The generation of ultra-relativistic positron beams with short duration ($tau_{e^+} leq 30$ fs), small divergence ($theta_{e^+} simeq 3$ mrad), and high density ($n_{e^+} simeq 10^{14} - 10^{15}$ cm$^{-3}$) from a fully optical setup is reported. The detected positron beam propagates with a high-density electron beam and $gamma$-rays of similar spectral shape and peak energy, thus closely resembling the structure of an astrophysical leptonic jet. It is envisaged that this experimental evidence, besides the intrinsic relevance to laser-driven particle acceleration, may open the pathway for the small-scale study of astrophysical leptonic jets in the laboratory.
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