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Entry  Sat Jun 12 19:41:04 2010, Alberto, Update, Locking, 40m Upgrade Optickle Model optickleIFOworkingpoint.pdf
    Reply  Sun Jun 13 08:28:44 2010, valera, Update, Locking, 40m Upgrade Optickle Model 
       Reply  Mon Jun 14 07:57:07 2010, alberto, Update, Locking, 40m Upgrade Optickle Model 
          Reply  Tue Jun 15 21:28:44 2010, alberto, Update, Locking, 40m Upgrade Optickle Model allTransferFunctions_DARMoff_0.pdfallTransferFunctions_DARM2AS_10pmDARMoffset.pdfJan_DARM2AS.pdf
Message ID: 3079     Entry time: Tue Jun 15 21:28:44 2010     In reply to: 3075
Author: alberto 
Type: Update 
Category: Locking 
Subject: 40m Upgrade Optickle Model 




 In my calculation of the digital filters of the optical transfer functions the carrier light is resonant in coupled cavities and the sidebands are resonant in recycling cavities (provided that macroscopic lengths are chosen correctly which I assumed).

Carrier and SB (f2) shouldn't be resonant at the same time in the SRC-arms coupled cavity. No additional filtering of the GW signal is wanted.

The SRC macroscopic length is chosen to be = c / f2 - rather than = [ (n+1/2) c / (2*f2) ] - accordingly to that purpose.

I calculated the frequency of the double cavity pole for the 40m SRC-arm coupled cavity.

w_cc = (1 + r_srm)/(1- r_srm) * w_c

where w_c is the arm cavity pole angular frequency [w_c = w_fsr * (1-r_itm * r_etm)/sqrt(r_itm*r_etm) ]

I found the pole at about 160KHz. This number coincides with what I got earlier with my optickle model configured and tuned as I said in my previous entry. See attachments for plots of transfer functions with 0 and 10pm DARM offsets, respectively.

I think  the resonance at about 20 Hz that you can see in the case with non-zero DARM offset, is due to radiation pressure. Koji suggested that I could check the hypothesis by changing either the mirrors' masses or the input power to the interferometer. When I did it frequency and qualty factor of the resonance changed, as you would expect for a radiation pressure effect.

Independently, Jan also calculated the pole frequency of the transfer function DARM / ASQ2 as we would expect it for the SRC-coupled cavity. He also found the pole at about 160KHz. I'm attaching the plot with the transfer function he calculated.
He also said that the little bump at the pole frequency is OK considering that our signal recycling cavity is not much shorter than the arms.

This gave me more confidence about my optickle model of the 40m. This is quite comforting since I used that model other times in the past to calculate several things (i.e. effects of higher unwanted harmonics from the oscillator, or, recently, the power at the ports due to the SB resonating in the arms).

I don't know anymore what Valera said that wasn't right.
Also, as he said, he set it for the carrier to be resonant in the SRC-arms couple cavity. But that is not our case.
Attachment 1: allTransferFunctions_DARMoff_0.pdf  13 kB  | Hide | Hide all
allTransferFunctions_DARMoff_0.pdf allTransferFunctions_DARMoff_0.pdf allTransferFunctions_DARMoff_0.pdf
Attachment 2: allTransferFunctions_DARM2AS_10pmDARMoffset.pdf  12 kB  | Hide | Hide all
allTransferFunctions_DARM2AS_10pmDARMoffset.pdf allTransferFunctions_DARM2AS_10pmDARMoffset.pdf allTransferFunctions_DARM2AS_10pmDARMoffset.pdf
Attachment 3: Jan_DARM2AS.pdf  5 kB  | Hide | Hide all
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