where w0 is the beam radius at the beam waist and λ the wavelength. A laser beam is often said to be “M² times diffraction-limited”.
A diffraction-limited beam has an M² factor of 1, and is a Gaussian beam. Smaller values of M² are physically not possible. A Hermite–Gaussian beam, related to a TEMnm resonator mode, has an M² factor of (2n + 1) in the x direction, and (2m + 1) in the y direction .
The M² factor of a laser beam limits the degree to which the beam can be focused for a given beam divergence angle, which is often limited by the numerical aperture of the focusing lens. Together with the optical power, the beam quality factor determines the brightness (more precisely, the radiance) of a laser beam. https://www.rp-photonics.com/m2_factor.html
The Rayleigh length (or Rayleigh range) of a laser beam is the distance from the beam waist (in the propagation direction) where the beam radius is increased by a factor of the square root of 2. For a circular beam, this means that the mode area is doubled at this point.
For Gaussian beams, the Rayleigh length is determined by the waist radius w0 and the wavelength λ: