A Green function method to study thin diffraction gratings

The anomalous features in diffraction patterns first observed by Wood over a century ago have been the subject of many investigations, both experimental and theoretical. The sharp, narrow structures - and the large resonances with which they are sometimes associated - arise in numerous studies in optics and photonics. In this paper we present an analytical method to study diffracted fields of optically thin gratings that highlights the nonanalyticities associated with the anomalies. Using this approach we can immediately derive diffracted fields for any polarization in a compact notation. While our equations are approximate, they fully respect energy conservation in the electromagnetic field, and describe the large exchanges of energy between incident and diffracted fields that can arise even for thin gratings.Comment: 19 pages, 8 figure

Impurity assisted nanoscale localization of plasmonic excitations in graphene

The plasmon modes of pristine and impurity doped graphene are calculated, using a real-space theory which determines the non-local dielectric response within the random phase approximation. A full diagonalization of the polarization operator is performed, allowing the extraction of all its poles. It is demonstrated how impurities induce the formation of localized modes which are absent in pristine graphene. The dependence of the spatial modulations over few lattice sites and frequencies of the localized plasmons on the electronic filling and impurity strength is discussed. Furthermore, it is shown that the chemical potential and impurity strength can be tuned to control target features of the localized modes. These predictions can be tested by scanning tunneling microscopy experiments.Comment: 5 pages, 4 figure