# Diffraction-limited Beams

Definition: beams with a minimum possible beam divergence for a given waist radius

German: beugungsbegrenzte Strahlen

Author: Dr. Rüdiger Paschotta

Cite the article using its DOI: https://doi.org/10.61835/7cl

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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.

For a given optical power, a diffraction-limited beam has the highest possible brightness (radiance).

The *M*^{2} factor of a light beam is a useful quantity for judging how far from diffraction-limited the beam is.

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## Questions and Comments from Users

2021-12-13

What is the relation of diffraction-limited spot size to the wavelength?

The author's answer:

That cannot be directly related. The diffraction-limited spot size can be far larger than the wavelength e.g. if you need to focus a beam over a large distance with limited numerical aperture.

2022-02-21

If we calculate the beam diameter of a laser beam at some large distance from the source, do we need to calculate the diffraction angle <$1.22 \: \lambda / D$> or the beam divergence angle <$\lambda / (\pi D)$>?

The author's answer:

If you want to know the Gaussian beam radius, you can take the beam divergence angle times the distance, assuming that the distance is much larger than the Rayleigh length.

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2021-07-26

What is a diffraction-limited spot size?

The author's answer:

That is the smallest possible beam radius at a beam focus, if diffraction is the limiting factor. It depends on boundary conditions like the distance to the focus and the aperture size of the used optics.