Metasurfaces: singularities of the scattering elements and applications of their polarimetric properties

The design of metasurfaces allows to tailor their optical response with specific spectral and polarization features. We will see how the spectral response of metasurfaces can be fully understood and predicted thanks to the singularities in the complex frequency plane of the scattering matrix elements. This approach turns out to be especially relevant for deriving the scattered field in the time domain providing fruitful insights in the time dynamics of the metasurface. The singularity expansion method offers a rigorous approach for deriving analytic expressions of dispersive dielectric permittivities that share the properties of linear transfer functions. This approach can be used to derive an improved expression of the Debye Drude Lorentz model that complies with the mathematical properties of complex analysis and exhibiting excellent fits with experimental data.