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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: 10705     Entry time: Wed Nov 12 21:18:32 2014     In reply to: 10700     Reply to this: 10713
Author: ericq 
Type: Update 
Category: LSC 
Subject: DRFPMI, PRFPMI HOM resonances 

So, with my last entry, I was guilty of just throwing stuff into the simulation and not thinking about physics... so I retreated to Siegman for some algebraic calculations of the additional Guoy phase accumulated by the HOMs in the arms -> their resonant frequencies -> the arm length offset where they should resonate. Really, this isn't completely precise, as I treated the arms independently, with slightly differing ETM radii of curvature, but I would expect the "CARM Arm" to behave as a sort of average of the two arm cavities in this regard. (EDIT: Also, I didn't really consider the effect of the coupled vertex cavities... so there's more to be done)

The basic idea I used was:

  • Assume ITMs are effectively flat, infinite Rc
  • Use 40mwiki values for ETM curvatures
  • Each additional HG order adds arccos(sqrt(1 - Larm/Rc)) of Guoy phase for a one way trip down the cavity (Eqn 19.19 in Sigman)
  • For each HOM order up to 5 of the carrier and first order sidebands, add the appropriate phase shift 
  • fold it onto +-FSR/2 of the carrier 00 resonance, convert to m

In practice, I threw together a python script to do this all and print out a table. I've highlighted the values within 10nm, but the closet one is 3.8nm

Results:

########## X Arm HOM Resonance Locations in nm ##########
Mode Order:      0     ,      1     ,      2     ,      3     ,      4     ,      5     

Carrier   :          +0,     +156.21,     -219.58,     -63.376,     +92.832,     +249.04
LSB 11    :     +59.563,     +215.77,     -160.02,     -3.8126,      +152.4,      -223.4
USB 11    :     -59.563,     +96.645,     +252.85,     -122.94,     +33.269,     +189.48
LSB 55    :     -234.18,     -77.975,     +78.233,     +234.44,     -141.35,     +14.857
USB 55    :     +234.18,     -141.61,       +14.6,     +170.81,     -204.98,     -48.776


########## Y Arm HOM Resonance Locations in nm ##########
Mode Order:      0     ,      1     ,      2     ,      3     ,      4     ,      5     

Carrier   :          +0,     +154.82,     -222.35,     -67.531,     +87.292,     +242.11
LSB 11    :     +59.313,     +214.14,     -163.04,      -8.218,      +146.6,     -230.57
USB 11    :     -59.313,      +95.51,     +250.33,     -126.84,     +27.978,      +182.8
LSB 55    :     -235.43,     -80.611,     +74.212,     +229.04,     -148.14,     +6.6809
USB 55    :     +235.43,     -141.74,      +13.08,      +167.9,     -209.27,     -54.452
 
Code is attached. Hopefully no glaring mistakes!
 
 
Attachment 1: HOMlist.py.zip  972 Bytes  Uploaded Thu Nov 13 00:03:34 2014
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