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Entry  Thu Sep 16 15:21:21 2021, Paco, DailyProgress, 1418 nm AUX ECDL, Free space AOM 
    Reply  Wed Sep 22 16:44:34 2021, Radhika, DailyProgress, 1418 nm AUX ECDL, Free space AOM 
       Reply  Mon Oct 4 17:44:34 2021, Radhika, DailyProgress, 1418 nm AUX ECDL, Free space AOM 
          Reply  Tue Oct 19 13:52:03 2021, Radhika, DailyProgress, 1418 nm AUX ECDL, 1418nm ECDL Frequency noise ECDL_diagram.pdfECDL_FNM_13-10-2021_151524.pdf
             Reply  Tue Mar 8 09:32:56 2022, Paco, DailyProgress, 1418 nm AUX ECDL, 1418nm ECDL Frequency noise schematic.pngraw_bn_spectrum.pngphase_timeseries.pngecdl_freqnoise.png
Message ID: 1928     Entry time: Tue Mar 8 09:32:56 2022     In reply to: 1927
Author: Paco 
Type: DailyProgress 
Category: 1418 nm AUX ECDL 
Subject: 1418nm ECDL Frequency noise 

[Paco, Radhika]

Beatnote recovery

Restarted ECDL characterization last Friday. After some lab cleanup, and beatnote amplitude optimization we borrowed Moku Lab from Cryo lab to fast-track phase noise measurements. Attachment #1 shows a sketch of our delayed self-heterodyne interferometer. The Marconi 2023A feeds +7 dBm to a  ZHA-3A amplfier which shifts the frequency of the laser in one of the arms using a free space AOM. The first order is coupled back into a fiber beamsplitter to interfere with a 10 m delay line beam.

Improved beatnote detection

The 38.5 MHz beatnote was barely detectable before when using PDA20CS2 because at unity (lowest) gain stage, the bandwidth was only 11 MHz... We instead switched to an FPD310-FC-NIR type which has a more adequate high-frequency response. Attachment #2 shows the beatnote power spectrum taken with Moku Lab spectrum analyzer. The two vertical lines indicate (1) the heterodyne beatnote frequency and (2) the "free spectral range" indicating the actual delay in the MZ arms, which is calibrated to c\tau/n = 9.73 m (using 1.46 for n, the fused silica fiber index).

Phase meter and freq noise calibration

We then tried using the phase meter application on the Moku. The internal PLL automatically detected the 38.499 MHz center frequency and produced an unwrapped RF phase timeseries (e.g. shown in Attachment #3). The MZ interferometer gives an AC signal

I_{\rm AC} = I_0 \cos(\Omega_0t + \phi(t + \tau) - \phi(t))

oscillating at \Omega_0 , i.e. the angular beatnote frequency. The delay (calibrated above) characterizes the response of the MZ relating the RF phase noise spectrum to the optical phase noise spectrum. The RF phase obtained through the phase meter has a fourier transform

\tilde{\phi}_{\rm RF}(\omega) = \tilde{\phi}(\omega) e^{-i \omega \tau} - \tilde{\phi}(\omega)

So the optical phase spectral density is related to the rf phase spectral density by a transfer function H(\omega) = e^{-i \omega \tau} - 1  Then, the RF & optical phase power spectral densities are related by S_{\phi_{\rm RF}}(\omega) = |1 - e^{-i \omega \tau}|^2 S_{\phi}(\omega)  or

S_{\phi}(\omega) = \frac{S_{\phi_{\rm RF}}(\omega) }{ 4 \sin^2(\omega \tau /2) }

Then, because the instantaneous laser frequency is 2 \pi \nu = \dot{\phi},  in fourier domain \tilde{\nu} = \frac{i\omega}{2 \pi} \tilde{\phi} the frequency and phase PSDs are related by the magnitude square of this transfer function like

S_{\nu}(\omega) = f^2 S_{\phi}(\omega)

Following this prescription, we compute an estimate for the frequency noise ASD (square root of the PSD) shown in Attachment #4. The frequency noise estimated by this method has several contributions and *does not* necessarily represent the free-running ECDL frequency noise.

Next steps

  • Noise budgeting (experiment)
  • Control loop (open/closed) models
Attachment 1: schematic.png  23 kB  | Hide | Hide all
Attachment 2: raw_bn_spectrum.png  109 kB  | Hide | Hide all
Attachment 3: phase_timeseries.png  24 kB  Uploaded Tue Mar 8 12:00:26 2022  | Hide | Hide all
Attachment 4: ecdl_freqnoise.png  78 kB  Uploaded Tue Mar 8 12:38:55 2022  | Hide | Hide all
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