Afshar As A First Stage In Multi-Stage Interference

[Erik Ayer]

TL;DR Summary

If Afshar's experiment were the first stage where the output was re-columnated and re-interfered, would there be interference in the second stage?

Afshar's experiment sent light through a double-slit then refocused it into "images" of the two slits. Wires placed in the dark part of the interference (right before or after the lens) didn't make much of a difference in the amount of light being detected. Here is the wiki for Afshar, and here is a pretty picture:

If, instead of being directed to detectors after refocusing, what would happen if the light was allowed to spread out again and overlap? My bet would be that there would again be interference. Since the wires are places in the dark parts of the interference pattern, the Afshar stage would have little effect on the second interference stage - just reduce its brightness slightly.

Now, if a second light source is added next to the first, just slightly to the side but also pointing at the double-slit, there would be a phase shift between the two slits at the second source, so its interference pattern in the Afshar stage (1) would be shifted and would make the overall interference pattern (stage 1) more complicated. The wires, however, would reduce that to some degree. My guess is that the second stage would still show interference, although probably not as clearly.

Instead of one extra light source, what if an infinite range of them were added? A possible way to do that would be to pass a laser through a cylindrical lens to spread out, then another cylindrical lens to focus it back up at the double slit (the first one in stage one). Refocusing that back down to the two spots and recolumnating wouldn't work since the light would be coming in from a range of directions. It would focus to a line (with just two sources, there would be four dots after focusing). I think the second stage would still show interference since a very limited part of that range would hit the second double slit, but the interference would be further degraded.

Finally, imagine there is just one light source, but there is a random phase delta between what goes through each slit. Again, this would result in the interference of stage 1 being shifted randomly and making a mess, but the wires would eliminate at least some of the interference patterns that were shifted. I would think that there would be some recognizable interference at the second stage. If the wires were thick such that one wire was close to the next, the interference at the second stage would be dimmer but clearer.

Does this sound about right or am I completely off base?

 

[eljose79]

I would like to start by saying that your thought process and ideas are very interesting and show a good understanding of the concepts involved in Afshar's experiment. However, there are a few points that I would like to clarify and expand upon.

Firstly, you are correct in your assumption that if the light is allowed to spread out again and overlap after being refocused, there would be interference again. This is because the wires placed in the dark part of the interference pattern would not affect the interference at the second stage, as you mentioned.

However, the addition of a second light source next to the first one would not necessarily result in a phase shift between the two slits at the second source. This is because the phase shift depends on the relative distance between the two sources and the double-slit, and it is not clear from the diagram provided if the second source is at a different distance from the double-slit than the first one. If the distance is the same, there would be no phase shift and the interference pattern at the second stage would remain the same.

Adding an infinite range of light sources, as you suggested, would indeed result in a line of light after focusing. However, this line would still have a finite width, and the amount of interference at the second stage would depend on the width of this line. If the line is very narrow, there would be a limited amount of interference at the second stage, but if the line is wide, there would be more interference.

Finally, the presence of a random phase delta between what goes through each slit would indeed result in a mess at the second stage. However, the wires would not eliminate any of the interference patterns, as they do not affect the phase difference between the two sources. The interference at the second stage would still be random and would not show any recognizable interference.

In conclusion, your ideas and thought process are on the right track, but there are some important factors that need to be taken into account in order to accurately predict the interference patterns at the second stage of Afshar's experiment. Keep exploring and questioning, that's the essence of science!