Optical apparatus for annealing a layer on a substrate, comprising: a plurality of frequency-converted repetitively-pulsed solid-state lasers , each thereof including a laser resonator formed between first and second resonator mirrors, the laser resonator including a gain-element in the form of a slab that is energized by optical pumping to provide a gain volume in the gain-element , the energized resonator producing a fundamental radiation beam (F), each solid-state laser further including at least one nonlinear crystal for converting a portion of the fundamental radiation beam (F) into an output beam having a wavelength in the ultraviolet region of the electromagnetic spectrum, each output beam having a cross-section characterized by mutually-orthogonal first and second transverse axes; a line-projector arranged to receive the output beams , form the output beams into a line-beam, and project the line-beam onto the layer on the substrate , the line-beam having a length and a width on the layer ; wherein cross-sectional dimensions of the gain volume, a resonator length between the first and second resonator mirrors, optical powers of the first and second resonator mirrors, and a propagation distance in the at least one nonlinear crystal are selected to achieve a beam-quality factor M 2 of the output beam in the first transverse axis greater than 50 and a beam-quality factor M 2 of the output beam in the second transverse axis greater than 20; and wherein output coupling from the laser resonator and a pulse-repetition frequency are selected to produce laser pulses of the output beam having a pulse energy greater than 100 millijoules, the pulse-repetition frequency being greater than 100 hertz. a plurality of frequency-converted repetitively-pulsed solid-state lasers , each thereof including a laser resonator formed between first and second resonator mirrors, the laser resonator including a gain-element in the form of a slab that is energized by optical pumping to provide a gain volume in the gain-element , the energized resonator producing a fundamental radiation beam (F), each solid-state laser further including at least one nonlinear crystal for converting a portion of the fundamental radiation beam (F) into an output beam having a wavelength in the ultraviolet region of the electromagnetic spectrum, each output beam having a cross-section characterized by mutually-orthogonal first and second transverse axes; a line-projector arranged to receive the output beams , form the output beams into a line-beam, and project the line-beam onto the layer on the substrate , the line-beam having a length and a width on the layer ; wherein cross-sectional dimensions of the gain volume, a resonator length between the first and second resonator mirrors, optical powers of the first and second resonator mirrors, and a propagation distance in the at least one nonlinear crystal are selected to achieve a beam-quality factor M 2 of the output beam in the first transverse axis greater than 50 and a beam-quality factor M 2 of the output beam in the second transverse axis greater than 20; and wherein output coupling from the laser resonator and a pulse-repetition frequency are selected to produce laser pulses of the output beam having a pulse energy greater than 100 millijoules, the pulse-repetition frequency being greater than 100 hertz. <EOS>