We present a compact end-side pumped solar laser concept designed to enhance efficiency in both multimode and TEM00-mode operations. The primary concentrator, a 1.0 m diameter off-axis parabolic mirror, efficiently collects and focuses solar rays into the laser head, which consists of a large fused-silica aspheric lens secondary concentrator, a conical-shaped pump cavity, and a single Nd:YAG crystal rod. Optimization of the solar laser system parameters was carried out using ZEMAX^© for nonsequential ray tracing and LASCAD^© for laser cavity analysis. Since our study is part of a solar laser project in desert regions of Algeria, 1200 W/m2 solar terrestrial irradiance was assumed, our numerical simulations achieved 38 W continuous-wave laser power in multimode operation, for a 5 mm diameter, 25 mm length Nd:YAG rod. This corresponds to a collection efficiency (CE) and solar-to-laser conversion efficiency (CVE) of 48.40 W/m2 and 4.03%, respectively, being 1.50 and 1.22 times higher than the previous experimental records of a single-beam Nd:YAG solar laser. For 980 W/m2 solar irradiance, 29.72 W laser power was calculated, leading to 37.84 W/m2 CE and 3.86% laser CVE, respectively, being 1.18 and 1.17 times more than previous experimental records. For TEM00-mode operation, utilizing a thin Nd:YAG laser rod with an adjusted pump cavity and optical resonator enabled efficient extraction of a fundamental-mode solar laser beam with a very high-quality factor (M2≤1.02). 15.63 W TEM00-mode laser power was obtained, corresponding to a CE of 19.91 W/m2, which is 2.52 and 1.86 times higher than the previous experimental and numerical records, respectively, of a single-beam Nd:YAG solar laser. By assuming 980 W/m2 solar irradiance, 10.64 W TEM00-mode laser power was numerically achieved, resulting in 13.55 W/m2 CE and 1.71 and 1.26 times enhancement than that of the previous experimental records by a single-beam Nd:YAG solar laser.