Diffraction index

The diffraction index  is a dimensionless quantity that characterizes a laser beam : the larger, the more difficult it is to focus the beam . H. the larger the smallest possible focus diameter. ${\displaystyle M^{2}}$ ${\displaystyle M^{2},}$

definition

The beam path of a real laser beam (green) has a greater divergence than that of a theoretical Gaussian beam (red)

The diffraction index indicates the divergence angle of a real laser beam compared to the divergence angle of an ideal Gaussian beam with the same diameter at the beam waist: ${\displaystyle \varphi }$

${\displaystyle M^{2}={\frac {\varphi _{\text{real}}}{\varphi _{\text{Gauss}}}}}$

By definition, a Gaussian beam has the diffraction index for real laser beams is always greater than one, e.g. B. is a typical value for the diffraction index of a fundamental mode laser ${\displaystyle M^{2}=1;}$ ${\displaystyle M^{2}}$ ${\displaystyle M^{2}=1{,}01...1{,}1.}$

The diffraction index is often casually referred to as "beam quality". Physically, however, this does not apply; strictly speaking, the entropy of the radiation is a measure of the quality of a radiation field. Instead of the diffraction index, two other quantities are sometimes used:

• the beam parameter product with the wavelength ${\displaystyle \mathrm {SPP} =M^{2}\cdot {\frac {\lambda }{\pi }}}$ ${\displaystyle \lambda }$
• the beam quality , also called beam propagation or K-factor: ${\displaystyle K}$ ${\displaystyle K={\frac {1}{M^{2}}}={\frac {\lambda }{\pi \cdot {\text{SPP}}}}}$

Typical values ​​and practical relevance

Typical M ² values ​​for high-power lasers are:

• 1.0–1.2 for single mode fiber lasers
• approx. 1.1–1.5 for carbon dioxide lasers
• approx. 1.5–20 for solid-state lasers
• > 20 for diode lasers .

When comparing the focusability of these lasers, however, the different wavelengths must also be taken into account (see above beam parameter product and beam quality).

Specifically, in the laser processing in laser cutting , laser welding or laser marking the beam quality has a large influence on the work result in laser welding, a high performs M ² value (and therefore a large angle of divergence or focus diameter) to a wider and less deep weld and when Laser marking for a blurred image.

literature

• Jürgen Eichler, Lothar Dünkel, Bernd Eppich: The beam quality of lasers - How do you determine the diffraction index and beam diameter in practice? In: Laser Technik Journal . tape 1 , no. 2 , October 2004, p. 63-66 , doi : 10.1002 / latj.200790019 .

Footnotes

1. ↑ DIN EN ISO 11146 - Part 1 (April 2005): Lasers and laser systems - Test methods for laser beam dimensions, divergence angles and diffraction figures - Part 1: Stigmatic and simple astigmatic rays (ISO 11146-1: 2005); German version EN ISO 11146-1: 2005. Pp. 9-10.