How accurate is the pole expansion of the scattering matrix?

Metasurfaces are flat arrangements of subwavelength optical building blocks that allow tailoring the propagation of light through such layers. They have huge potential for applications such as flat lenses, holograms, displays, or classical and quantum sensors. The building blocks of metasurfaces are mostly designed via numerical calculations, which are often time-consuming and cumbersome. A more elegant way is describing the optical response of these building blocks in terms of their resonant states. This is often not only faster but provides additional insight due to the physically meaningful resonant states. Several formulations for the resonant expansion have been derived so far. However, a thorough comparison of these formulations is lacking, and some effects have been mostly disregarded. Therefore, we are going to address the following questions related to the resonant expansion of the optical response: What are the advantages and disadvantages of the various formulations and how can we include all contributions correctly? Our work will be of utmost importance for the modeling of metasurfaces. Particularly, we see huge potential for applications in optical sensing.