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Entry  Mon Nov 9 10:08:38 2020, anchal, Summary, ECDL, AUX wavelength finesee requirements in mariner with 1418 nm ECDL (Preliminary) AUX_Finesse_Study_With_ECDL.pdf
    Reply  Wed Nov 11 16:09:22 2020, anchal, Summary, ECDL, AUX wavelength finesee requirements in mariner - Added Excess Scatter Noise AUX_Finesse_Study_With_ECDL.pdf
Message ID: 2518     Entry time: Wed Nov 11 16:09:22 2020     In reply to: 2515
Author: anchal 
Type: Summary 
Category: ECDL 
Subject: AUX wavelength finesee requirements in mariner - Added Excess Scatter Noise 

An issue was raised with last calculation about the fact that our sensing of PDH signal isn't ideal and in the real world there is scattering, clipping extra adding excess noise in the PDH loop. This noise primarily comes by the intensity noise imparted on promptly reflected light from the cavity via various shaking optics etc on the table before it goes to the PDH reflection RF photodiode.

This noise's coupling to the PDH loop is identical to how shot noise of light couples into the PDH loop i.e.:

  • Intensity noise of light is converted into voltage oise by the PDH photo diode.
  • This is compared against the cavity finesse amplified real PDH error siganl at this stage.
  • Therefore, in frequency noise, the affect of this intensity noise is smaller for higher finesse cavities since cavity finesse only amplifies the PDH signal anf not the scattering noise.

Excess noise estimate

  • I used this measurement taken in 40m with Koji to estimate this noise.
  • This measurement contained a beatnote between IR coupled AUX light and the main laser IR pick-off when X-arm is locked to the main laser and AUX laser is locked to X-arm.
  • So this noise measurement is an upper bound on the total noise in AUX laser frequency when it is locked to the X-arm.
  • I compared this against the noise budget model for AUX PDH loop I have which uses the same control loop as the uPDH box used here.
  • I found a bulge of excess noise below 100 Hz and it seemed to go done as 1/f^2 there. I was reminded by a chat I had with Rana and another professor sometime last year when Rana mentioned scattering noise showing up as "Scatter shelf" looking something like this.
  • So I modeled excess noise as the difference between the noise budget and the measured noise with it extending after 100 Hz with the same roll off as in 10-100 Hz.

Calibration noise budget

  • I took the excess noise measured, converted it to W/rtHz by using current AUX PDH discriminant and photodiode gain, and normalized by the power (9.6mW) to get this noise in RIN/rtHz.
  • Then I assumed that the same RIN would be imparted in the Mariner AUX loop and calculated excess intensity noise at the PDH loop by multiplying the above number with assumed 10mW of incident power to get it in W/rtHz.
  • From here, I fed it to the same input as I feed the shot noise in the loop and calculated the effect in the overall noise budget.
  • For high bandwidth and gain PDH loops required for calibration, this kind of noise would dominate up to a kHz before getting taken over by the residual laser frequency noise.
  • I have again plotted cases for three choices of finesse/mirror transmission. If we used 99.95% reflectivity (1000 ppm transmission, finesse of 3140) we would be fine for most calibration lines except the one around 40 Hz. (assuming drive strength of 1e-13 m everywhere).
  • Otherwise, if possible, we should go for higher finesse. Case (c) plotted here (Page 3), shows that for 99.995% reflectivity (100 ppm transmission, finesse of 31415), we will be fine in all over the range with cavity pole dropping to 63 Hz. This would be really nice of course, if it is possible.
  • So we recommend HR coatings for 1418 nm in the Mariner to be 99.995% reflective (giving total power transmission of 100 ppm).
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