## Characterization of micro-structured Metasurfaces: from the properties of single subunit to a Lagrangian approach for the whole structure

In recent years metamaterials have gained a large interest in the scientific community. Due to their structure, comprised by repeated microscopic subunits, metamaterials can be used to extend the optical and magnetic properties of common materials and realize systems with new characteristics, like the negative refractive index or the coherent perfect absorber.

In this work we show two different approaches to the characterization of a metamaterial. At one side there is the design and the investigation of the single subunit (usually a microantenna). A different perspective considers the discrete structure as a “continuum”, with the introduction of an optical Lagrangian function, governing light propagation through metasurfaces.

At the end, Lagrangian approach is applied to two particular kinds of metasurfaces