Résumé
New photonic devices such a metamaterials and meta surfaces are made of a large number of scattering elements strongly interacting. The modeling of these structures requires handling many degrees of freedom that can become prohibitive in terms of computing capacities. In this work we propose to define a new mathematical object that we call the ”holographic scattering matrix”. It allows to describe a cluster of scatterers by an operator defined on the boundary of a surface enclosing the scatterers. Elements with gain or loss can be handled. This allows to generalize the so-called Fast Multipole Algorithm to go beyond the spherical harmonics.