  In this paper, we investigate the so-called Bopp-Podolsky electrodynamics.
The Bopp-Podolsky electrodynamics is a prototypical gradient field theory with
weak nonlocality in space and time. The Bopp-Podolsky electrodynamics is a
Lorentz and gauge invariant generalization of the Maxwell electrodynamics. We
derive the retarded Green functions, first derivatives of the retarded Green
functions, retarded potentials, retarded electromagnetic field strengths,
generalized Lienard-Wiechert potentials and the corresponding electromagnetic
field strengths in the framework of the Bopp-Podolsky electrodynamics for
three, two and one spatial dimensions. We investigate the behaviour of these
electromagnetic fields in the neighbourhood of the light cone. In the
Bopp-Podolsky electrodynamics, the retarded Green functions and their first
derivatives show fast decreasing oscillations inside the forward light cone.
