Past exam of the optics and electrodynamics course of the University of Cambridge / 2016 / Paper 1 / 4 / c / Solution

Choose one circular convention as ${\mathbf{e}}_R=(\hat{\mathbf{z}}+i\hat{\mathbf{y}})/\sqrt{2}$ with time dependence $e^{-i\omega t}$. Reversing the handedness convention changes the sign of $i$ but not the result here. The scattered complex amplitude isThe scalar factor contributes a common phase to both output components. Consequently the scattered wave is linearly polarized along $\mathbf{v}$, rather than circular or elliptical, withThe dominant longitudinal needle response has rank one, so both incident circular components emerge in the same real output direction.