  Maxwell's equations are solved when the amplitude and phase of the
electromagnetic field are determined at all points in space. Generally, the
Stokes parameters can only capture the amplitude and polarization state of the
electromagnetic field in the radiation (far) zone. Therefore, the measurement
of the Stokes parameters is, in general, insufficient to solve Maxwell's
equations. In this Letter, we solve Maxwell's equations for a set of objects
widely used in Nanophotonics using the Stokes parameters alone. Our method for
solving Maxwell's equations endows the Stokes parameters an even more
fundamental role in the electromagnetic scattering theory.
