Elli, Dave, Evan
Summary
After today's work to get SRMI locked (LHO#16993), we were able to take some preliminary measurements of the SRC using the aux laser. More work will be necessary before quoting any numbers about the length or Gouy phase.
Details
A brief description of the setup: on IOT2R, there is an auxiliary NPRO (Lightwave) which shoots into the back of IM4 and thereby probes the corner optics. Some of the light is reflected back onto IOT2R (along with some PSL light). An NF1611 is used to read out the beat of the PSL and the aux laser. On ISCT6, there is a second NF1611 which probes OMC REFL (which also contains a beat of the PSL and the aux laser, after these beams have been through the corner optics).
For this measurement, we detuned the aux laser by about 200 MHz relative to the PSL. We then locked the IOT2R beat frequency to the LO of a network analyzer (actuating on the aux NPRO PZT). While Elli kept SRMI locked, we swept the analyzer's LO by about 10 MHz. We recorded the transfer function (ISCT6 beat) / (analyzer LO).
Then Dave clipped beam in front of the ISCT6 PD, and we took another TF. This should in theory allow modes of odd order to contribute more strongly to the ISCT6 beat note.
Then Dave unclipped the beam again, and we took another TF with a −200 MHz detuning.
We're still trying to make sense of the data, but here are some initial impressions:
- The sweeps for the negative detuning have much broader peaks than the sweeps for the positive detuning.
- The positive-detuning sweeps have two peaks per FSR, regardless of whether the PD is clipped or not. There also is not much difference between the clipped and unclipped data (by eye, anyway).
Also, some useful numbers:
- The as-built SRC length is (as far as I know) nominally 56.008 m, as given in D0902838, so we expect an FSR of 2.68 MHz.
- The SRM transmissivity is supposed to be 37%, so the finesse of the SRC at zero detuning is 13.5. [Although I am somewhat confused here: Kiwamu claims that the installed optic is SRM-w14, but galaxy lists SRM-05 (with 20% transmissivity) as "H1 install".]
- The above two numbers give the SRC HWHM as 99 kHz.
- With an as-built SRC Gouy phase of 19°, we expect a transverse mode spacing of 141 kHz.
The data are attached. 02 is at positive detuning, no clipping; 03 is at positive detuning, clipping; and 04 is at negative detuning, no clipping.
Reploted the sweep 02 with the linear phase term removed. Markers are at 192.67 MHz (blue), 193.40 MHz (green) and 195.35 MHz (orange).
The marker offset between blue and green is 0.73 MHz, whereas between blue and orange it is 2.68 MHz.
If the large peaks are the 45.5 MHz sidebands and the carrier, the 9.1 MHz sidebands would be expected at an offset of 1.07 MHz.
Attached is a diagram of the electrical part of the measurement.
I can't remember what the first amplifier on the AS port 1611 is, so I'll fill it in later. Also, I think the next amplifier (ZFL-2500-VH) is only good down to 500 MHz, so we should replace it if we're going to do measurements at 200 MHz.
Here is the same plot for the negative frequency sweep. The markers are at -195.05 MHz and -197.65 MHz.
Notice, there is a sign flip in the phase—indicating that a dark or bright fringe is located between the two measurement regions.
I calculated the auto-correlation by patching the data of the two regions together and filling in a constant value. In case of the magnitude I used -38.3 dB and zero for the phase.
The first plot shows the auto-correlation of the phase in the frequency range from 380 MHz to 400 MHz. The blue data points are the data. The red curve is a fit of a cosine function with a gaussian amplitude profile. The orange makers indicate the region included in the fit. The center green marker is the fitted value for the minimum of the auto-correlation function. Its neighboring green markers are calculated by assuming the minimum corresponds to the 146th free-spectral-range. The purple marker are the predicted values from the as-built SRC length.
The second plot is the same for the magnitude.
The fitted values for the phase and magnitude auto-correlation extrema are 390.579 MHz and 390.504 MHz, respectively. Again, assuming 146 FSR, this corresponds to cavity lengths of 56.032 m and 56.043 m. The achieved accuracy seems to be around 1 cm—hinting that the SRC could be 3 cm long. Not sure I believe it without some further tests.
