Phenomenological approach to light scattering by small particles and directional Fano's resonances

Abstract

The exact Mie solution, describing light scattering by a spherical particle, is examined within the framework of a phenomenological approach. It is shown that many important properties of the solution, actually, are consequences of general principles, such as the energy conservation, optical theorem, transverseness of electromagnetic waves, etc., and may be obtained without solving the corresponding diffraction problem explicitly. This sheds a new light on the physical meaning of these properties and highlights new prospects to analyze analogous problems, which do not admit exact solutions. As an example, the developed approach is applied to inspect the Fano resonances in optics. It is shown that at light scattering by a small uniform spherical particle even in the extreme non-dissipative case the scattering cross-section always has a Lorenzian line shape, that is the conventional Fano resonances are forbidden. However, the system may exhibit another type of Fano's resonances, namely the directional Fano resonances with a typical asymmetric line shape for the intensity of light with a given polarization scattered along a given direction, while the cross-section preserves a Lorenzian profile. These resonances are discussed in detail.