So, with my last entry, I was guilty of just throwing stuff into the simulation and not thinking about physics... so I retreated to Siegman for some algebraic calculations of the additional Guoy phase accumulated by the HOMs in the arms -> their resonant frequencies -> the arm length offset where they should resonate. Really, this isn't completely precise, as I treated the arms independently, with slightly differing ETM radii of curvature, but I would expect the "CARM Arm" to behave as a sort of average of the two arm cavities in this regard. (EDIT: Also, I didn't really consider the effect of the coupled vertex cavities... so there's more to be done)

The basic idea I used was:

• Assume ITMs are effectively flat, infinite Rc
• Use 40mwiki values for ETM curvatures
• Each additional HG order adds arccos(sqrt(1 - Larm/Rc)) of Guoy phase for a one way trip down the cavity (Eqn 19.19 in Sigman)
• For each HOM order up to 5 of the carrier and first order sidebands, add the appropriate phase shift 
• fold it onto +-FSR/2 of the carrier 00 resonance, convert to m

In practice, I threw together a python script to do this all and print out a table. I've highlighted the values within 10nm, but the closet one is 3.8nm

Results: