We explore theoretically the optical response of two-dimensional (2D) materials patterned at the nanoscale into either arrays of ribbons along a planar surface or spherical particles. Fourier-Floquet decomposition of the electromagnetic fields is used in order to obtain the reflectance, transmittance and absorbance of the nanoribbon array. The spherical particles are treated with Mie theory, with the boundary conditions modified to accommodate a surface conductivity at the interface. We consider the excitonic response of hexagonal boron nitride in the ultraviolet, and of the transition-metal dichalcogenide ${\mathrm{WS}}_2$ in the visible. Unlike what is expected from graphene, where plasmons have proven very sensitive to geometry, the excitonic response of nanoribbon arrays is found to show weak tunability with the array parameters. To enhance tunability with the geometry of the system, or via hybridization with the substrate, nanospheres with a 2D semiconductor coating are demonstrated to provide a superior platform. Overall, we find that the localized nature of excitons in 2D semiconductors largely limits tunability with geometry, but their hybridization with other optical modes in the nanopatterning setup still holds promise for controllable light-matter interactions.

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• Electrical conductivity
• Exciton polariton
• Excitons
• Nanophotonics
• Permittivity