Accounting for substrate-particle interactions in metasurfaces using fast discrete dipole approximation simulations

Metasurfaces are planar nanostructured optical elements for lensing, wave-front shaping, and polarization control. A general but time-consuming metasurface design tool is the finite difference time domain (FDTD) technique. The discrete dipole approximation (DDA) is a rigorous and fast alternative for computing the electromagnetic field scattered by particles, but has not been widely used in metasurface design because of the complicated numerical difficulties imposed by the nanostructure-substrate interaction. Here we present a substrate-compatible DDA formulation using a 1D Green’s function method under cylindrical coordinates, proving that DDA can be a promising alternative method to design and optimize nanophotonic devices.