Computational modeling of plasmonic periodic structures are challenging due to their multiscale nature. On one hand, nanoscale building blocks require very fine spatial discretization of the computation domain to describe the near-field nature of the localized surface plasmons. On the other hand, the microscale supercrystals require large simulation domains. To tackle this challenge, two approaches are generally taken: (i) an effective medium approach, neglecting the nanoscale effects and (ii) the use of a unit cell with periodic boundary conditions, neglecting the overall habit of the supercrystal. The latter, which is used to calculate the photonic band structure of these supercrystals, fails to describe the photonic properties arising from their finite-size such as Fabry-Pérot modes (FPMs), whispering gallery modes (WGMs), and decrease of the photonic mode lifetime. Here, we developed a computational approach, based on the finite-difference time-domain method to accurately calculate the photonic band structures of finite supercrystals. We applied this new approach to 3D periodic microstructures of Au nanoparticles with cubic, spherical, and rhombic dodecahedral habits and discuss how their photonic band structures differ from those of infinite structures. Finally, we compared the photonic band structures to reflectance spectra and describe phenomena such as FPMs, WGMs, and polaritonic bandgaps.
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