Affiliations: [a] The Blackett Laboratory, Imperial College London,
London SW7 2EZ, UK. E-mail: s.r.lguenneau@imperial.ac.uk
| [b] California Institute of Technology, Applied and
Computational Mathematics, Pasadena CA 91125, USA. E-mail:
geuzaine@acm.caltech.edu
| [c] Institut Fresnel, UMR 6133, Faculté de
Saint-Jérôme case 162, F13397 Marseille Cedex 20, France. Tel.: +44 04 91
28 87 79; Fax: +44 04 91 67 44 28; E-mail: {nicolet,zolla}@fresnel.fr | [d] Department of Mathematical Sciences, University of
Liverpool, Peach Street, Liverpool L69 3BX, UK. E-mail: abm@liv.ac.uk
Correspondence:
[*]
Corresponding author.
Correspondence:
[**]
C. Geuzaine is a FNRS Postdoctoral Scholar with the Montefiore Department, University of Liege, B-4000 Liege, Belgium
Abstract: The propagation of electromagnetic waves in three-dimensional
periodic structures is studied here using the finite (edge) element method. The
use of the Floquet-Bloch theory leads to special boundary conditions. In the
quasi-static limit, we obtain the effective properties for a periodic array of
dielectric spheres and compare these numerical results with two other
homogenization approaches, namely Clausius-Mossotti theory and two-scale
method.
