# Reverse of diffraction

Can we arrange a practical in such a way that the dark and bright bands in diffraction grating be allowed to pass through the same slit to get the original light (i.e the incident light before diffraction), just like we reverse the arrows in reflection and refraction

• You might want to look at a zone plate. – M. Enns Jun 23 at 18:35
• You might want to take a look at holography. – Aron Jun 24 at 3:33
• Another term for this (in addition to the ones in the answers) is "color mixing", which happens in some severe thunderstorms where red and blue light mix and create green light. – Todd Wilcox Jun 24 at 18:03
• Liked chirped pulse amplification - en.wikipedia.org/wiki/Chirped_pulse_amplification? – Jon Custer Jun 24 at 19:36

Reversing diffraction is precisely what is done in Fourier Optics!

There, instead of placing a screen after the slit to see the diffraction pattern, a lens is put there instead. If you arrange the diffraction image to lie at the back focal plane of the lens, you will see the image of the slit itself at the front focal plane of the lens.

This procedure of reversing diffraction relies on a fundamental Fourier transform property of a thin lens. The idea is that placing an object exactly one focal length $$+f$$ away from the lens will produce an image of the object one focal length $$-f$$ on the opposite side that is the Fourier transform of the object.

This is shown in the image below

Optics is time-reversal invariant, so the short answer is "yes".

As a practical matter it is essentially impossible to set up the exact reversed situation, but we can set up good approximations in some cases (and in particular in electromagnetic bands not including visible light). Once the approximation is good enough it becomes useful.

A "phased array" transmitter is exactly a mechanism for focusing electromagnetic waves by emitting them from many places with carefully arranged phase off-sets. They are difficult to build, tune, and operate effectively; but they are a thing.

• Am I right in thinking that audio phased-array transmitters are what they sometimes use to disperse crowds? – Dancrumb Jun 24 at 17:08
• Not sure. I think I read that they were trying out sonic phased arrays for that purpose at one time. I'm even less sure how the electromagnetic projectors work, though I would consider phased arrays as a good candidate. – dmckee Jun 24 at 17:14
• @Dancrumb I'm pretty sure what we might call an "audio phased-array transmitter" is called a "line array" in the sound reinforcement industry, and those are used to gather and entice crowds to dance and have a good time at rock concerts. – Todd Wilcox Jun 24 at 18:41
• @ToddWilcox a line array is generally fed in-phase, giving a fixed pattern which depends on its geometry. If you feed each speaker through an independent delay network, and adjust those phase delays to "target" the point where the sound reinforces without moving the speakers, then it becomes a phased-array. – hobbs Jun 24 at 21:23
• @hobbs Most line arrays are running exactly like that. There's a speaker management controller and each powered array element has DSP that allows for both filtering and delay for that element. So you pretty much fly the arrays the same way for every show, and then you "aim" and "focus" them before each show for best coverage for the individual venue. – Todd Wilcox Jun 24 at 21:41

for light beams, you might also consider something called a corner reflector or retro-reflector. this is a glass prism cut in such a way that any beam of light entering it is reflected back at almost exactly the same angle that it made going into the prism. if you constructed a flat plate containing a large number of small corner reflectors and placed it at the location of the screen in the experiment you describe, then all the light striking the plate across its width would be reflected back to the slit.

I do not know how that collection of beams coming back into the slit would behave when they all meet!

• Glass corner cubes aren't so simple. Rays do not counterpropagate on themselves. And each of the six possible paths of a ray through a corner cube affects the phase of the light differently. Metallic reflecting corner cubes help, but since metals are not perfect conductors, there is still a small phase/polarization effect, but there is energy lost. – garyp Jun 23 at 22:03
• In the flat plate example you give the light would diffract very strongly off all of the edges of the corner plates. I doubt it'd work at all. – aquirdturtle Jun 24 at 7:52
• Corner reflectors do amazing (but not desirable) things to the wavefront. There's always an edge and a point-corner, so the return is at best six wedges. – Carl Witthoft Jun 24 at 14:58
• @CarlWitthoft, got it. I wasn't expecting the corner cube idea to preserve phases. – niels nielsen Jun 24 at 17:48

In order to reverse the light in a double-slit interferometer to form a single beam, it is necessary to exactly time-reverse the light from the band pattern -- including the relative phase of each part of every band. This can be done, but it is not easy. Because a hologram records phase as well as amplitude, the method that will work best is to record the band pattern as a hologram, then reconstruct the hologram in reverse.