My latest adventure in interferometry
This weekend was graduation weekend which meant two days of events in which we, the faculty, basically serve as eye candy. Thus that means listening to lots of speeches. Fortunately, our current Dean is a master at getting through all the graduates’ names quickly. At any rate, this being the first graduation with our newly reduced parking capacity (someone told us we had too much — I’m not kidding), traffic was worse than usual and so I hung out in the lab for a bit after the ceremony ended waiting until I could get out of the parking lot in a timely fashion.
So, let me first say that I have an increasingly god-like reverence for experimentalists. Lesser mortals would go utterly insane from the combination of tedium and unexpected results. As a theorist, I figure that I’m already insane so it doesn’t matter. After an entire semester of getting nothing but parallel lines on my outputs, I ended up getting the “bull’s eye” pattern which is clearly a laser cavity mode (at that point, I was ready to beat my head against the wall).
Curiously (or not?), I got it when the arms were each 8 inches long or 16 inches long but not when the arms were 18 inches long or 20 inches long. In the latter two cases, absolutely nothing I did produced an interference pattern whereas it was pretty easy in the former two cases (the closer it was to a parallelogram, the better the pattern). Now, this summer I’m ordering some fully-gimbaled mirror holders that match the mirror surface up with the center line to make aligning easier. I’m hoping I can quantify some of the nuances of the alignment a bit better with these.
Anyway, that all leads me to two conclusions:
- the interference pattern in an MZI has something to do with cavity modes; and
- textbooks (and even some papers) on optics, particularly on MZIs and Michelsons, are complete crap.
On another note, in reply to my last post on this topic, someone noted that my calculation of the coherence length might be incorrect and should actually be closer to 300 microns. So in doing it again, I got a completely different number. Maybe someone can locate my error. The linewidth of the laser I’ve got (if I’m reading it correctly) is 2 nm. I have no idea if the lineshape is Lorentzian or Gaussian, but I’m just going to guess Lorentzian for now. Thus the coherence time is given by . Now, I think, upon further reflection, that is the half width of the lineshape in angular frequency units. Since , then which, for a half line width of 1 nm gives rad/s. The coherence time is then s. The coherence length is then m or 561 nm. If my mistake was in the linewidth and it is actually 2 nm, then the coherence length is actually 112 nm.
Now, if it is a Guassian beam instead of a Lorentzian beam, the coherence time is actually . This changes the coherence length for a half line width of 1 nm to 234 nm. So it doesn’t seem to matter what I do, I’m consistently getting a coherence length that is in the hundreds of nanometers. As was pointed out, I should be getting a number closer to 300 microns. Where’s my error?