โ Scribed by Toufic Abboud; Habib Ammari
No coin nor oath required. For personal study only.
We study the influence of the curvature of a circular cylindrical grating on the diffraction of a TE or TM polarized electromagnetic plane wave. For every ratio of the wave length to the period d, we prove the local approximation in the planar field by a plane infinite grating, when the radius R of the circular grating goes to ลฝ . infinity. The error estimates are optimal and of order O drR outside some transition regions corresponding to a tangent Bragg's mode or to transition between the region of direct illumination and the region of shadow, where the ลฝ ลฝ 2r3 1r3 .. error is like O dr R
. In each region, we calculate the first corrector, solution of an infinite plane grating diffraction problem.
๐ SIMILAR VOLUMES
A hierarchy of effective boundary conditions is derived for a Helmholtz equation with Dirichlet or Neumann boundary conditions. These generalized impedance boundary conditions approximate the effect of thin dielectric layers with perfectly conducting inclusions covering an object. Well-posedness of