On the applicability of discrete dipole approximation for plasmonic particles

Abstract

It has been recognized that the commonly used discrete dipole approximation (DDA) for calculating the optical properties of plasmonic materials may exhibit slow convergence for a certain region of the complex refractive index. In this work we investigate the quantitative accuracy of DDA for particles of different shapes, with silver as the plasmonic material. As expected, the accuracy and convergence of the method as a function of the number of dipoles is relatively good for solid spheres and rounded cubes whose size is of the same order as the wavelength of the localized surface plasmon resonance in silver. However, we find that for solid particles much smaller than the resonance wavelength, and for silver–silica core-shell particles in particular, DDA does not converge to the correct limit even for 106 dipoles. We also find that the slow convergence tends to be accompanied by strong, discretization dependent oscillations in the particle׳s internal electric field. We demonstrate that the main factor behind the slow convergence of the DDA is due to inaccuracies in the plasmonic resonances of the dipoles at the surface of the particles.