Does reflection (straight back) not reverse the helicity of a photon? That would solve the angular momentum bit, I think. Sent from my iPhone
On Jun 1, 2015, at 5:17 PM, Warren D Smith <warren.wds@gmail.com> wrote:
Here is a puzzle concerning the optics of polarized light. Every state of polarization has its opposite. For linear polarization, it's linear but rotated 90 degrees. For ere is a puzzle concerning the optics of polarized light. Every state of polarization has its opposite. For linear polarization, it's linear but rotated 90 degrees. For circular polarization, it's circular with opposite helicity. For general elliptic polarization, it's elliptic with the ellipse rotated 90 degrees, and the helicity reversed. On the Poincaré sphere, opposite states of polarization are represented by diametrically opposite points. The puzzle is to construct an optical device that reverses the polarization state. For any input, the output is the opposite polarization. Or, prove that it can't be done. -- Gene. For general elliptic polarization, it's elliptic with the ellipse rotated 90 degrees, and the helicity reversed. On the Poincaré sphere, opposite states of polarization are represented by diametrically opposite points. The puzzle is to construct an optical device that reverses the polarization state. For any input, the output is the opposite polarization. Or, prove that it can't be done. -- Gene
--WDS: There is a sense in which it cannot be done for a flow-thru device. For linear polarization, it can be done, you just rotate the plane of polarization by 90 degrees by passing it thru a sugar solution; also faraday effect works. But when you said "for circular polarization, it's circular with opposite helicity" that seems to be the death blow. Because the input is photons with clockwise spin while the output is photons with anticlockwise spin. This means, in view of conservation of angular momentum, your device will be forced into rotation, faster the longer you run it. I.e. it is applying torque to your light, and the light is applying torque to it. So this is not, and cannot be, a "passive device" of the usual 100% efficiency optical variety.
Having said that, maybe this does not bother you.
And anyhow here is a "back at you" device: An ordinary mirror in combination with sugar solution layer of the correct thickness will input a light beam (normal to mirror) and output one (reflected) that is both circularly helicity-reversed and also linear polarization rotated 90. Does that satisfy you?
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