The discrete dipole approximation for light-scattering simulations

Light scattering by small particles is widely used in remote sensing of various objects ranging from metal nanoparticles and macromolecules to atmospheric aerosols and interstellar dust, being in some cases the only available approach to characterize their geometric or optical properties. Moreover, the structure of electromagnetic fields near a particle is also of major importance for other phenomena, such as surface-enhanced Raman scattering or electron energy-loss spectroscopy. All these applications require accurate light-scattering simulations, which is not trivial for particles of arbitrary shape and internal structure with sizes comparable to or larger than the wavelength. The discrete dipole approximation (DDA) is one of the general methods to handle such problems. In this I will provide an introduction to the DDA, including both the basic underlying physical picture and rigorous derivation starting from the integral form of Maxwell’s equation for the electric field. The latter shows that the DDA is a numerically exact method and a special case of volume-discretization method of moments. Apart from the standard problem of far-field scattering by single isolated particles, the DDA can also be applied to particles in complicated environments (e.g. on substrate) and to other electromagnetic physical phenomena. I will also discuss computational aspects, including the latest efficiency improvements, and briefly review the existing open-source DDA codes, which made the method so popular in the light-scattering community.