Part 1 : Nanoparticles Module 5 : Absorption and scattering by a particle
Lecture 2 : Poynting vector and Time averaged Poynting vector
 
Stokes parameters for a collection of randomly separated particles are sum of the Stokes parameters for individual particles. This imply that for large $r$ (i.e., in the far-field region), compared to the dimension of the region of scatterers, the scattering matrix for a collection of particles is just the sum of the scattering matrices for individual particles. Note that the 16 matrix elements for a single particle are not all independent; only seven of them can be independent corresponding to four $\vert S_j\vert$s and three different phases between $S_j$s, which then give nine independent expressions. In general. the 16 elements may reduce in number because of symmetry in the problem. Further $S_{ij}$ must be independent of $\phi$ for any particle or collection of particles which remain invariant with respect to arbitrary rotation about the $z$-axis.
If the incident beam is unpolarized (i.e., $Q_i=U_i=V_i=0$), then $I_s/I_i = S_{11}$, $Q_s/I_i=S_{21}$, $U_s/I_i =S_{31}$, $V_s/I_i =S_{41}$ (apart from the multiplying factor $(qr)^{-2}$ in each case). Thus $S_{11}$ specifies the angular distribution of the scattered light for given unpolarized incident light. The scattered light, in general, is partially polarized with degree of polarization $\sqrt{(S_{21}^2 +S_{31}^2+S_{41}^2)/S_{11}^2}$, which shows that scattering is a mechanism for polarizing light.
If the incident beam is Right Circularly Polarized (RCP), then for the scattered light, $I_{Rs}/I_i=S_{11}+S_{14}$ (in general, this does not imply that the scattered light is RCP). Similarly, if the incident light is Left Circularly Polarized (LCP), then for the scattered light $I_{Ls}/I_i=S_{11}-S_{14}$ (again in general, this does not imply that the scattered light is LCP). This means $S_{14}=(I_{Rs}-I_{Ls})/(2I_i)$.