Scattering detection of a solenoidal Poynting vector field

The Poynting vector S plays a central role in electrodynamics as it is directly related to the power and the momentum carried by an electromagnetic wave. In the presence of multiple electromagnetic waves with different polarizations and propagation directions, the Poynting vector may exhibit solenoidal components which are not associated to any power flow. Here, we demonstrate theoretically and experimentally that the presence of such solenoidal components has physical consequences, and it is not a mere artifact of the gauge invariance of S. In particular, we identify a simple field configuration displaying solenoidal components of S and theoretically show that a judiciously designed scatterer can act as a "Poynting vector detector" which when immersed in such field distribution would experience a transverse optical force orthogonal to the incidence plane. We experimentally validate our theoretical predictions by observing a pronounced asymmetry in the scattering pattern of a spherical nanoparticle.