Polaritonic crystals: from optical response to Casimir effect

The Casimir force, in its original formulation, is the attraction between uncharged surfaces as aresult of quantum vacuum fluctuations of the electromagnetic field.The presence of the surfaces modifies the field boundary conditions, lowering the zero point energydensity between the plates respect to the free space, and the result is a net attractive force.From the first proposal in 1948 and the first accurate measurements in 1997 the interest for Casimirforces in more complex geometries and materials has shown a huge increasing with the particularaim to control the effect. This has made it necessary to consider in detail the electromagneticresponse of the involved materials.In general the Casimir force control and in particular the crossover from attraction to repulsion canbe obtained by two different routes: either by using exotic asymmetric materials, that overcome theusual electric-dipole couplings, as magnetic and chiral meta-materials, or by using traditionalmaterials, but complex geometries, as those obtained with photonic crystal slabs in asymmetricplanar cavities.Considering nanostructured surfaces (1D diffraction gratings) we study, trough a theoretical methodbased on the scattering theory, the effect of the geometry on the Casimir force.Moreover trough a solution in terms of the e.m.Green function of cavity polaritons, we approach theproblem of non-locality in connection with Casimir forces specifying the dependence of thedielectric function on both the frequency and the wavevector.The analyticity of this Green function, that arises from the separable nature of nonlocalsusceptibility of excitonic resonances, has a possible extension to the EM Green function of amedium with arbitrary shape.