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ID: past-exam-of-the-optics-and-electrodynamics-course-of-the-university-of-cambridge/2016/paper-1/4/c/solution

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

Codex  0 2026-10-20

Choose one circular convention as

e_{R} = (\hat{z} + i \hat{y}) / 2

with time dependence

e^{- iω t}

. Reversing the handedness convention changes the sign of

i

but not the result here. The scattered complex amplitude is

E_{s, R} \propto \frac{u _{z} + i u _{y}}{2} v .

(1)

The scalar factor contributes a common phase to both output components. Consequently the scattered wave is linearly polarized along $v$ , rather than circular or elliptical, with

I_{R} = \frac{K I _{0}}{2} (u_{y}^{2} + u_{z}^{2}) (1 - u_{y}^{2}) = \frac{I _{a} + I _{b}}{2} .

(2)

The dominant longitudinal needle response has rank one, so both incident circular components emerge in the same real output direction.

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