Erik Ayer
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- TL;DR Summary
- The density matricies for H/V mixtures are the same as for D/A mixtures. Somewhere, my reasoning is wrong...
The density matricies for statistical mixtures of horizontal and vertical polarizations are the same as for mixtures of diagonal and anti-diagonal mixtures, so there should be no experiment that behaves differently for each mixture. I had an idea about it that's got to be wrong and am hoping someone can point out the flaw(s) in my reasoning.
If the H/V mixture is sent to a double-slit experiment with quarter wave plates in front of the slits, one with the fast axis horizontal and the other vertical, H will keep its polarization but be delayed at one slit, V will also keep its polarization but be delayed at the other slit. This results in the interference patterns overlapping and becoming indistinguishable. Diagonal and anti-diagonal polarizations will get converted into left- and right-circular polarization at each slit and not interfere at all.
If a lens is in the zone where H and V interference happens (or lack of it for D/A), if will focus the light to images of the two slits. For H/V, the light at each will be a mixture of H and V. For D and A, they get converted to circular and there ends up being a mixture of left- and right-circular polarization at each image.
If beam blocks, like wires or 3D-printed "jail bars" are put into the interference area such that they are where the bright fringes of one of the interference patterns are at, they will block most of that polarization in the H/V mixture but evenly block the circular polarization from D/A. At the images, they will get a lot of one polarization and little of the other for H/V but get an even mixture of left- and right-circular polarization for D/A. Putting H and V polarizers in the images and detecting light levers would then give different amounts of light for H/V and equal amounts of light for D/A.
That can't be. What am I doing wrong?
If the H/V mixture is sent to a double-slit experiment with quarter wave plates in front of the slits, one with the fast axis horizontal and the other vertical, H will keep its polarization but be delayed at one slit, V will also keep its polarization but be delayed at the other slit. This results in the interference patterns overlapping and becoming indistinguishable. Diagonal and anti-diagonal polarizations will get converted into left- and right-circular polarization at each slit and not interfere at all.
If a lens is in the zone where H and V interference happens (or lack of it for D/A), if will focus the light to images of the two slits. For H/V, the light at each will be a mixture of H and V. For D and A, they get converted to circular and there ends up being a mixture of left- and right-circular polarization at each image.
If beam blocks, like wires or 3D-printed "jail bars" are put into the interference area such that they are where the bright fringes of one of the interference patterns are at, they will block most of that polarization in the H/V mixture but evenly block the circular polarization from D/A. At the images, they will get a lot of one polarization and little of the other for H/V but get an even mixture of left- and right-circular polarization for D/A. Putting H and V polarizers in the images and detecting light levers would then give different amounts of light for H/V and equal amounts of light for D/A.
That can't be. What am I doing wrong?