The state of a free photon's polarization is of the form a|-1> + b|1> up to a global phase. (Aside: a photon is a spin-1 particle, not spin-1/2, so it ought to have *three* polarization states: -1, 0, and 1. What happened to the 0 state?) The NOT gate swaps a and b, taking right-polarized to left-polarized and vice-versa. Linearly polarized states are (a, b) = (1, i) and (1, -i), but these are eigenvectors of the NOT gate. Similarly, swapping linear polarizations preserves circular polarization. It's impossible. On Mon, Jun 1, 2015 at 4:40 PM, Eugene Salamin via math-fun <math-fun@mailman.xmission.com> wrote:
Yes, mirrors are allowed. -- Gene
From: Henry Baker <hbaker1@pipeline.com> To: math-fun <math-fun@mailman.xmission.com> Cc: gene_salamin@yahoo.com Sent: Monday, June 1, 2015 1:42 PM Subject: Re: [math-fun] A polarization puzzle
Are mirrors allowed (in addition to other types of polarizers) ? Don't mirrors invert most everything about light?
Rotations in geometry are a combination of 2 reflections; perhaps mirrors can help here.
At 01:19 PM 6/1/2015, Adam P. Goucher wrote:
I don't know enough about optics to know whether this is correct or not, but I can believe that a negative solution might be of the form `polarising filters can only apply orientation-preserving transformations to the Poincaré sphere, whereas the antipodal map is orientation-reversing'.
Sincerely, Adam P. Goucher
Sent: Monday, June 01, 2015 at 9:10 PM From: "Eugene Salamin via math-fun" <math-fun@mailman.xmission.com> To: math-fun <math-fun@mailman.xmission.com> Subject: [math-fun] A polarization puzzle
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 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
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