ИСТИНА

The problem of the Fano resonances in light scattering by an obstacle is discussed. It is shown that despite a certain similarity between the Fano resonances in quantum scattering of particles by a potential with a quasi-discrete level [1] and the ones at elastic light scattering by a finite-size obstacle, there is a dramatic difference between these two cases. In both the cases the phenomenon is based upon interference of the so-called resonant and background partitions of the incident wave, which results in a typical asymmetric Fano profile with a pronounced peak at the point of the constructive interference and compete (or almost complete) suppression of the scattering at the point of the destructive one. However, in the case of the quantum scattering the resonant and background partitions both are related to one and the same partial wave, while in optics they are related to different electromagnetic modes. This difference in the nature of the resonances gives rise to differences in their manifestations. The general arguments are illustrated by inspection of the Fano resonances in the case of light scattering by a sphere, when the scattering is described by the exact Mie solution. It is shown that if the roles of the resonant and background partitions are played by modes with different multipole moments, a new phenomenon, namely the directional Fano resonances may be observed. In this case the the asymmetric Fano profile may be obtained at the scattering along any given direction, while along other directions the profile is symmetric Lorenzian (Breit-Wigner). The profile of the extinction (scattering) cross section is also Lorenzian. If the resonant and background partitions are presented by different modes with the same multipole moment the entire extinction (scattering) cross section profile may be asymmetric Fano. It results in almost complete suppression of the net scattering at the frequencies of the destructive interference (invisibility of the obstacle). The case is characterized by multiple Fano’s resonances at different frequencies. Two examples of such a kind, namely for a sphere with a large value of dielectric permittivity and the one with spatial dispersion are discussed in detail. The results obtained shed new light on this important and interesting phenomenon and may be employed in various applications.