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). Higher-order Hermite–Gaussian or Laguerre-Gaussian beams are not diffraction-limited.
A laser which operates on the fundamental transverse resonator mode will usually have a diffraction-limited output, since the shape of this is usually close to Gaussian. Non-ideal beam quality can be caused either by intracavity beam distortions, e.g. in the gain medium, which can either deform the fundamental mode (but usually only with a moderate effect on beam quality) or can (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.
The M2 factor of a light beam is a useful quantity for judging how far from diffraction-limited the beam is.
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