The recent progress in solar-pumped laser with Fresnel lens and Cr:Nd:YAG ceramic medium has revitalized solar laser researches, revealing a promising future for renewable reduction of magnesium from magnesium oxide. Here we show a big advance in solar laser collection efficiency by utilizing an economical Fresnel lens and a most widely used Nd:YAG single-crystal rod. The incoming solar radiation from the sun is focused by a 0.9 m diameter Fresnel lens. A dielectric totally internally reflecting secondary concentrator is employed to couple the concentrated solar radiation from the focal zone to a 4 mm diameter Nd:YAG rod within a conical pumping cavity. 12.3 W cw laser power is produced, corresponding to 19.3 W/m2 collection efficiency, which is 2.9 times larger than the previous results with Nd:YAG single-crystal medium. Record-high slope efficiency of 3.9% is also registered. Laser beam quality is considerably improved by pumping a 3 mm diameter Nd:YAG rod.