  In this research, we report the experimental evidence of the directional Fano
resonances at the scattering of a plane, linearly polarized electromagnetic
wave by a homogeneous dielectric sphere with high refractive index and low
losses. We observe a typical asymmetric Fano profile for the intensity
scattered in, practically, any given direction, while the overall extinction
cross section remains Lorentzian. The phenomenon is originated in the
interference of the selectively excited electric dipolar and quadrupolar modes.
The selectivity of the excitation is achieved by the proper choice of the
frequency of the incident wave. Thanks to the scaling invariance of the Maxwell
equations, in these experiments we mimic the scattering of the visible and near
IR radiation by a nanoparticle made of common superconductor materials (Si, Ge,
GaAs, GaP) by the equivalent scattering of a spherical particle of 18 mm in
diameter in the microwave range. The theory developed to explain the
experiments extends the conventional Fano approach to the case when both
interfering partitions are resonant. The perfect agreement between the
experiment and the theory is demonstrated.
