For comparison with experimental observations I ran some more simulations of SB locked PRMI POP 18MHz buildup.

The attached plot shows the modeled POP 18MHz signal as detected directly in transmission of PR2 (i.e. no additional POP pick-off optics considered). I tuned the demod phase to put all the signal in I phase at the starting (cold) point on the left hand side of the x-axis. The Q phase signal is also shown on the plot, along with the AS port power (unavaliable in practice of course).

The different colors represent different ITMX non-thermal substrate lens cases, ranging from -15uD to 15uD power. I wanted to look at a range of ITMX lens cases because of the questions thrown up by the beam size measurement analysis I posted on Friday (10237). As usual, I expect the ITMX lens is indistinguishable from PR2-PR3 distance offset. I also assumed no susbtrate lens in ITMY: this could certainly impact the required heating to optimize the power buildup. However it would also affect the maximum buildup level due to a) changing the PRC mode mismatch with the IMC beam and b) changing beam sizes at the BS thus affecting clipping (unmodeled here).

Just to clarify, here are some specific things included in the model:

• Input beam power 10W
• Input beam defined by IMC mode, propagated through PMMT to PRM
• PRX eigenmode calculated between PRM and ITMX HR surface
• PRY eigenmode calculated between PRM and ITMY HR surface
• Mode mismatches occurring at PRM (IMC<->PRY) ans BS (PRX<->PRY)
• TEMs up to order 4 considered in calculation
• ITMX non-thermal substrate lens (varied)
• ITMY thermal lens from ring heater (varied)
• MICH lock using REFL45Q signal
• PRCL lock using REFL45I signal
• Design value of PR2-PR3 distance, with measured value of PR3 Rc
• IMC FSR = 9.0994548MHz
• 9.0994548MHz modulation depth = 0.1, sidebands up to order 2 considered
• 45.497274MHz modulation depth = 0.07, sidebands up to order 2 considered
• ITMY ring heater actuation gain = -13.6uD/W

And some specific things not included in the model:

• Clipping at the beam-splitter
• Non-thermal substrate lens in ITMY
• Thermal lens in ITMX (should be none anyway)
• Any kind of surface figure maps beyond Rcs and lenses
• BS lens / curvature

Maybe the best short version I can give is this:

If the beam size measurements are to be believed, and assuming no ITMY non-thermal susbtrate lens, I expect ~8W should match ITMX and ITMY reflected curvatures best, and this should give the best PRMI buildup (about a factor 9 better than the cold state). In this case, the PRMI buildup should be relatively unaffected by BS clipping, as the beam sizes remain small.

If the beam size measurements are discounted and we assume the -12.5uD lens from surface figure measurements (and still no ITMY non-thermal lens), I expect ~9.8W should match ITMX and ITMY reflected curvatures best. This is unlikely to give the best PRMI buildup, as BS clipping starts to dominate losses as the PRY mode approaches the PRX mode and the contrast defect gets small. We've seen something of a trade-off between CD and BS clipping in determining PR gain at LLO, coming largely from the -80km lens setting the PRY beam size at the BS significantly larger than the design. We'd expect the same thing at LHO but switched between X/Y.

I include the simulations files here. It was run with the Matlab script "runlockedPRMIbuildup.m" calling the main kat file "H1_PRMI_RH_POP18.kat". It takes quite a while to run, due to the HOMs and locks, so included the .mat file with the results for convenience. You can just run the second block in the Matlab script to plot the results saved in the .mat file. If running the finesse simulation itself, you should use Finesse v1.1 or higher, which has the simultaneous sideband field computation feature included (see here for details).