  The transverse mode of an atom laser beam that is outcoupled from a
Bose-Einstein condensate is investigated and is found to be strongly determined
by the mean--field interaction of the laser beam with the condensate. Since for
repulsive interactions the geometry of the coupling scheme resembles an
interferometer in momentum space, the beam is found show filamentation.
Observation of this effect would prove the transverse coherence of an atom
laser beam.
