Glossary entry

Beam quality (M²)

The beam propagation ratio, comparing the divergence of a real laser beam to that of an ideal Gaussian beam of the same waist size. M² ≥ 1, with M² = 1 corresponding to a diffraction-limited beam.

Optics & beams Lasers & gain Lab practiceUpdated September 2026

The beam quality parameter $M^{2}$ (also called the beam propagation ratio) is defined by the relation between a beam's waist size, divergence, and wavelength:

M^{2} = \frac{π w_{0} θ}{λ},

where $w_{0}$ is the beam waist radius ( $1 / e^{2}$ intensity) and $θ$ is the asymptotic far-field divergence half-angle. For an ideal Gaussian beam, $M^{2} = 1$ . For real beams, $M^{2} \geq 1$ , with higher values indicating that the beam diverges faster than the diffraction limit for its waist size.

$M^{2}$ controls how tightly a beam can be focused. For a beam of given input radius $w_{in}$ focused by a lens of focal length $f$ , the achievable focused waist is

w_{focus} = M^{2} \cdot \frac{λ f}{π w_{in}} .

Beam quality is therefore the figure of merit for applications requiring tight focus: laser cutting, microscopy, optical trapping, lithography.

Typical $M^{2}$ values:

Source	Typical $M^{2}$
Single-mode HeNe laser	1.0–1.05
Single-mode fiber laser output	1.05–1.1
Single-spatial-mode semiconductor laser	1.1–1.3
Edge-emitting semiconductor laser, fast axis	1.0–1.5
Edge-emitting semiconductor laser, slow axis	5–50
Multi-mode fiber-coupled diode laser	5–100
High-power solid-state laser (e.g., kW fiber laser)	1.1–3
LED	$\geq 100$

For asymmetric beams (broad-area edge emitters, fiber-coupled outputs with elliptical modes), $M^{2}$ is reported separately for the two principal axes as $M_{x}^{2}$ and $M_{y}^{2}$ .

The ISO 11146-1 standard specifies the procedure for $M^{2}$ measurement: hyperbolic fit to the beam width at $\geq 10$ propagation positions, using the D4σ second-moment width. Methodology is covered in M² Beam Quality Measurement by the Knife-Edge Method. Where no camera is available, the width at each position can be taken by a knife-edge scan instead.

The Gaussian Beam Calculator takes $M^{2}$ as an input and shows its effect on the Rayleigh range, the divergence and the focused spot.