  We derive the radiation power from a single Josephson junction (JJ) and from
layered superconductors in the flux-flow regime. For the JJ case we formulate
the boundary conditions for the electric and magnetic fields at the edges of
the superconducting leads using the Maxwell equations in the dielectric media
and find dynamic boundary conditions for the phase difference in JJ which
account for the radiation. In a finite-length JJ the power conversion
efficiency is determined by the dissipation inside JJ and it tends to unity as
dissipation vanishes independently of mismatch of the junction and dielectric
media impedances. We formulate also the dynamic boundary conditions for the
phase difference in intrinsic Josephson junctions in layered high-temperature
superconductors at the boundary with free space. Using these boundary
conditions, we find the dynamic phase difference in the linear regime for
rectangular and triangular lattices of Josephson vortices and evaluate
radiation into a free space for these simple cases.
