Beam parameter product

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, ${\displaystyle \lambda /\pi }$, where ${\displaystyle \lambda }$ 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:

${\displaystyle \mathrm {BPP} =\varphi \cdot w_{0}=M^{2}\cdot {\frac {\lambda }{\pi }}}$.

With:

${\displaystyle \varphi }$ the half angle in far field

${\displaystyle w_{0}}$ the beam waist

${\displaystyle M^{2}}$ the beam quality factor, M squared

${\displaystyle \lambda }$ 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.