Discrete-dipole approximation (DDA), which is used for computing scattering and absorption by particles of arbitrary geometry and material, is extended to the case of a rectangular cuboidal point lattice using an accurate, analytical expression of the polarizability of each cuboidal element at optical frequencies of up to 100 nm in size. This polarizability formulation (cuboidal lattice with depolarization or CLD) is shown to be more accurate in the computation of the extinction, scattering, and absorption cross sections when simulating dielectrics compared to other available and commonly used expressions of the polarizability. This can be used to reduce the number of dipoles used, and therefore, the computation time while achieving the same accuracy of other formulations. The CLD formulation was applied to the Mie scattering problem and the results were compared to results from other DDA formulations, as well as to the Mie analytical solution for metal and dielectric spheres. Metal cubes were also simulated and different formulations compared.
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