It is well known that gravity and neutrino oscillation can be used to probe
large extra dimensions in a braneworld scenario. We argue that neutrino
oscillation remains a useful probe even when the extra dimensions are small,
because the brane-bulk coupling is likely to be large. Neutrino oscillation in
the presence of a strong brane-bulk coupling is vastly different from the usual
case of a weak coupling. In particular, some active neutrinos could be absorbed
by the bulk when they oscillate from one kind to another, a signature which can
be taken as the presence of an extra dimension. In a very large class of models
which we shall discuss, the amount of absorption for all neutrino oscillations
is controlled by a single parameter, a property which distinguishes extra
dimensions from other mechanisms for losing neutrino fluxes.Comment: Introduction enlarged; conclusions added. To appear in Phys. Rev.