A laser beam is called diffraction-limited if its potential to be focused to small spots is as high as possible for the given wavelength, limited only by the unavoidable diffraction. In other words, its beam quality is ideal.
More precisely, ideal beam quality means that a beam waist with a given beam radius, generated from the beam by focusing e.g. with a curved mirror, is associated with the minimum possible beam divergence angle. What exactly this means depends on the definition of the beam radius and beam divergence. If second moments are used for the definition of both quantities, the minimum beam parameter product is reached for a Gaussian beam, which has not only a Gaussian intensity profile but also flat wavefronts at the beam waist (beam focus).
A laser which operates on a single transverse resonator mode will usually have a diffraction-limited output, since that single mode is usually the fundamental resonator mode, and the shape of this is usually close to Gaussian. Non-ideal beam quality can be caused by intracavity beam distortions, e.g. in the gain medium, which can either deform the fundamental mode or (more frequently) cause transverse multimode operation. Note that the beam quality of a laser depends not only on the strength of intracavity distortions, but also on certain details of the resonator design; optimization of the latter can be essential for reaching a diffraction-limited output.
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