemrabet, K. | Laadj, T.

Affiliations: AMNEDP Laboratory, Department of Mathematics, USTHB, Algiers, Algeria. E-mails: [email protected], [email protected], [email protected]

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: We consider the diffraction of time-harmonic electromagnetic waves by a perfectly conducting planar obstacle, coated by thin contrasted multi-layers of dielectric materials. A partial Fourier transform is used to derive an impedance condition that links the tangential components of the electric and magnetic fields, and transfers the boundary condition from the obstacle’s face to the other face of dielectric multi-layers. We first determine the exact formula and construct approximations of the impedance condition for one dielectric thin layer; after that, we extend the obtained result to multi-layers.

Keywords: Time-harmonic Maxwell’s system, scattering, thin dielectric layers, impedance operator

DOI: 10.3233/ASY-161391

Journal: Asymptotic Analysis, vol. 101, no. 1-2, pp. 1-15, 2017