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(Acronym: BPP)
Definition: product of the beam radius in a focus and the far-field 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, standard deviations 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.

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 does not change 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 used equipment (e.g. a beam profiler) and the available space (which has to extent over several Rayleigh lengths).
A related, less frequently used quantity is the diameter-divergence product.
See also: beam radius, beam divergence, beam quality, M2 factor, beam profilers


