A persistent feature of multiple scattering of waves in the time-domain: A tutorial

•Assessed the mathematical nature of frequency-domain multiple scattering.•Assessed the physical nature of time-domain multiple scattering.•Exposed the multi-particle paths in frequency-domain multiple scattering.•Exposed the temporal sequence of scattered pulses in time-domain multiple scattering.

The equations for frequency-domain multiple scattering are derived for a scalar or electromagnetic plane wave incident on a collection of particles at known positions, and in the time-domain for a plane wave pulse incident on the same collection of particles. The calculation is carried out for five different combinations of wave types and particle types of increasing geometrical complexity. The results are used to illustrate and discuss a number of physical and mathematical characteristics of multiple scattering in the frequency- and time-domains. We argue that frequency-domain multiple scattering is a purely mathematical construct since there is no temporal sequencing information in the frequency-domain equations and since the multi-particle path information can be dispelled by writing the equations in another mathematical form. However, multiple scattering becomes a definite physical phenomenon in the time-domain when the collection of particles is illuminated by an appropriately short localized pulse.