Simulating optical properties of extremely oblate inhomogeneous particles with the discrete dipole approximation

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The discrete dipole approximation (DDA) is a general volume-discretization method for simulating optical properties of arbitrary particles. We employ the formulation of the DDA with rectangular-cuboid dipoles (voxels) and analyze it in the limit of very small thicknesses of both dipole and scatterer. Taking the limit of zero thickness greatly simplifies the theoretical formulation, resulting in the Rayleigh-Debye-Gans approximation combined with the boundary conditions at the plane interface. This can also be computed in the framework of the DDA, for which we developed a specialized modification of the open-source code ADDA. We also proved that the scattering quantities computed with the standard (3D) code are independent of number of dipoles along the particle thickness, when the latter is sufficiently small. This justifies the usage of dipole monolayers for practical simulations, including those for finite-width metasurfaces.