A high-efficiency laser pumping device is provided, wherein a dielectric with or without a tapered aperture is used to accept, guide, and concentrate a pump light toward a laser gain material. Preferably, the dielectric is also a heat insulator between the pump-light source and the laser gain material. The pump-light source includes an array of light-emitting diodes, or an array of laser diodes, or an array of mixed light-emitting-diodes and laser diodes. Preferably, the input and output faces of the dielectric are optically coated with dielectric layers to maximize the pump brightness toward the laser gain material. A high-efficiency laser-pumping system with active cooling apparatus is further provided, wherein a plural number of the optical-guiding and thermal-insulation dielectrics are arranged to receive the pump lights from a plural number of pump-light sources, configured to concentrate all the pump light toward a laser gain material.