Summary:

Having played around with a toy finesse model, I went about setting up a model in which the RC folding mirrors are not flipped. I then repeated the low-level tests detailed in the earlier elog, after which I ran a few spatial mode overlap analyses, the results of which are presented here. It remains to do a stability analysis.

Overview of model parameters (more details to follow):

• PRC length = 6.7727m (chosen using , N=0 - I adjusted the position of the PRM to realize this length in the model, while leaving all the other vertex optics in the same positions as in elog 9590
• SRC length = 5.4182 (chosen using  but not , M and N being integers, for M=2 - as above, I adjusted the position of the SRM to realize this in the model, while leaving all other vertex optics in the same positions as in elog 9590. It remains to be verified if it is physically possible to realize these dimensions in vacuum without any beam clipping etc but I think it should be possible seeing as the PRM and SRM had to be moved by less than 2cm from their current positions..
• For the losses, I used the most recent numbers we have where applicable, and put in generic 25ppm loss for all the folding mirrors/BS/AR surfaces of arm cavity mirrors/PRM/SRM. Arm round trip loss was equally distributed between ITMs and ETMs
• Arm lengths used: L_X = 37.79m, L_Y = 37.81m
• To set the "tunings" of the various mirrors, I played around with a few configurations to see where the various fields resonated - it turns out that for PRM, ITMX, ITMY, ETMX and ETMY, the "phase" in the .kat file can be set as 0. while that for the SRM can be set as 90. In the full L1/H1 interferometer .kat files, these are tuned even further to the (tenth?!) decimal place, but I think these values suffice for out purposes.

Results (general note: positive RoC in these plots mean a concave surface as seen by the beam):

• Attachments #1, #2 and #3 reproduce the low-level tests performed earlier for this updated model - i.e. I look at the arm transmission with no PRM/SRM, circulating PRC power with no ETMs, and circulating SRC power with no ETMs. Everything looks consistent here... In Attachment #2, there is no legend, but the (almost overlapping) red and green lines are meant to denote the +f1 and +f2 sidebands.
• Attachments #4 and #5 are a summary of the mode-overlap scans for the PRC and SRC. What I did was to vary the radius of curvature of the RC mirrors (finesse only allows you to vary Rcx and Rcy, so I varied both simultaneously) and calculate the mode overlap between the appropriate pairs of cavities (e.g. PRX and XARM) in the tangential and saggital planes. The take-away here is that there is ~5% mode-mismatch going from an RoC of 1000m to 300m. I've also indicated the sag corresponding to a given RoC - these are pretty tiny, I wonder if it is possible to realize a sag of 1um? I suppose it is given that I've regularly seen specs of surface roughness of lambda/10?
• Attachment #6 shows the PRC gain (calculated as T_PRC * (transmitted arm power with PRM / transmitted arm power without PRM) as a function of the RoC of PR2 and PR3. As a sanity check, I repeated this calculation with lossless HR surfaces (but with nominal 25ppm losses for AR surfaces of ITMs, and BS etc), shown in Attachment #7. I think these make sense too...
• Attachment #8 - in order to investigate possible mode mismatch between the arm modes due to different radii of curvature of the ETMs, I kept the ETMY RoC fixed at 57.6m and varied the ETMY RoC between 50m and 70m (here, I've plotted the mode matching efficiency as a function of the RoC of the ETM in the X and Y directions separately - the mode overlap is computed as  where x and y denote the overlap in the tangential and saggital planes respectively. It would seem that we only lose at most a couple of percent even if the RoCs are mismatched by up to 10m...
• Attachment #9 - .kat file and the various pykat scripts used to generate these plots...

Next step is to carry out a stability analysis...