40m QIL Cryo_Lab CTN SUS_Lab TCS_Lab OMC_Lab CRIME_Lab FEA ENG_Labs OptContFac Mariner WBEEShop
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Entry  Wed Jan 30 11:16:32 2013, Jenne, Update, Locking, Mode spacing calc 
    Reply  Wed Jan 30 15:45:09 2013, Zach, Update, Locking, Mode spacing calc HOM11.pngHOM55.png
       Reply  Thu Jan 31 14:30:50 2013, Jenne, Update, Locking, Mode spacing calc Half_PRC_Configs.pdf
          Reply  Thu Jan 31 15:20:46 2013, Zach, Update, Locking, Mode spacing calc 
Message ID: 7975     Entry time: Thu Jan 31 15:20:46 2013     In reply to: 7973
Author: Zach 
Type: Update 
Category: Locking 
Subject: Mode spacing calc 

I should mention that I just found a bug in how it treats odd-mirror-number cavities. For such cavities, HG modes with odd horizontal indices should receive an extra roundtrip phase of pi/2 (due to the rotation by the cavity). Because of a numbering convention issue, arbcav actually used to apply this phase shift to even-order modes. Essentially, the only difference is that the fundamental mode was shifted to anti-resonance. Everywhere else, there are modes at both corresponding locations in frequency space, and so it does not back a big difference in terms of cavity design.

Thanks to this IMC modeling we are doing at the workshop, I caught it! It has been fixed in the SVN.


I have calculated (using Zach's sweet software) the expected mode content for the various possible PRCs that we can make. 

Also, Zach was right about the factor of 2.  I see now that I was calculating the mode spacing between a plane wave and a HOM, so the guoy phase had a factor of (n+m+1).  The right thing to do is to get the spacing between the 00 mode and HOMs, so the guoy phase just has (n+m).  Switching from n+m+1=2 to n+m=1, that fixes the factor of 2 problem.

 I attach my results as a pdf, since I'm listing out 5 configurations.  Each config has a cartoon, with a small (hard to read) HOM plot, and then at the end, each HOM plot is shown again, but larger.  Also, "TM" is the "test mirror", the flat G&H that we're using as the cavity end mirror.


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