Fano collective resonance as complex mode in a two dimensional planar metasurface of plasmonic nanoparticles

Fano resonances are features in transmissivity/reflectivity/absorption that owe their origin to the interaction between a bright resonance and a dark (i.e., sub-radiant) narrower resonance, and may emerge in the optical properties of planar two-dimensional (2D) periodic arrays (metasurfaces) of plasmonic nanoparticles. In this Letter, we provide a thorough assessment of their nature for the general case of normal and oblique plane wave incidence, highlighting when a Fano resonance is affected by the mutual coupling in an array and its capability to support free modal solutions. We analyze the representative case of a metasurface of plasmonic nanoshells at ultraviolet frequencies and compute its absorption under TE- and TM-polarized, oblique plane-wave incidence. In particular, we find that plasmonic metasurfaces display two distinct types of resonances observable as absorption peaks: one is related to the Mie, dipolar resonance of each nanoparticle; the other is due to the forced excitation of free modes with small attenuation constant, usually found at oblique incidence. The latter is thus an array-induced collective Fano resonance. This realization opens up to manifold flexible designs at optical frequencies mixing individual and collective resonances. We explain the physical origin of such Fano resonances using the modal analysis, which allows to calculate the free modes with complex wavenumber supported by the metasurface. We define equivalent array dipolar polarizabilities that are directly related to the absorption physics at oblique incidence and show a direct dependence between array modal phase and attenuation constant and Fano resonances. We thus provide a more complete picture of Fano resonances that may lead to the design of filters, energy-harvesting devices, photodetectors, and sensors at ultraviolet frequencies.