A low-divergence 1.06 micrometer wavelength beam from a total-internal-reflection, face-pumped laser (TIR-FPL) is focused onto the end of a quartz optical fiber to a spot having a size smaller than the fiber diameter and with a beam cone angle less than twice the numerical aperture of the fiber. The fiber transmits the energy to emerge at the other end where it is collimated and focused onto material to be processed. A laser average output power level greater than 400 watts can be transmitted through an optical fiber having a diameter less than 600 micrometers.