  We investigate the electron transport in smooth graphene pn junctions,
generated by gradually varying electrostatic potentials. The numerically
calculated coherent current flow patterns can be understood largely in terms of
semi-classical trajectories, equivalent to the ones obtained for light beams in
a medium with a gradually changing refractive index. In smooth junctions,
energetically forbidden regions emerge, which increase reflections and can
generate pronounced interference patterns, for example, whispering gallery
modes. The investigated devices do not only demonstrate the feasibility of the
gradient-index electron optics in graphene pn junctions, such as Luneburg and
Maxwell lenses, but may have also technological applications, for example, as
electron beam splitters, focusers and waveguides. The semi-classical
trajectories offer an efficient tool to estimate the current flow paths in such
nano-electronic devices.
