Spontaneous light emission in complex nanostructures

The spontaneous emission of an excited atom surrounded by different materials is studied in the framework of a semiclassical approach, where the transition dipole moment acts as the source of the emission field. The emission in the presence of semiinfinite media, metallic nanorings, spheres, gratings, and other complex geometries is investigated. Strong emission enhancement effects are obtained in some of these geometries associated to the excitation of plasmons (e.g., in nanorings or spheres). Furthermore, the emission is shown to take place only along narrow angular distributions when the atom is located inside a low-index dielectric and near its planar surface, or when metallic nanogratings are employed at certain resonant wave lengths. In particular, axially symmetric gratings made of real silver metal are considered, and both emission rate enhancement and focused far-field emission are achieved simultaneously when the grating is decorated with further nanostructures.This work has been supported in part by the Basque Departamento de Educacion, Universidades e Investigacion, the University of the Basque Country UPV/EHU (Contract No. 00206.215-13639/2001) and the Spanish Ministerio de Ciencia y Tecnologia (Contract No. MAT2001-0946).Peer reviewe

Denumerants of 3-numerical semigroups

Denumerants of numerical semigroups are known to be difficult to obtain, even with small embedding dimension of the semigroups. In this work we give some results on denumerants of 3-semigroups S=S=. Closed expressions are obtained under certain conditions.Peer ReviewedPostprint (published version

An algorithm to compute the primitive elements of an embedding dimension three numerical semigroups

We give an algorithm to compute the set of primitive elements for an embedding dimension three numerical semigroups. We show how we use this procedure in the study of the construction of L-shapes and the tame degree of the semigroup.Peer ReviewedPostprint (author’s final draft