# Does a retroreflector depolarize light or preserve polarisation?

In case the retroreflector is just a glas window, the Fresnel equations apply and for an incidence angle of $$\theta = 0^\circ$$ the reflectivities $$R_p$$ and $$R_s$$ for parallel and perpendicular polarized light are the same (about 4%), thus the polarisation of incoming light is preserved, correct?

From the answer in Polarization and mirrors I learned that a (perfect) mirror would preserve polarisation as well.

But what about corner reflectors? Or cat's eyes on bicycles and retroreflectors on clothes like sailor jackets, life vests, working clothes etc. (no idea how these retroreflectors work at all...)?

And how is all this in case of circular polarisation instead of linear polarisation?

## 1 Answer

The picture below is from 2 and it shows a dihedral corner reflecting various polarizations assuming that the incident plane wavefront is parallel with the dihedral edge. Notice that if the wave is polarized parallel with or perpendicular to the dihedral edge then the reflected wave will have the same polarization as the incident one. If instead the polarization is neither parallel nor perpendicular to the edge then the reflected wave will not have the same polarization. The restriction of having the incident wave perpendicular to the edge can be overcome by adding a third plane forming a trihedral corner reflector ("cat's eye"), see 1. This will allow retro-reflection in the same direction as the incident wave and since it suffers 3 (not 2 as in the dihedral) reflections the reflected wave will have the same polarization as the incident one.

In practice there is always some amount of depolarization because there is diffraction effects at the edges and some other details at the apex, etc.

2: Robertson: "Targets for Microwave Radar Navigation", BSTJ 1947, pp852-869

• many thanks for the explanation! Is there any easy-to-understand reason why mirrors actually preserve polarisation? I think you cannot use Fresnel equation, correct? (that's the reason why I have put the example with retroreflection on a glass window in the intitial question). – Charles Tucker 3 May 14 at 14:21
• The example is RF, so the "mirror" is metal $\sigma = \infty$. Still the polarization is not preserved by one reflection unless the ray is perpendicular to the surface or the the ray is parallel with the surface normal. For oblique incidence the reflected ray is not parallel with the incident so its polarization must also rotate to be orthogonal to the ray. For reflection off a dielectric interface the polarization will be similarly affected with the proviso that there is also a refracted ray that can suffer multiple internal reflections and when it finally comes out – hyportnex May 14 at 18:05
• it can lead to further depolarization if the incident wave comes at an oblique angle but I do not know much about this... – hyportnex May 14 at 18:06
• many thanks, that helps! – Charles Tucker 3 May 14 at 18:24