= Double-pass quarter-wave plate
For a reciprocal ideal <quarter-wave plate> followed by a mirror at <normal incidence>, use the same fixed transverse laboratory axes for the forward and returning <Jones vectors>. If the axes coincide with the plate's fast and slow axes, each pass has <Jones matrix> $J=\operatorname{diag}(1,i)$ up to a common <phase factor>. A polarization-independent mirror has scalar reflection coefficient $r_m$, so the returned <Jones vector> is $r_mJ^2\mathbf e=r_m\operatorname{diag}(1,-1)\mathbf e$. The plate acts twice as a <half-wave plate>, rather than undoing its <phase retardation>.
For input <linear polarization> at <angle> $\alpha$ to the fast axis, the returned line is at $-\alpha$ modulo $\pi$. At $\alpha=45^\circ$ it is perpendicular to the original line. An axis-aligned input instead returns along the same line. General <elliptical polarization> requires its full input <Jones vector>; no unique returned state follows from the word “polarized” alone. The propagation direction reverses, so comparing descriptions of <circular polarization> must also specify the viewing convention.
Back to article page
