In this paper we discuss a compact, laser-plasma-based scheme for the
generation of positron beams suitable to be implemented in an all-optical
setup. A laser-plasma-accelerated electron beam hits a solid target producing
electron-positron pairs via bremsstrahlung. The back of the target serves as a
plasma mirror to in-couple a laser pulse into a plasma stage located right
after the mirror where the laser drives a plasma wave (or wakefield). By
properly choosing the delay between the laser and the electron beam the
positrons produced in the target can be trapped in the wakefield, where they
are focused and accelerated during the transport, resulting in a collimated
beam. This approach minimizes the ballistic propagation time and enhances the
trapping efficiency. The system can be used as an injector of positron beams
and has potential applications in the development of a future, compact,
plasma-based electron-positron linear collider