I have used Optickle to model the effect of changing the phase between the 11MHz and 55MHz EOMs. Also, I have looked at what modulation order is most significant (we hope it's -22*11 and -11*22).
First, so that we can compare these numbers more directly to measurements, I have included in the model the fraction of light that gets to each PD. I'm assuming that the Faraday is about 80% transmissive, but I don't know what the true number is. Here's a cartoon showing the attenuation factors.
EDIT, 26March2015, JCD: REFL path updated. See elog 11172.
To model the change in relative phase between the 11MHz and 55MHz modultions, I have held the 11MHz EOM stationary, and moved the 55MHz EOM. Since I needed an actual distance, I used a conversion factor,
The sensing matrix was measured at 143Hz. It has been corrected from mevans-meters to Newtons as the denominator.
The big thing to notice here is that the PRCL magnitude is not changing by a factor of 20. More like a factor of 2. BUT, I have not yet included the fact that Koji also reduced the 55MHz modulation amplitude by a factor of 3.
As for the mysterious degeneracy of all the REFL PDs, I think we need to take a more careful measurement. It's possible that we were seeing the real thing for REFL33, but the others don't seem to change in degeneracy with relative modulation phase.
Why does it even matter for the 3*f1 signal what is going on with the f2 modulation? Well, it appears that we are definitely being dominated by the 44*11 and 55*22 components.
To check this, I restricted Optickle to various orders of modulation (ex. up to second order only includes the [-22, -11, 0, 11, 22] MHz components), and plotted them all. The change in the signal between one trace and another is the contribution from that extra modulation order. The traces are only minutely different between orders, after the 5th order. So, since they're all overlapping with the 5th order trace anyway, I don't plot them.
EDIT: to clarify, when I said "up to X order", I meant up to that order in 11MHz sidebands. Optickle is applying the 11MHz and 55MHz modulations in the same way every time, but then I specify up to what order to include in the summation of different contributions to the field at a given port. So, for the "up to 2nd order", I only include cross terms that come from [-22, -11, 0, 11, 22] MHz. For the next order, I only include terms that come from [-33, -22, -11, 0, 11, 22, 33] MHz, etc. So, there are no 55MHz effects when I'm only including contributions up to 2nd order (since there is a maximum cross beatnote of 44MHz), but starting with 3rd order, I do start to see signals in, for example, REFL55 and AS55, since I get terms from -22*33 and -33*22. The first order in 55MHz (i.e. 55MHz*Carrier) only starts to show up when I calculate "up to 5th order" and above, since that includes [-55, -44, -33, -22, -11, 0, 11, 22, 33, 44, 55] MHz.
What happens if I reduce the 55MHz modulation depth by 10dB? Since we are dominated by 55MHz-related signals, the signal at REFL 33 goes down. The maximum change we could have seen for the REFL33 PRCL signal (difference between max of blue trace and min of orange trace) is a factor of 27.
Where are we on the x-axis of these plots, and where was the maximal cancellation place that Koji found? I need to re-check that part of the code tomorrow, to make sure that I've included all of my contributions from different components of the (field* field) matrix.
But, the moral of the story for tonight is that at least for the REFL33 signal, it's actually plausible that the optical gain went down by a factor of 20, and that the MICH and PRCL signals were degenerate. I suspect that the total cancellation place that Koji found was somewhere around 175 degrees on the x-axis of these plots and that our nominal place is around 0 deg - around there, both the magnitude and the phase situations are possible simultaneously. |