  In this paper we study wave propagation and scattering near a rotating black
hole. In particular, we assume a coherent emission source near the black hole
and investigate the wavefront distortion as seen by a distant observer. Near
the observer, the propagating wave can be decomposed using the
Laguerre-Gaussian mode basis and its wavefront distortion can be characterized
by the decomposition coefficient. We find that this decomposition spectrum is
symmetric for wave sources located near a Schwarzschild black hole, but is
generically asymmetric if the host black hole is rotating. The spectrum
asymmetry, or the net orbital angular momentum carried by the wave, is
intimately related to the black hole spin and mass, the wave frequency and the
locations of the source and the observer. We present semi-analytical
expressions and numerical results for these parameter-dependences. If the
radiation is temporally coherent, our results show that the secondary images of
the source can be almost as bright as its primary image. In the case of
temporally-incoherent radiation, we show that the non-fundamental spectrum
components could be resolved by spatially-separated telescopes, although that
would be degenerate with the telescope direction. Finally, our results suggest
that the black-hole-induced spectrum asymmetry is generally too weak to be
observed in radio astronomy, even if the observer were located near a caustic
point.
