I should mention that I just found a bug in how it treats odd-mirror-number cavities. For such cavities, HG modes with odd horizontal indices should receive an extra roundtrip phase of pi/2 (due to the rotation by the cavity). Because of a numbering convention issue, arbcav actually used to apply this phase shift to even-order modes. Essentially, the only difference is that the fundamental mode was shifted to anti-resonance. Everywhere else, there are modes at both corresponding locations in frequency space, and so it does not back a big difference in terms of cavity design.
Thanks to this IMC modeling we are doing at the workshop, I caught it! It has been fixed in the SVN.
I have calculated (using Zach's sweet software) the expected mode content for the various possible PRCs that we can make.
Also, Zach was right about the factor of 2. I see now that I was calculating the mode spacing between a plane wave and a HOM, so the guoy phase had a factor of (n+m+1). The right thing to do is to get the spacing between the 00 mode and HOMs, so the guoy phase just has (n+m). Switching from n+m+1=2 to n+m=1, that fixes the factor of 2 problem.
I attach my results as a pdf, since I'm listing out 5 configurations. Each config has a cartoon, with a small (hard to read) HOM plot, and then at the end, each HOM plot is shown again, but larger. Also, "TM" is the "test mirror", the flat G&H that we're using as the cavity end mirror.