  We study theoretically the ac Josephson effect in superconducting planar
d-wave junctions. The insulating barrier assumed to be present between the two
superconductors may have arbitrary strength. Many properties of this system
depend on the orientation of the d-wave superconductor: we calculate the ac
components of the Josephson current. In some arrangements there is substantial
negative differential conductance due to the presence of mid-gap states. We
study how robust these features are to finite temperature and also comment on
how the calculated current-voltage curves compare with experiments. For some
other configurations (for small barrier strength) we find zero-bias conductance
peaks due to multiple Andreev reflections through midgap states. Moreover, the
odd ac components are strongly suppressed and even absent in some arrangements.
This absence will lead to a doubling of the Josephson frequency. All these
features are due to the d-wave order parameter changing sign when rotated
$90^{\circ}$. Recently, there have been several theoretical reports on parallel
current in the d-wave case for both the stationary Josephson junction and for
the normal metal-superconductor junction. Also in our case there may appear
current density parallel to the junction, and we present a few examples when
this takes place. Finally, we give a fairly complete account of the method used
and also discuss how numerical calculations should be performed in order to
produce current-voltage curves.
