In laser science, the beam parameter product (BPP) is the product of a laser beam's divergence angle (half-angle) and the radius of the beam at its narrowest point (the beam waist).[1] The BPP quantifies the quality of a laser beam, and how well it can be focused to a small spot. A Gaussian beam has the lowest possible BPP, <math>\lambda/\pi</math>, where <math>\lambda</math> is the wavelength of the light.[1] The ratio of the BPP of an actual beam to that of an ideal Gaussian beam at the same wavelength is denoted M² ("M squared"). This parameter is a wavelength-independent measure of beam quality.
Measurement of the BPP
The BPP can be easily measured by placing an array detector or scanning-slit profiler at multiple positions within the beam after focussing it with a lens of high optical quality and known focal length. Measurements must be taken both at the beam waist and far from it. The beam diameter at each point is four times the standard deviation of the beam's intensity profile in two perpendicular directions (usually horizontal and vertical). The measurement at the beam waist gives the waist size, while the measurements far from the waist allow the divergence to be calculated. In principle, a single measurement far from the waist would be sufficient if the position of the waist were accurately known. In practice, measurements at multiple distances are typically taken for better accuracy, and combined using linear regression.
References
- ^ a b Beam parameter product. Encyclopedia of Laser Physics and Technology. Retrieved on 2006-09-22.
