Encyclopedia … combined with a great Buyer's Guide!

# Beam Parameter Product

Author: the photonics expert

Acronym: BPP

Definition: product of the beam radius in a focus and the far-field half-angle beam divergence

The beam parameter product (BPP) of a laser beam is defined as the product of beam radius (measured at the beam waist) and the beam divergence half-angle (measured in the far field). The usual units are mm mrad (millimeters times milliradians). The BPP is often used to specify the beam quality of a laser beam: the higher the beam parameter product, the lower is the beam quality.

The BPP can also be defined for non-Gaussian beams. In that case, second moments should be used for the definitions of beam radius and divergence. The smallest possible beam parameter product is then achieved with a diffraction-limited Gaussian beam; it is <$\lambda / \pi$>. For example, the minimum beam parameter product of a 1064-nm beam is ≈ 0.339 mm mrad.

## Beam Quality Calculations

 Center wavelength: M2 factor: calc (from BPP) Beam parameter product: calc (from M2) Beam waist radius: calc (using the BPP and divergence half-angle) Divergence half-angle: calc (using the BPP and beam waist radius)

Enter input values with units, where appropriate. After you have modified some values, click a “calc” button to recalculate the field left of it.

For non-circular beams, the BPP can be different e.g. in the vertical and horizontal direction.

Note that the BPP remains unchanged when the beam is sent through some non-aberrative optics, such as a thin lens. If that lens generates a focus with smaller beam waist radius, the beam divergence will increase correspondingly. For measuring the BPP, it is thus allowed to form a focus of convenient size, dependent on the equipment used (e.g. a beam profiler) and the available space (which has to extent over several Rayleigh lengths).

Non-ideal optics can “spoil” the beam quality and thus increase the BPP. In some special cases, slight aberrations of an optical element (such as a spherical lens) can somewhat reduce the BPP of a laser beam, if the beam has distortions which can be compensated with that element.

A related, less frequently used quantity is the diameter–divergence product.

## More to Learn

Encyclopedia articles:

## Questions and Comments from Users

2021-02-18

How can I find <$w_0$> from the BPP? It seems that I'll know only the product of beam radius and divergence.