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# Beam Parameter Product

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Acronym: BPP

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

German: Strahlparameterprodukt

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 λ / π. 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 Beam parameter product: calc Beam waist radius: calc Divergence half-angle: calc

After you have modified some values, click a "calc" button to recalculate the field left of it.

Figure 1: Beam parameter product and M2 values of various laser types. Due to the longer wavelength, CO2 lasers have a larger beam parameter product than diffraction-limited 1-μm solid-state lasers, but still compare favorably with lamp-pumped systems.

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.

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# Trouble with Specifications

Specifications for lasers and other photonics products are essential for the process of buying such things. Nevertheless, many do not properly deal with them:

• Many product specifications by suppliers lack quality – they are incomplete, not sufficiently clear, etc.
• Buyers are often not aware of what they really need. For example, they forget essential requirements.

Various problems can arise:

• Due to a lack of clarity, tedious communications between supplier and buyer are required.
• Product specifications raise expectations which cannot be met.
• Conflicts can arise over such issues.

Our Photonics Spotlight article and our encyclopedia article on laser specifications give you important hints. In case of doubt, contact RP Photonics to get competent and impartial advice.

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