# Beam Parameter Product

The Beam Parameter Product (BPP) quantifies the quality of a laser beam and how well it can be focused to a small spot. It is the product of a laser beam's far-field divergence angle (half-angle) and the radius of the beam at its narrowest point (the beam waist).

For minimal degradation of the BPP in transmission through the fiber, the incoupling optics have to be optimised. The standard way to describe the BPP is to measure the beam waist radius in which 86% (1/e²) of the radiation falls and the divergence angle (half angle) measured with the same 86% values. The 86% BPP values are not the optimum for use in design of fiber optics, as then losing 14% of the power in the incoupling. Optoskand calculations are based on the BPP measured at the 98% values, both regarding beam waist and angle.

The lower beam parameter product - the better beam quality.

The relation between the two BPP values is depending on the beam profile. As a rule of thumb we normally use a factor 1.5 as the relation between the 86% (1/e²) and 98% BPP value.

BPP98% / BPP86% = 1.5 98% BPP = R x α (mm x mrad)

86% BPP = r x β (mm x mrad)

A different and very common beam quality measurement is the M² value. The M² value is a normalization of the BPP value. The normalization is made against a diffraction limited beam with the specific wavelength.

M² = BPP / BPP0
BPP0 = λ / π

The M² value has no unit.
BPP0 = diffraction limited beam
M² ≥ 1 The BPP value of the laser beam coming out from a fiber optic cable is measured as the fiber core radius multiplying the output divergence angle (half angle). Smaller fiber core radius and/or smaller output divergence angle give a better beam quality (lower BPP value).
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