The data with the increased modulation depth of the 6MHz in LN3 to 3dB (purple lines in the figures) can be compared to the normal conditions with -28dB modulation of the 6MHz (blue lines).

In the figures we compare two photodiodes B4 PD1 and PD2, which see the same power. The differences are that PD2 has an analog notch at 6MHz, which reduces the line by a factor ~20. Also itis a 3mm diameter photodiode compared to 2mm for PD1, which means that above ~20MHz the response of the PD2 photodiode is a factor 2 smaller than of the PD1 photodiode due to the photodiode capacitance.

Figure 1 shows the broadband RF spectrum, the dominant lines are the 56MHz+/-6MHz, 12MHz and 6MHz. On PD2 the 56MHz+/-6MHz lines are a factor 2 lower due to the PD size. The 12MHz line is about the same in both. And the 6MHz is a factor 20 lower in PD2 due to the notch.

Figure 2 zoom into the region between 1MHz and 20MHz. Comparing purple and blue the 12MHz line is increased by a factor 1000 as expected from the 31dB increase in modulation. The 6MHz, 2MHz and 14MHz are increased by a factor 30 in both photodiodes, also expected from the 31dB increase in modulation. The 14MHz and 2MHz are the beat notes between the 8MHz and 6MHz, in principle the height should be half way in between on a log scale between the 12MHz and the 16MHz, hower they are almost equal to the 16MHz, a factor 3 smaller than expected. The probable reason is that the overlap between the 6MHz and 8MHz beam shape is poor, of the order of 50% in amplitude (so ~30% in power). The only sign of non linearity in PD1 on that figure is the small line 4MHz.

Figure 3 zoom between 2MHz and 50MHz, there are several lines which are much higher in PD1 than in PD2, the 3*6MHz line is a factor ~20 higher, and the 7*6MHz is a factor 10 higher. The 5*6MHz line is a factor 4 higher. The 4*6MHz and 6*6MHz line are a factor 2 higher in PD1, but that is expected due to the larger size of PD2. An additional 2dB of 6MHz modulation was causing PD1 to saturate, so this increase in odd harmonics of the 6Mhz shows the beginning of the distorsion in the signal due to non linearities close to saturation, not however that these harmonics are over 2 orders of magnitude smaller than the 6MHz itself.

2mW RMS of RF spectrum appears to be a limit of this photodiode design. It consistent with LNA (ABA-52563) data sheet saturating at 1V RMS, assuming there is no other gain factor than the 2.592 into the DAQ. The notch at 6MHz on PD2 is able to reduce this RMS by a factor 2 to ~1mW. The next three contributors in PD1 are the 12MHz, 50MHz and 62MHz which each contribute ~0.7mW RMS, for a total of 1.2mW RMS (in PD2 the 50MHz and 62Mhz are smaller due to the PD size).

The biggest limitation to increasing the modulation depth is the 12MHz as increasing the modulation to 13dB would increase its amplitude by a factor 10 to 7mW RMS. So a notch at 12MHz would be definitely needed to reduce the amplitude to 0.4mW RMS. An already notched 6MHz would increase by a factor 3 to 0.3mW RMS. Notching the 50MHz and 62MHz, is impossible without removing also the 56MHz. So these would increase each of these sidebands 2.1mW RMS, for a total of 3mW RMS. The LNA planned for O4 (PHA-13LN+) starts to distort signals for a 7dB higher signal according to the data sheet. So should be able to handle 4.5mW RMS with the same distorsion as seen here for PD1 with 2mW RMS. So a notch at 6MHz and 12MHz with the new LNA should be able to handle 13dB of 6MHz modulation with a factor 1.5 of margin with regard to the start of distorsions. However, the power increase from 25W to 40W is equal to that margin of 1.5. So keeping the power at 40mW on these photodiodes may be needed, by dumping some of the power on SPRB on a beam dump.

Figure 4 shows the situation for B1. The 6MHz saturates the photodiode with 4mW RMS. The new high finesse OMC design will reduce the 6MHz power on B1 by a factor 10. Also signal recycling will reduce the amount of 6MHz reaching the photodiode by another factor 8, as the 6MHz is not resonant in the SRC. This gives in total a decrease by a factor 80 in power, or a factor 9 in the 6MHz beat with the carrier. If the 6MHz modulation depth is increased to 13dB, the 6MHz beat would increase by a factor 3/9, and the 12MHz would increase by a factor 10/80. In total this would give 1.3mW RMS on the photodiode for the 6MHz, and 0.04mW RMS for the 12MHz. The filtering of the 56MHz will not change for O4, but the power of the sidebands might increase by a factor 5. This would bring the 56MHz to 0.3mW RMS. In conclusion notches should not be necessary for the B1 photodiode in O4, but we might consider it as a precaution for the 6MHz, if it doesn't have an impact on the squeezing signal planned for O4 at ~4MHz.

Analysis remains to be done for B1p and B2.

For B1p there are two photodiodes, PD2 sees 10 times less power than PD1, and it has notches at 2MHz, 6MHz and 12MHz.

Figure 1 compares B1p PD1 and PD2 in broad band. As expected the 56MHz is smaller in PD2 by a factor 10 compared to PD1, because of the lower power.

Figure 2 zooms into the 1-20MHz region. The 6MHz is a factor 200 smaller in PD2 (10 due to power and 20 due to notch), the 2MHz is smaller by more than a factor 200 for the same reasons. The 12MHz is smaller only by a factor 100, so the notch might be less effective and provide only a factor 10 of attenuation.

