Accurate and fast modeling of scattering from random arrays of nanoparticles using the discrete dipole approximation and angular spectrum method

The coupling of optical near fields and far-field scattering by arrays of nanoparticles can be harnessed to improve superresolution imaging, sub-diffraction limit beam focusing, or specialized sensing applications. Numerical simulation and optimization of all these processes commonly entails calculating far-field electric field distributions. However, widelyused simulation techniques such as finite difference time domain (FDTD), Mie theory, and the discrete dipole approximation (DDA) are computationally intensive for large numbers of particles and consequently restrict the size of the domain. Alternatively, the angular spectrum method (ASM) combined with a thin-object approximation, which are commonly used in lens-free holography and other applications to reconstruct images, are well-suited for computationallyefficient large-area calculations. But this approach is not necessarily accurate for nanostructured surfaces. Here we investigate the accuracy of the ASM in modeling the scattered field from a plane wave incident on a plane of randomly assembled nanoparticles. Many super-resolution, sub-diffraction limit, or specialized sensing applications utilize randomly distributed nanoparticles for the ease of placement. We investigate the dipole matched transmission model (DMT) using ASM for polystyrene and gold nanoparticles 30 nm, 60 nm, and 100 nm in diameter for various fill fractions of the nanoparticle plane. We compare the results from the ASM with DDA, which is validated against Mie theory calculations.