Beam parameter product

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The beam parameter product (SPP; English beam parameter product , BPP) is a physical parameter that describes the beam quality and thus the focusability of a laser beam . The SPP has the dimension length × angle and is usually given in mm × mrad . The beam parameter product is a concept of Gaussian optics . It has the same meaning for the Gaussian beam as the etendue for a beam of geometrical optics .

definition

Beam path of a laser beam through the focus

The mathematical relationship is:

It is

  • half the opening angle in the far field
  • w 0 of the radius of the laser beam at its thinnest point ( w for engl.  waist , waist), d. H. half the focal point diameter
  • M 2 is the diffraction index ; the larger M 2 , the more difficult it is to focus the beam, i.e. H. the larger the smallest possible focus diameter. M 2 cannot be less than 1.0.
  • the wavelength .

The above Formula can be derived from the general wave equation with paraxial approximation .

application

The SPP is a quality parameter of laser beams with regard to beam propagation, focusability and focus length . In the case of fiber-optic- coupled laser sources, it is of particular importance for coupling into the fiber. If the laser output radiation is to be coupled into another glass fiber without loss of power, the SPP of the coupling fiber must not be smaller than that of the laser source:

The SPP of the glass fiber is defined by the numerical aperture  NA and the core diameter.

In the case of unshielded laser sources for material processing that are expanded by means of collimators and thus guided over great distances and focused with focusing lenses , the diffraction index  M 2 is often specified instead of the SPP . In any case, fiber coupling is not relevant for carbon dioxide lasers because there is not yet a sufficiently low-loss fiber structure for the laser wavelength of 10.6 µm.

consequence

The SPP of a laser beam does not change when it passes through a lens . From this it follows with the above formula:

  • A laser beam is never parallel , but always has an opening angle greater than zero in the far field.
  • The focal point of a laser beam always has a diameter greater than zero. With realistic values, the smallest focus diameter for an ideal beam is approximately one wavelength.
  • To achieve a small focal point, you need a large beam diameter in front of the focusing lens and a short focal length .

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 ( wiley-vch.de [PDF; 421 kB ; accessed on January 28, 2011]).

Individual evidence

  1. Research on chalcogenides or photonic crystal | photonic crystal fibers are not yet ready for practice