Assessing the limits of Rayleigh–Debye–Gans theory: Phasor analysis of a bisphere

Abstract

Rayleigh–Debye–Gans (RDG) theory is a commonly used approximation for light scattering and absorption by nanoparticles in the visible spectrum. The aim of this study is to advance our understanding for the origin of empirically observed deviations between accurate calculations of forward scattering and the absorption cross-sections and those predicted by RDG. For this purpose, we investigate the internal electric field within bi-spherical nanoparticles in several cases. The fixed-size constituent spheres of the bispheres are either separated or overlapped and are investigated using the discrete dipole approximation (DDA). To study the internal electric fields, we apply a phasor approach, which provides a semi-graphical way to understand the deviation of the forward scattering (A) and that of the absorption cross section (h) with respect to the RDG. The phasor approach reveals the influence of the bisphere orientation, absorption function E(m), scattering function F(m), and wavelength. It is observed that RDG tends to overestimate the forward scattering, i.e., A<1, as well as absorption h<1 for larger size parameters, and thus, shorter wavelengths. At the opposite limit, a decreasing absorption function E(m) leads to RDG underestimating the true scattered intensity. An explanation for this effect is a competition between the non-uniformity of the internal electric field and the phase shift of the phasors, leading to different results than those predicted by RDG and the amount of dipoles scattering in-phase.