In B1p PD1 the 6MHz is comparable to the 56MHz, so with 13dB of modulation it would be a factor 3 higher and cause issues, as the line height would be at 3mW RMS, the 12MHz would stay more manageable at 1mW RMS.

Figure 3 shows B2 PD2 in a wide frequency range and Figure 4 zooms into the 1-20MHz range, that photodiode has notches at 16MHz, 49MHz and 61MHz. The 2MHz and 14MHz have a height comparable to the 12MHz and 16MHz, which are roughly equal, so this is just the beat between the 6MHz and 8MHz. The only unexpected behavior is that the 2MHz is a factor 2 higher than the 14MHz, this is due to the 14MHz being reduced by the 16MHz notch. This factor 2 is already present when the 6MHz modulation is at -28dB (blue curve). Note that there 2MHz harmonics at 4MHz, 10MHz, 18MHz, ... I expect this is due to the VGA which has a gain setting 10 times higher than for other PDs and is known to have distorsion at the ~50dBc level (VIR-0215A-20).

A concern is that B2 PD2 sees currently only 3mW of power, and for O4 we plan to increase this by a factor 10. This would bring the spectrum RMS 3mW when the 6MHz is reduced to -28dB, so already at the limit of what the new RF read-out chain could handle. Furthermore, increasing the 6MHz modulation from 3dB to 13dB would put the 12MHz at 20mW RMS, the 2MHz at 20mW RMS, the 6MHz at 6mW RMS and the 14MHz at 6mW RMS. It would also bring the 56+/-6Mhz at 2mW RMS each. So even by adding notches at 2MHz, 6MHz and 12MHz (which would also reduce the 14MHz by a factor 2-3), it would bring the total RMS to ~5mW, probably slightly more than the new RF read-out chain can handle. And also this would bring the number of notches from 3 to 6, while only the space for 3 notches is available on the PCB.

Note that in this and the previous logbook entry I have misread the label of the y axis. So the power should be in uW and not in mW. However, this powers seems far too low for me, so I expect the calibration factor into mW to be wrong.

The main issue with the RMS values in the entries above is not the calibration but a bug in dataDisplay.

Figure 1 shows the RF spectrum of B2 and the time series in dataDisplay.

Figure 2 shows the same computed from data in matlab. The spectrum is exactly the same. The correctly computed RMS is shown in red and the way it is computed in dataDisplay is shown in yellow. The difference is that dataDisplay forgets that the sample data has gaps, so the spectral resolution is not 1Hz but much poorer than that. All the RMS values are wrong by a factor 110 because of this. This also shows that the voltage RMS is not the right quantity to look at for saturations. The voltage RMS is computed to be 0.1V but the peak value of the time series (figure 1) is slightly above 0.2V. If the signal was a pure sine wave at 0.1V RMS should give a peak value of 0.15V. But here with have several RF frequencies that can add up coherently (depending on the phase between them).

Then looking at the calibration. The DAQ corrects for the gain of the variable gain stage. However the demodulation mezzanine has an additional total gain of 4.5dB due to the (VIR-0215A-20), and the LNA on the photodiode PCB (ABA-52563) has a gain of 21.5dB, so in total a 26dB gain. This means that a 1mA of RF current, converted by 50 Ohm resistor, yields a voltage recorded by the ADC of 1V. Below the PD response pole (~12MHz) 1mA of current correspond to an optical power of 1.296mW assuming a 90% quantum efficiency of PDs. This means that the calibration factor for the RF data should be 1.296 mW/V, whereas it is 2.59 mW/V in the configuration file. So wrong by a factor 2.

This factor 2 error is also visible on the spectra level, see figure 4 for an example. B4 PD1 has a power of 40mW, which should give a shot noise at 1.15e-7 mW/rtHz, instead the spectrum is shown at ~2.5e-7 mW/rtHz because of this factor 2 error in the calibration.

Figure 3, coming back to the B4 PD1 data which close to saturation, they are reaching 0.8mW with the wrong calibration factor. So they correspond to 0.3 V in the DAQ before calibration, 0.4V at the input of the VGA (AD8370) and 0.2V at the output of the LNA (ABA-52563). The VGA has been measured to saturate at 0.75V (1.5 Vpp) in low gain mode, 0.375V at the output of the LNA because of 6dB gain of the transformer in front of the VGA. while for the LNA the 0.2V is a factor 5 below the 1dB compression point at 10dBm (1V amplitude). So it seems the VGA starts to become non-linear from our point of view for signals that are slightly less than a factor 2 smaller than the saturating amplitude.

For O4, the new VGA ADL5205, has been measured to saturate at 2.8V (5.7 Vpp, after taking into account the 3dB gain of the transformer in front of the VGA), so that is the maximum voltage that can be sent out by the LNA, a factor 7 increase over the current situation. The new LNA (PHA-13LN+) has its 1dB compression at 16dBm instead of 10dBm, which correspond to an amplitude of 2V. So the LNA will become the new limit on the dynamic, with a total improvement of a factor 5, assuming the 1dB compression will not spoil to much the signals.

These data also provide us with information on the stability of the 6MHz sideband optical gain.

Figure 1 and 2 shows examples for -9dB and -3dB of modulation depth. In both cases the stability is about the same, with 20% fluctuations in the 2f (12MHz) magnitude, for the 56MHz the stability is better, with fluctuations of ~5%.