| Quote: |
|
| Quote: |
|
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. |