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, , where 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.
The general wave equation, assuming paraxial approximation, yields:
.
With:
the half angle in far field
the beam waist
the beam quality factor, M squared
the wavelength.
The quality of a beam is important for many applications. In fiber-optic communications beams with an M2 close to 1 are required for coupling to single-mode optical fiber. Laser machine shops care a lot about the M2 parameter of their lasers because the beams will focus to an area that is M4 times larger than that of a Gaussian beam with the same wavelength and D4σ waist width; in other words, the fluence scales as 1/M4. The rule of thumb is that M2 increases as the laser power increases. It is difficult to obtain excellent beam quality and high average power (100 W to kWs) due to thermal lensing in the laser gain medium.
^ abPaschotta, Rüdiger. "Beam parameter product". Encyclopedia of Laser Physics and Technology. RP Photonics. Archived from the original on 18 October 2006. Retrieved 2006-09-22.
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