  We investigate how beams with orbital angular momentum (OAM) behave under
total internal reflection. This is studied in two complementary experiments: In
the first experiment, we study geometric shifts of OAM beams upon total
internal reflection (Goos-H\"anchen and Imbert-Fedorov shifts, for each the
spatial and angular variant), and in the second experiment we determine changes
in the OAM mode spectrum of a beam, again upon total internal reflection. As a
result we find that in the first case, the shifts are independent of OAM and
beam focussing, while in the second case, modifications in the OAM spectrum
occur which depend on the input OAM mode as well as on the beam focussing. This
is investigated by experiment and theory. We also show how the two methods,
beam shifts on the one hand, and OAM spectrum changes on the other, are related
theoretically.
