# What is the polarization of an EM wave after it suffers scattering?

If a linearly polarized classical monochromatic electromagnetic radiation undergoes a scattering, does the scattered electric field have the same polarization as the incident electric field? I am looking for an answer (or deduce the conclusion mathematically) from classical electromagnetic theory of scattering.

It depends on what the wave is scattered from. The simplest case to study (as an exercise to get intuition) is scattering of a monochromatic EM wave in vacuum from an infinite metal plane: in this case the boundary condition is that the component of the electric field along the surface should be zero. This may add a phase of $$\pi$$ to one or both components of the electric field, but no other transformations occur.