  We analyze transverse phase locking for vortex motion in a superconductor
with a longitudinal DC drive and a transverse AC drive. For both square and
triangular arrays we observe a variety of fractional phase locking steps in the
velocity versus DC drive which correspond to stable vortex orbits. The locking
steps are more pronounced for the triangular arrays which is due to the fact
that the vortex motion has a periodic transverse velocity component even for
zero transverse AC drive. All the steps increase monotonically in width with AC
amplitude. We confirm that the width of some fractional steps in the square
arrays scales as the square of the AC driving amplitude. In addition we
demonstrate scaling in the velocity versus applied DC driving curves at
depinning and on the main step, similar to that seen for phase locking in
charge-density wave systems. The phase locking steps are most prominent for
commensurate vortex fillings where the interstitial vortices form symmetrical
ground states. For increasing temperature, the fractional steps are washed out
very quickly, while the main step gains a linear component and disappears at
melting. For triangular pinning arrays we again observe transverse phase
locking, with the main and several of the fractional step widths scaling
linearly with AC amplitude.
