  We study the propagation properties of a single vortex in square
Josephson-junction arrays (JJA) with free boundaries and subject to an applied
dc current. We model the dynamics of the JJA by the resistively and
capacitively shunted junction (RCSJ) equations. For zero Stewart-McCumber
parameter $\beta_c$ we find that the vortex always escapes from the array when
it gets to the boundary. For $\beta_c\geq 2.5$ and for low currents we find
that the vortex escapes, while for larger currents the vortex is reflected as
an antivortex at one edge and the antivortex as a vortex at the other, leading
to a stationary oscillatory state and to a non-zero time-averaged voltage. The
escape and the reflection of a vortex at the array edges are qualitatively
explained in terms of a coarse-grained model of a vortex interacting
logarithmically with its image. We also discuss the case when the free
boundaries are at $45$ degrees with respect to the direction of the vortex
motion. Finally, we discuss the effect of self-induced magnetic fields by
taking into account the full-range inductance matrix of the array, and find
qualitatively equivalent results.
