Summary:

The mode-matching between the LO and AS beams is now ~50%. This isn't probably my most average mode-matching in the lab, but I think it's sufficient to start doing some other characterization and we can try squeezing out hopefully another 20-30% by putting the lenses on translation stages, tweaking alignment etc.

Details:

The main change was to increase the optical path length of the IFO AS path, see Attachment #1. This gave me some more room to put a lens and translate it.

• The LO path uses two lenses, f=200mm and f=100mm to focus the collimator output beam, which is supposedly ~1200um diameter, to something like 400um diameter (measured using beam profiler but not very precisely).
• This beam is  fairly well collimated, and the beam size is close to what the PMC cavity will want, I opted not to tweak this too much more.
• For the AS beam, the single bounce reflection from ITMY was used for alignment work.
• There is a 2" f=600mm lens upstream (not seen in Attachment #1). This supposedly makes a beam with waist ~80um, but I couldn't numerically find a good solution numerically if this assumption is true, so I decided to do the mode-matching empirically.
• A single f=150mm lens got me a beam that seemed pretty well collimated, and roughly the same size as the LO beam, so I opted to push ahead with that. Later, I measured with the beam profiler that the beam is ~600um in diameter, so the beam isn't very well matched to the LO spot size, but I decided to push ahead nevertheless.
• Patient alignment work enabled me to see interference fringes.
  • Note that the ITM reflection registers 30 cts (~80 uW). Assuming 800mW transmission through the IMC, I would have expected more like 800mW * 5.637% * 50% * 98.6% * 50% * 10% * 30% * 50% * 50% = 80uW, so this is reasonable I guess. The chain of numbers corresponds to T_PRM * T_BS * R_ITM * R_BS * T_SRM * T_vac_OMC_pickoff * R_in_air_BS * R_homodyneBS.
  • The IFO AS beam appears rather elliptical to the eye (and also on the beam profiler). It already looks like this coming out of the vacuum so not much we can do about it right now I guess. By slightly rotating the f=150mm focusing lens so that the beam going through it at ~10 degrees instead of normal incidence, I was able to get a more circular beam as measured using the beam profiler.
  • With the AS beam blocked, the LO beam registers 240 cts on each DCPD (~0.7 mW). 
  • The expected fringe should then be (sqrt(240) + sqrt(30))^2 - (sqrt(240) - sqrt(30))^2 ~ 440 cts pp.
  • The best alignment I could get is ~200 cts pp, see Attachment #2.

Next steps:

Try the PRMI experiments again, now that I have some confidence that the beams are actually interfering.

See Attachment #3 for the updated spectra - the configuration is PRMI locked with carrier resonant and the homodyne phase is uncontrolled. There is now much better clearance between the electronics noise and the MICH signal as measured in the DCPDs. The "LO only" trace is measured with the PSL shutter closed, so the laser frequency isn't slaved to the IMC length. I wonder why the RIN (seen in the SUM channel) is different whether the laser is locked to the IMC or not? The LO pickoff is before the IMC.