Solar-pumped solid-state lasers are promising for renewable extreme-temperature material processing. Here we report a large improvement in solar laser beam brightness by pumping a thin Nd:YAG single crystal rod. A fused silica light guide of 14mm×22mm rectangular cross-section is used to both transmit and homogenize the concentrated solar radiation from the focal zone of a 2.88m 2 parabolic mirror to the entrance aperture of a modified 2D-CPC flooded pump cavity, within which a 4mm diameter rod is efficiently pumped. 2.2% slope efficiency is reached. Laser beam brightness figure of merit B is three times higher than that of the most recent solar-pumped Nd:YAG laser by a Fresnel lens. The introduction of the rectangular cross-section light guide has also ensured a much more stable laser emission than previous pumping schemes.