Dynamic Fano resonances: From toy model to resonant Mie scattering

Based on the substantial difference in the response time for the resonant and background partitions at stepwise variations of the exiting signal, a simple exactly integrable model describing the dynamic Fano resonance (DFRs) is proposed. The model does not have any fitting parameters, may include any number of resonant partitions and exhibits high accuracy. It is shown that at the point of the destructive interference any sharp variation of the amplitude of the excitation (no matter an increase or a decrease) gives rise to pronounced "flashes" in the intensity of the output signal. In particular, the flash should appear behind the trailing edge of the exciting pulse, when the excitation is already over. The model is applied to explain the DFRs at the light scattering by a dielectric cylinder with two resonant modes excited simultaneously and exhibits the excellent agreement with the results of the direct numerical integration of the Maxwell equations.