Model Order Reduction of Large-Scale Metasurfaces Using a Hierarchical Dipole Approximation

Advances in the field of metasurfaces require simulation of large-scale metasurfaces that extend over many light wavelengths. Adopting standard numerical methods leads to models featuring a large number of degrees of freedom, which are prohibitive to solve within a time window compatible with the design workflow. Therefore, this demands developing the techniques to replace large-scale computational models with simpler ones, still capable of capturing the essential features but imposing a fraction of the initial computational costs. In this work, we present a simulation approach in order to handle reduced order analyses of large-scale metasurfaces of arbitrary elements. We use the discrete dipole approximation in conjunction with the discrete complex image method and hierarchical matrix construction as a common theoretical framework for dipole approximation in the hierarchy of individual elements and the array scale. We extract the contributions of multipoles in the scattering spectra of the nanoantennas forming the metasurface and retrieve their dynamic polarizabilities. The computational complexity of modeling the array problem is then significantly reduced by replacing the fine meshing of each nanoantenna with its dynamic polarizability. The solver is developed to model several fully functional metasurfaces of different types including a one-atom-thick metasurface made of graphene with chemical doping interruptions, a multifocusing lens made of plasmonic V-shaped nanoantennas, and a multicolor hologram consisting of dielectric nanobars. The performance of the method is evaluated through comparison with full-wave simulations, and a significant computational gain is observed while the accuracy of the results is retained owing to the preserved coupling information between dipolar modes.