We develop a method for 3D doubly periodic electromagnetic scattering. We
adapt the Müller integral equation formulation of Maxwell's equations to
the periodic problem, since it is a Fredholm equation of the second kind. We
use Ewald splitting to efficiently calculate the periodic Green's functions.
The approach is to regularize the singular Green's functions and to compute
integrals with a trapezoidal sum. Through asymptotic analysis near the
singular point, we are able to identify the largest part of the smoothing
error and to subtract it out. The result is a method that is third order in
the grid spacing size. We present results for various scatterers, including
a test case for which exact solutions are known. The implemented method does
indeed converge with third order accuracy. We present results for which the
method successfully resolves Wood's anomaly resonances in transmission.
@article{1222716950,
author = {Nicholas, Michael J.},
title = {A higher order numerical method for 3-d double periodic electromagnetic
scattering problem},
journal = {Commun. Math. Sci.},
volume = {6},
number = {1},
year = {2008},
pages = { 669-694},
language = {en},
url = {http://dml.mathdoc.fr/item/1222716950}
}
Nicholas, Michael J. A higher order numerical method for 3-d double periodic electromagnetic
scattering problem. Commun. Math. Sci., Tome 6 (2008) no. 1, pp. 669-694. http://gdmltest.u-ga.fr/item/1222716950/