Summary:

It looks like we can have a stable SRC of length 4.044 m without getting any new mirrors, so this is an option to consider in the short-term.

Details:

• The detailed calculations are in the git repo. 
• The optical configuration is:
  • A single folding mirror approximately at the current SR3 location.
  • An SRM that is ~1.5m away from the above folding mirror. Which table the SRM goes on is still an open question, per the previous elog in this thread. 
• The SRC length is chosen to be 4.044 m, which is what the modeling tells us we need for operating in the SR tuning instead of RSE.
• Using this macroscopic length, I found that we could use a single folding mirror in the SRC, and that the existing (convex) G&H folding mirrors, which have a curvature of -700m, happily combine with our existing SRM (concave with a curvature of 142m) to give reasonable TMS and mode-matching to the arm cavity.
• The existing SRM transmission of 10% may not be optimal but Kevin's calculations say we should still be able to see some squeezing (~0.8 dB) with this SRM.
• Attachment #1 - corner plot of the distribution of TMS for the vertical and horizontal modes, as well as the mode-matching (averaged between the two modes) between the SRC and arm cavity.
• Attachment #2 - histograms of the distributions of RoCs and lengths used to generate Attachment #1. The distributions were drawn from i.i.d Gaussian pdfs.

gautam 245pm: Koji pointed out that the G&H mirrors are coated for normal incidence, but looking at the measurement, it looks like the optic has T~75ppm at 45 degree incidence, which is maybe still okay. Alternatively, we could use the -600m SR3 as the single folding mirror in the SRC, at the expense of slightly reduced mode-matching between the arm cavity and SRC.