About eight years ago I saw a video presentation about lasers from
M.I.T. If my memory is correct, the problem is something like this:
Take a single (transverse 00) mode randomly polarized He-Ne laser
(without a Brewster window). Observe the output with a Fabry-Perot
scanning interferometer. Place a Polaroid filter between the exit
window of the laser and the scanning interferometer. As the laser
warms up, one can observe successive longitudinal modes of the laser
on the scanning interferometer. If my memory is correct, one can
observe that the successive laser modes have polarizations that are
90 degrees apart from each other, tuning them in by rotating the
Polaroid. The video presentation left one with the question, "Why?"
I was able to replicate the demonstration in our lab. I discussed this
with several people, some quite expert with lasers, but did not come up
with a conclusive answer.