Collective resonant modes of a meta-surface

A periodic layer of resonant scatterers is considered in the dipolar approximation. An asymptotic expression for the field diffracted is given in terms of an impedance operator. It is shown that surface Bloch modes appear as a collective effect due to the resonances of the scatterers.Comment: 9 pages, 7 figures, extended paper from SPIE Optics+Photonics, Nanostructured Thin Films VI;submitted to Journal of Nanophotonic

Robust equilibrated a posteriori error estimators for the Reissner-Mindlin system

We consider a conforming finite element approximation of the Reissner-Mindlin system. We propose a new robust a posteriori error estimator based on H(div) conforming finite elements and equilibrated fluxes. It is shown that this estimator gives rise to an upper bound where the constant is one up to higher order terms. Lower bounds can also be established with constants depending on the shape regularity of the mesh. The reliability and efficiency of the proposed estimator are confirmed by some numerical tests