To significantly improve the solar-pumped laser beam brightness, a multi-Fresnel lens scheme is proposed for side-pumping either a single-crystal Nd:YAG or a core-doped ceramic Sm3+ Nd:YAG disk. Optimum laser system parameters are found through ZEMAX and LASCAD numerical analysis. An ultrahigh laser beam figure of merit B of 53 W is numerically calculated, corresponding to a significant enhancement of more than 180 times over the previous record. 17.7 W/m2 collection efficiency is also numerically attained. The strong thermal effects that have hampered present-day rod-type solar-pumped lasers can also be largely alleviated.