Here's a Finesse modeling of what we're expecting to observe with this test. It uses Gautam's base model of the 40m IFO with appropriate modifications for the needed configuration.
The idea is to lock the IFO in the SRMI configuration, with the phase-locked AUX beam injected from the AS port. The AUX beam is imprinted with AM sidebands and slightly misaligned relative to the SRC so as to transfer power into HOM1. The RF network analyzer provides the drive signal for the AOM, and its frequency is swept to coherently measure the transfer function [reflected AUX beam / drive]. The reflected AUX beam is sensed by the AS110 PDA10CF.
It is also possible to drive PM sidebands as Koji suggests, but the squeezer group has encouraged using AM for practical advantages. The SNR with AM is a bit higher (less power lost into harmonics at large modulation index), there is a broadband AOM already available aligned to the SQZ beam at LLO, and there is also concern that driving strong PM could interfere with the SQZ control loops.
Expected SRMI Response
Attachment #1 shows the expected response to swept-AM in SRMI. Resolving just the FSR and the first-order mode splitting is sufficient to extract the SRC Gouy phase.
Expected response in the SRMI configuration.
Expected DRMI Response
Since the 40m has not been opearted in SRMI since ~2016 (last done by Eric Q.), Gautam believes it may take some time to relock this configuration. However, the modeling indicates that we can likely obtain sufficient sensitivity in DRMI, which would allow us to proceed faster. Attachment #2 shows the expected response to swept-AM in DRMI. The PRC leakage signal turns out to be significantly smaller than the SRC reflection (a factor of ~30 in amplitude), so that the signal still retains its characteristic shape to a very good approximation. The tradeoff is a 10x reduction in SNR due to increased PSL shot noise reaching AS110.
Expected DRMI response. The main difference is a 10x increase in shot noise on AS110.
Based on this, we should proceed with DRMI scans instead of PRMI next week.
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The PRC FSR is, of course, very close to twice of our f1 moudlation frequency (11MHz x 2 = 22MHz) .
I still don't understand what response the measurement is looking for. I understood the idea of using the subcarrier as a stablized carrier to the PRC with a certain freq offset from the main carrier. I suppose what was swept was the AOM modulation frequency (i.e. modulation frequency of the AM applied to the subcarrier). If that is the case, the subcarrier seemed fixed at an arbitorary frequency (i.e. 50MHz) away from the carrier. If one of the AM sidebands hits the PRC resonance (i.e. 22, 44, 66MHz away from the main carrier), you still have the other sideband reflected back to the AS. Then the RF signal at the AS is still dominated by this reflected sideband. I feel that the phase modulation is rather suitable for this purpose.
If you are talking about ~MHz AM modulation by the AOM and scanning the PLL frequency from 1MHz to 60MHz, the story is different. And this should involve demodulation of the AS signal at the AM modulation frequency. But I still don't understand why we don't use phase modulation, which gives us the PDH type signal at the reflection (i.e. AS) port...
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