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Thu Jul 17 13:08:37 2008
HOM resonances in the arms
On Tuesday night we attempted to lock the full DRFPMI in the optical spring configuration with the +f2 sideband resonant in the SRC.
Despite having no problems locking on the +f2 in a DRM we couldn't lock the full IFO.
There was some discussion about whether a +f2 higher order mode resonance in the arms could cause this problem.
I calculated the positions of the first six higher order modes for the carrier and all sidebands (using Siegman p 762 (23) with a plus sign).
Plot attached. Colors indicate different frequency components, numbers are the mode index (m+n). Thick lines are fundamental modes of
the sidebands. Heights of HOM indicators have been scaled by 1/(m+n)^2.
It appears that the first order transverse mode of the +166 is indeed partially resonant. We might try to tweak the sideband frequencies a
little to see if this helps us. It would probably be prudent to measure the MC length first.
L = 38.5750; %average of Alberto's recent measurements elog #556
Retm = 57.375;
f166 = 165.977195e6;
f33 = 33.195439e6;
Uploaded Thu Jul 17 14:15:01 2008