Here we report a significant advance in solar-pumped laser beam brightness by pumping a 3 mm diameter Nd:YAG single-crystal rod with a heliostat-parabolic mirror system. The incoming solar radiation is first collected and focused by the system. A rectangular fused silica light guide and a 2D-CPC concentrator are then combined to further compress the concentrated solar radiation into the laser rod within a V-shaped pumping cavity. 4.4W continuous-wave TEM00 mode (M-2 <= 1.05) 1064 nm solar laser power is finally produced, attaining 4.0 W laser beam brightness figure of merit, which is 2.1 times higher than the previous record by a Fresnel lens. 0.81% TEM00 mode laser slope efficiency is achieved. (C) 2014 Elsevier B.V. All rights reserved.