I Another Interferometry question please

[desertshaman]

TL;DR Summary

Interferometry question

Hi people :)
I am once again mystified, and ask "Why?"

The attached .png shows the light paths of an interferometer.
Between the beam splitter and mirror 3 the light is guided through an excursion which lengthens the path that the light must take to get from the laser source to the detector.
Geometry suggests that a detector which is sensitive to photons coming from either direction (a 50nm screen as used in electron microscopy might work?) could be moved along the path between mirrors 2 and 3 (up and down in the drawing) to equalise the path lengths of the 2 arms of the interferometer.
If this works, why ain't it done this way, please?

 

[.Scott]

The detector is opaque. If you put it between M2 and M3, there will be no interference pattern. And if the detector isn't opaque, it will not detect.
I suppose if you got the detector down to the atomic level, where a single atom was illuminated from both sides, then maybe it would work.
But, I think you get the reason why it "ain't" done that way.

 

[Cthugha]

Also, even if you had a detector with equivalent detection efficiency for photons arriving from both sides, such a detector would be an experimental nightmare.

The quantity you are interested in is the path length difference of the two photons as a fraction of their wavelength. Now the detector itself is likely spatially somewhat extended and the wavelength of light inside the material is its wavelength in vacuum divided by the refractive index of the material. If you consider silicon, the refractive index is already about 3.4, so for standard 532 nm laser light, the thickness of the 50 nm screen is already one third of the wavelength in the material. Therefore, the effective path length difference between the two paths will become a function of the position within the sheet, which will make analysis of the results extremely horrible.

There is a good reason why you want both beams to be merged again before the detector.

Also, in the setup you describe, there will be light going back from the interferometer into the laser, which may result in instabilities of the laser itself.

 

[desertshaman]

Thank you.
I think I see...
The 2 halves of the divided energy of the photon must be realised in the same detecting atom. My design would result in a scattered pattern on each side of the detector, despite the detector being very thin.

 

[PeterDonis]

The 2 halves of the divided energy of the photon

There is no such thing. A beam splitter splits the photon's wave function (there are a lot of dragons lurking beneath that innocuous-sounding statement, but I think we can ignore them for this discussion), but that's not the same thing as splitting the photon's energy.

 

[desertshaman]

Thankyou :)
I have noticed that photon physics is full of "dragons".
It is the wavefunction which is divided.

A full understanding of these phenomena is reportedly difficult to gain. Mmm hmmm.
From my present level of understanding, the clarities I seem to perceive turn straight away into weird mirrors, and reaching for certainty is like snatching at ghosts.
:)