Current Mode Matching and Gouy Phase Between Steering Mirrors
We found in 40m elog ID 3330 ( http://nodus.ligo.caltech.edu:8080/40m/3330) a documentation done by Kiwamu, where he measured the waist of the green. The waist of the green is about 35µm. Using a la mode, I was able to calculate the current mode matching, and the Gouy phase between the steering mirrors. In a la mode, I used the optical distances,which is just the distance measured times its index of refraction. I contacted someone from ThorLabs (which is the company that bought Optics For Research), and that person told that the Faraday IO-5-532-LP has a Terbium Gallium Garnet crystal of a length of 7mm and its index of refraction is 1.95. The current mode matching is 0.9343, and the current Gouy phase between steering mirrors is 0.2023 degrees. On Monday, Nick and I are planning to measure the actual mode matching. The attached below is the current X-arm optical layout.
Calculation For the New Optical Layout
Since the current Gouy phase between the steering mirror is essentially zero, we need to find a way how to increase the Gouy Phase. We tried to add two more lenses after the second steering mirror, and we found that increasing the Gouy phase result in a dramatically decrease in mode matching. For instance, a Gouy phase of about 50 degrees results in a mode matching of about .2, which is awful. We removed the first lens after the faraday, and we added two more mirrors and two more lenses after the second steering mirror. I modified the photo that I took and I place where the new lenses and new mirrors should go as shown in the second pictures attached below. Using a la mode, we found the following solution:
label z (m) type parameters
----- ----- ---- ----------
lens 1 0.0800 lens focalLength: 0.1000
First mirror 0.1550 flat mirror none:
Second mirror 0.2800 flat mirror none:
lens 2 0.4275 lens focalLength: Inf
lens 3 0.6549 lens focalLength: 0.3000
lens 4 0.8968 lens focalLength: -0.250
Third mirror 1.0675 flat mirror none:
Fourth mirror 1.4183 flat mirror none:
lens 5 1.6384 lens focalLength: -0.100
Fifth mirror 1.7351 flat mirror none:
Sixth mirror 2.0859 flat mirror none:
lens 6 2.1621 lens focalLength: 0.6000
ETM 2.7407 lens focalLength: -129.7
ITM 40.5307 flat mirror none:
The mode matching is 0.9786. The different Gouy phase different between Third Mirror and Fourth Mirror is 69.59 degrees, Gouy Phase between Fourth and Fifth 18.80 degrees, Gouy phase between Fifth and Sixth mirrors is 1.28 degrees, Gouy phase between Third and Fifth 88.38 degrees, and the Gouy phase between Fourth and Sixth is 20.08 degrees. Bellow attached the a la Mode code and the Plots.
Plan for this week
I don't think we have the lenses that we need for this new setup. Mostly, we will need to order the lenses on Monday. As I mention, Nick and I are going to measure the actual mode matching on Monday. If everything look good, then we will move on and do the Upgrade.