Fabry-Perot Interferometer mirrors

[dykuma]

TL;DR Summary

What type of mirrors are used in the construction of a Fabry-Perot Interferometer?

I am trying to build a Fabry-Perot interferometer to make some narrow band filters, and I was wondering if anyone can go into the specifics of whether there's anything special about the types of mirrors used in construction.

I started by trying to see how hard it really is to make one on my own, using really cheap things that I have laying around. For mirrors I used a normal glass mirrors with the back paint on the back removed to create a first surface mirror. The mirrors are highly reflective (probably around 80~90% at least) and while I can't say how flat they are precisely, they seemed to be mostly distortion free.

Anyway, after messing with it for a while I was able to produce a fringe pattern (image below shows a fringe patter created after a green laser passed through it), but it's dim, and shifted greatly towards the blue end of the spectrum. It was basically impossible to produce a fringe pattern with red light unless the source was very bight. I think that the problem might be that my mirrors are absorbing most of the light as it's being transmitted through the aluminum layer. Possibly the front layer of aluminum is too thick, and so it's absorbing most of the light that passes through it?

What I want to know, especially from anyone who's actually constructed a F-P before, is did you have to use special mirrors? Is there a proper that I should look for when buying a mirror to make a F-P, like layer thickness or material type (such as gold or silver instead of aluminum)? I can't seem to find any sources on exactly what types of mirrors are used, except that they are "thin" mirrors and highly reflective.

 

[sophiecentaur]

TL;DR Summary: What type of mirrors are used in the construction of a Fabry-Perot Interferometer?

I am trying to build a Fabry-Perot interferometer to make some narrow band filters,

OH boy! I just wish we could make those things in the amateur workshop. Astrophotography needs narrow band filters to see Oxygen and Hydrogen lines and we all need to spend multiple £k on them.

The surface of a FP mirror needs to optically flat* over a reasonable area and the optical spacing between two mirrors needs to be as good if you are to get a peak that covers the whole surface. Also, the reflectivity needs to be very high if you want a very narrow.

That image of yours looks (to me) as if the path length over the width of the field varies by at least a dozen wavelengths (all those rings, instead of a uniform level). A narrow filter width between two mirrors in a FP cell requires a lot of reflections, to add up to give the effect of a single long cavity.

I found this link which contains some basic discussion about FP resonators. Worth a good look. There are many others of course, including Wiki. The problem, as usual is that Google trends to present you with 1. Adverts, 2. very basic stuff or 3. The latest 'scholarly' stuff. So you need to do a lot of delving to get what you want. Perhaps @Andy Resnick could point you in the right direction.

* I remember my old Prof telling us that the best technicians produce good flats by grinding faces together, using three different faces and swapping between them to avoid any build up of curvature that you get with using just two faces. Takes a long time and a lot of elbow grease. That was a long time ago but the alternative will be to use very expensive equipment which we don't have at home.

 

[dykuma]

I found this link which contains some basic discussion about FP resonators. Worth a good look.

Thanks for the response, I appreciate it. Also sorry for taking so long to respond, I've been busy.

Right, so the mirror I used wasn’t intended to be the final one. Mostly I was interested in seeing if it was possible at all to get fringes before I either attempted to make my own mirror or purchased one at a much greater cost. The space between the mirrors was narrow on purpose. I could get it aligned at greater distances, but it was harder for me to image the fringes at that distance. I was also pleased to see that I could (or at least I think I could) see the mode splitting of the spectrum of the 532 nm laser.

Anyway, equation 2 in that paper is really helpful, because I think it gets closer to what I’m trying to ask. I guess I was being naïve, but what I expected I guess is that ANY reasonably flat mirror with a high reflectance could achieve a high transmission of light. The way I was taught was that a single mirror with a reflectance of 99% would allow ~1% of the light past, but two mirrors properly aligned would allowed ~100% because of resonance in the cavity.

Instead, F-P mirrors seem to be a very tight balancing act between high reflectance and low absorption. The greater the reflecance, the greater the resolution is of the interferometer, but the thicker the layer also causes greater absorption, so the transmission of light is still low ultimately (which makes some sense I guess, as I think great resolution usually means a dimmer spectrum with other types of interferometers). I’m guessing that my cheap mirror’s aluminum surface was too thick to allow light to pass which is why it’s so dim (assuming it wasn't also because it wasn't flat enough). And this is where I get stuck. What are the ideal but practical parameters for a F-P mirror? If were picking parts off a shelf, what parts would I look at? Obviously I guess it's at least λ/4 flatness, R=.99, T=.09, A=.01, but places I usually look (like Thorlabs or Edmund Optics) don't list out mirrors like this (specifically in terms of absorption/transmission unless I missed it) or mirrors specifically for Fabry-Perots.

Edit: I should add that I'm aware that when constructing narrow band filters using F-Ps, usually a seperate filter is already added somewhere in the optical path. F-P's allow multiples of the target wavelength to pass, and so the additional filter is used to remove those wavelengths, as well as to possibly sharpen the peak of the target wavelength. I guess that it might also be the case that these filters are needed when the reflectance of the mirrors are intentionally lower. Basically it brings off band light down enough that a less than ideal secondary filter can easily remove it?

 

[sophiecentaur]

Right, so the mirror I used wasn’t intended to be the final one.

As far as I know, the Fabry-Perot resonator is used as a narrow band filter. This is very different use of a mirror from other applications. The FP works on multiple reflections with very accurately controlled path lengths. This job can't be done with off the shelf mirrors. Fringes (equivalent to Newton's Rings ) are a no no. The spacing has to be very accurately controlled because there are many reflection paths- this means that the aperture won't be great.

But what is your final application? Do you think you could do better than a diffraction grating - if you want to do spectroscopy. Gratings are cheap enough.

or mirrors specifically for Fabry-Perots.

Probably available by special order at a price - hundreds of quid, no doubt.

 

[dykuma]

But what is your final application? Do you think you could do better than a diffraction grating - if you want to do spectroscopy. Gratings are cheap enough.

I want to try to do spectroscopy of TLE's (sprites and things like that). They are quick and very faint, so using a regular narrowband filter might make them too hard to see. I was inspired by how solar telescopes use F-P's to observe fainter solar flares, and figured something similar was possible here.

 

[sophiecentaur]

I was inspired by how solar telescopes use F-P's to observe fainter solar flares, and figured something similar was possible here.

Not home made, I'm sure - or everybody would bet doing it. The numbers are just not right, I think.

 

[dlgoff]

As far as I know, the Fabry-Perot resonator is used as a narrow band filter. This is very different use of a mirror from other applications. The FP works on multiple reflections with very accurately controlled path lengths. This job can't be done with off the shelf mirrors. Fringes (equivalent to Newton's Rings ) are a no no. The spacing has to be very accurately controlled because there are many reflection paths- this means that the aperture won't be great.

Bold by me.
This brings up memories of the Modern Optics class I had while getting my Engineering Physics BS. Her are some photos of the Text, I still have, and a couple photos about the Fabry-Perot interferometer:

 

[sophiecentaur]

The OP should do a google search for the prices of FP etalons. That would be the best way to estimate just how hard they are to make without full lab facilities.