lens mode scattering matrix
Lenses do not currently apply any modal scattering when a beam propagates through it - unless there is a direct beam parameter mismatch.
In reality, a displaced beam (HG00 + HG10) will have some more complicated interaction with a lens, which neither v2 or v3 models correctly, in theory it should become misaligned from the axis and astigmatic. I believe we should be doing something similar to what this paper describes, although I haven't fully digested it yet.
Ljiljana M. Janicijevic, "Hermite-Gaussian beam transformation by a shifted spherical lens at normal incidence," Appl. Opt. 25, 4353-4361 (1986)
Of course from the title this is just a part of the problem, as you can also have a beam going through some non-normal incident lens, or through some substrate which has a lens in it.