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Entry  Wed Nov 12 01:30:39 2014, ericq, Update, LSC, DRFPMI, PRFPMI HOM resonances HOMs.zipDRFPMI_HOMscan.pngPRFPMI_HOMscan.png
    Reply  Wed Nov 12 21:18:32 2014, ericq, Update, LSC, DRFPMI, PRFPMI HOM resonances HOMlist.py.zip
       Reply  Fri Nov 14 02:43:05 2014, ericq, Update, LSC, PRFPMI HOM resonances HOMcurves.pdfHOMpeaks.pdfprfpmiHOM.zip
Message ID: 10713     Entry time: Fri Nov 14 02:43:05 2014     In reply to: 10705
Author: ericq 
Type: Update 
Category: LSC 
Subject: PRFPMI HOM resonances 

I've extended my analysis to the PRFPMI case, with the current working knowledge of radii of curvature and cavity lengths. However, losses were not included.

I do not see any HOM activity within about 20nm of the carrier TM00 resonance. 

Basically, what I did was use the standard formulae for the reflection and transmission coefficients of FB cavities viewed as compound mirrors. However, I modified the normal spatial propagation terms to include the additional Guoy phase accumulated by the HOMs. I created these coefficients for each arm individually, and then used (rX + rY)/2 as a mirror in the PRC, and used that to create the transmission coefficient for the PRFPMI as a whole, as a function of frequency offset from the carrier, spatial mode order and CARM offset. As a check, this produced the correct finesse for the carrier lock to the single arm and PRFPMI. 

Here is a PRFPMI CARM FSR of all of the fields' power transmission coefficients, up to order n+m=5. 

HOMcurves.pdf 

One can observe some split peaks. There are two causes, the biggest effect is the mismatch between ETM radii of curvatures (ETMX:59.48, ETMY:60.26):, followed by asymmetric arm length(X:37.79, Y:37.81). (I judged this by the visual change of the plot when changing different factors). 

In the following plot, I broke down the peaks by mode order:

 HOMpeaks.pdf

Code, plots attached!

 

Attachment 3: prfpmiHOM.zip  880 kB
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