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.

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{\pi w_0 \theta}{\lambda},

where $w_0$ is the beam waist radius ( $1/e^2$ intensity) and $\theta$ 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 $w_\text{in}$ focused by a lens of focal length $f$ , the achievable focused waist is

w_\text{focus} \;=\; M^2 \cdot \frac{\lambda f}{\pi w_\text{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 or SLD	$\geq 100$

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.