Two tractable models of dynamic light scattering and their application to Fano resonances

We introduce two tractable analytical models to describe dynamic effects at resonant light scattering by subwavelength particles. One of them is based on a generalization of the temporal coupled-mode theory, and the other employs the normal mode approach. We show that sharp variations in the envelope of the incident pulse may initiate unusual, counterintuitive dynamics of the scattering associated with interference of modes with fast and slow relaxation. To exhibit the power of the models, we apply them to explain the dynamic light scattering of a square-envelope pulse by an infinite circular cylinder made of GaP, when the pulse carrier frequency lies in the vicinity of the destructive interference at the Fano resonances. We observe and explain intensive sharp spikes in scattering cross-sections just behind the leading and trailing edges of the incident pulse. The latter occurs when the incident pulse is over and is explained by the electromagnetic energy released in the particle at the previous scattering stages. The accuracy of the models is checked against their comparison with results of the direct numerical integration of the complete set of Maxwell’s equations and occurs very high. The models’ advantages and disadvantages are revealed, and the ways to apply them to other types of dynamic resonant scattering are discussed.