Beam parameter product

The beam parameter product ( SPP; english beam parameter product, BPP ) is a physical parameter that describes the beam quality and therefore the focusing ability of a laser beam. The SPP has the dimension of length x angle and is usually given in mm × mrad.

Definition

The mathematical relationship is:

It is

• Half the opening angle in the far field
• W0 ( waist w for engl., waist) the beam radius at its thinnest point, ie half the focal point diameter
• The beam quality M2; the larger M2, the worse the beam is to be focused, ie the greater is the smallest possible spot size.
• Is the wavelength.

The above-mentioned Formula can be derived from the general wave equation under paraxial approximation.

Application

The SPP is preferred, with glass-fiber -coupled laser sources. If the laser output without loss of power can be coupled to another optical fiber, the input coupling fiber to the SPP may not be smaller than that of the laser source:

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

In contrast, in free radiating laser heads for materials processing ( collimator, Fokusator ) is specified, the beam quality factor M2 instead of the SPP. Even when a carbon dioxide laser is preferred, M2, since the typical quartz fiber for beam transmission is not transmissive for the laser wavelength of 10.6 microns.

Consequence

The SPP of a laser beam does not change when passing through a lens. It follows with the above formula:

• A laser beam is not parallel, but always has an aperture angle greater than zero in the far field.
• The focal point of a laser beam has a diameter always greater than zero. With realistic values ​​obtained for an ideal beam as the smallest focal diameter approximately one wavelength.
• To achieve a small focal point, it takes a large beam diameter in front of the focusing lens and a short focal length.