Geometrical gain of a luminescent solar concentrator is drastically increased by laying out a luminescent fiber in a luminescent plate with air gap around it and attaching a photovoltaic (PV) cell to the tip of the fiber. The plate converts an incident photon to a first photoluminescence (PL) photon, and the fiber converts it to a second PL photon. Thus, the fiber carries the optical power as a leaf vein transports water and nutrients. The probability of the first PL photon resulting in the second PL photon reaching the PV cell can be measured by exciting a single spot on the plate with a laser beam. In experiment, 2 mm-thick, 50 mm-square and 50 mm-diameter circular devices were assembled with off-the-shelf components. For each case, geometrical gain exceeded 1000 and this probability averaged over the incident area was of the order of 0.01. Connecting multiple small-area devices to a single PV cell with a clear fiber would increase geometrical gain further and alleviate the absorption and scattering of PL photons during waveguiding.