What would one observe if instead of using a point source to illuminate the two slits a screen parallel to the two slits where portions of the screen are brighter and darker according to the relevant interference pattern, picture related.

I would expect the light to have a focus at one point based on Fermat's principle of ray reversibility in optics but I am unsure if that would apply here this being a wave phenomena. enter image description here

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    $\begingroup$ Don't forget to specify the phase coherence of the source. I think one could do this with a microwave antenna, to some extent. I'm just wondering if you could successfully invert a single slit diffraction pattern. $\endgroup$ – JEB Mar 8 '18 at 17:08
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    $\begingroup$ Phased Arrays can do something like this, I've never heard of one in visible light, but the math seems pretty similar to longer wave lengths where it is common. $\endgroup$ – user118047 Mar 8 '18 at 20:42
  • $\begingroup$ I’ve seen it done with visible light, by teachers. The source was a photographic slide of the pattern, illuminated by a laser pointer. $\endgroup$ – Frédéric Grosshans Mar 9 '18 at 14:14

If light at the screen is time-reversed and sent back toward the slits, the light will form two bright lines and pass back through the slits.

Exactly how to accomplish that is not necessarily obvious. However, the easiest way would be to record a hologram at the screen using the slits-diffracted light, then reconstruct the hologram using the reverse of whatever reference beam was used in recording the hologram. Recording and reconstructing the hologram this way ensures that the relative phase of the light at different places on the screen is properly accounted for.

Actually,the pattern on the screen constitutes a hologram in which light from the first slit can be considered to be the object beam and light from the second slit can be considered to be the reference beam. If the time-reverse of the light from the second slit is used to illuminate a photo of the pattern, diffraction from the pattern will send a portion of the illumination beam through the first slit.

  • $\begingroup$ This is extremely implausible, as what you are describing is an analog fourier transform in photonics. If this was possible, there would be no need to award the nobel prize in physics for its discovery. $\endgroup$ – donlan Feb 7 at 15:37
  • $\begingroup$ electron6.phys.utk.edu/optics421/modules/m6/… $\endgroup$ – donlan Feb 7 at 15:37
  • $\begingroup$ It is precisely the way holograms work. Yes, Denis Gabor received the Nobel prize for inventing holography. After lasers became available, holography became accessible even to grade school children. $\endgroup$ – S. McGrew Feb 7 at 17:02
  • $\begingroup$ Ah, then you have an extreme blind spot in computing, as this is, trivially, the Fourier transform in optics. Which means quantum computing is already here, in photonics, and I have no idea what everyone is doing with the qbits. Further, encryption is already worthless. $\endgroup$ – donlan Feb 7 at 17:25
  • $\begingroup$ You may be right about the blind spot in computing. I got my start in optics by studying analog optical computing, which is largely based on the optical Fourier transform. Analog optical computing fell out of favor when computers got thousands of times faster than they were in the 1980's, but I think it still has something to offer. $\endgroup$ – S. McGrew Feb 7 at 17:41

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