  The multipolar expansion of the electromagnetic field plays a key role in the
study of light-matter interactions. All the information about the radiation and
coupling between the incident wavefield and the object is embodied in the
electric and magnetic scattering coefficients $\{a_{\ell m}, b_{\ell m} \}$ of
this expansion. However, the experimental determination of $\{a_{\ell m},
b_{\ell m} \}$ requires measuring the components of the scattered
electromagnetic field in all directions, something that is enormously
challenging. In this Letter, we demonstrate that a single measurement of the
Stokes vector at an angle of choice unlocks fundamental Nanophotonics
magnitudes that are concealed in the scattered field. The unveiled quantities
are: $\left[|a_{\ell m}|^2, |b_{\ell m}|^2, \Re \{ a_{\ell m} b^*_{\ell m} \},
\Im \{ a_{\ell m} b^*_{\ell m} \} \right]$. Strikingly, our Stokes polarimetry
approach allows for distinguishing between the magnetic and electric nature of
the radiated electromagnetic field. Thereby, our findings, supported by exact
analytical theory, can find applications across all branches of Nanophotonics
and Optics, and greatly facilitate routine light-scattering measurements.

Optics