# Beam Parameter Product

Author: the photonics expert Dr. Rüdiger Paschotta

Acronym: BPP

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

Units: mm · mrad

DOI: 10.61835/d8y Cite the article: BibTex plain textHTML Link to this page LinkedIn

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.

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:

## Suppliers

The **RP Photonics Buyer's Guide** contains 30 suppliers for laser beam characterization instruments. Among them:

### Gentec Electro-Optics

Gentec Electro-Optics offers a variety of camera-based instruments. This includes compact laser beam profilers and more complex instruments for measuring M^{2} beam quality factor by automatically analyzing the beam propagation. Besides, we offer optical power meters and various accessories.

### DataRay

DataRay offers a full range of ISO 11146-compliant beam profilers, both camera and scanning slit-based.

Camera-based systems include the WinCamD, BladeCam, and TaperCamD series, all of which are USB 2.0 or 3.0 port-powered. These cameras produce a 2D false color digital image of the beam intensity. From these images, XY profiles may be shown for any location on the beam at any angle.

Beam profiling cameras are typically both the optimal and most economical choice when the beam wavelength and diameter are appropriate.

### Edmund Optics

Laser beam analysers from Edmund Optics include devices such as profiler systems that evaluate data from beam images to provide information such as beam location, peak intensity position, stability, or beam density. For example, there are different kinds of laser beam profilers and autocorrelators for ultrashort pulse characterization.

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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.

The author's answer:

Indeed, you cannot calculate the beam radius when you know only the beam parameter products. At least, you would have to know the beam divergence in addition.