NOTE: There was a small bug in my initial calculation. The plots and numbers have been updated with the fixed values. The conclusion remains the same.
Using Nic's a la mode mode matching program, I've calculated the PRC mode and g-parameter for various PR2/3 scenarios. I then looked at the overlap of the resultant PRC eigenmodes with the ARM eigenmode. Here are the results:
NOTE: each optical element below (PR2, ITM, etc.) is represented by a compound M matrix. The z axis in these plots is actually just the free space propagation between the elements, not the overall optical path length.
ARM
This is the ARM mode I used for all comparisons:
 
| |
tangential |
sagittal |
| gouy shift, one-way |
55.63 |
55.63 |
| g (from gouy) |
0.303 |
0.303 |
| g (product of individual mirror g) |
0.303 |
0.303 |
PRC, nominal design (flat PR2/3)
This is the nominal "as designed" PRC, with flat PR2/3 folding mirrors.
 
| |
tangential |
sagittal |
| gouy shift, one-way |
14.05 |
14.05 |
| g (from gouy) |
0.941 |
0.941 |
| g (product of individual mirror g) |
0.942 |
0.942 |
ARM mode matching: 0.9998
PRC, both PR2/3 flipped
This assumes both PR2 and PR3 have a RoC of -600 when not flipped, and includes the affect of propagation through the substrates.
 
| |
tangential |
sagittal |
| gouy shift, one-way |
19.76 |
18.45 |
| g (from gouy) |
0.886 |
0.900 |
| g (product of individual mirror g) |
0.888 |
0.902 |
ARM mode matching: 0.9806
PRC, only PR2 flipped
In this case we only flip PR2 and leave PR3 with it's bad -600 RoC:
 
| |
tangential |
sagittal |
| gouy shift, one-way |
18.37 |
18.31 |
| g (from gouy) |
0.901 |
0.901 |
| g (product of individual mirror g) |
0.903 |
0.903 |
ARM mode matching: 0.9859
Discussion
I left out the current situation (PR2/3 with -600 RoC) and the case where only PR3 is flipped, since those are both unstable according to a la mode.
I guess the main take away is that we get slightly better PRC stability and mode matching to the arms by only flipping PR2. |