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Message ID: 10191     Entry time: Sun Jul 13 17:06:35 2014
Author: Andres 
Type: Update 
Category: 40m Xend Table upgrade 
Subject: Xarm Table Upgrade Calculation and Diagrams of possible new table layout 

 Current Mode Matching and Gouy Phase Between Steering Mirrors

We found in 40m elog ID 3330 ( http://nodus.ligo.caltech.edu:8080/40m/3330a 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.


Attachment 1: CurrentOpticalLayout.png  19.323 MB  Uploaded Fri Jul 11 19:49:54 2014  | Hide | Hide all | Show all
Attachment 2: NewSetUp.PNG  19.401 MB  | Hide | Hide all | Show all
Attachment 3: AlaModeSolutionplots.png  35 kB  | Hide | Hide all | Show all
Attachment 4: EntireScaleRangeAlaModeSolution.png  33 kB  | Hide | Hide all | Show all
Attachment 5: NewXarmOptimizationFromFaraday.m  7 kB  | Show | Hide all | Show all
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