The general wave equation, assuming paraxial approximation, yields: With: 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.
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.
[2] The BPP can be easily measured by placing an array detector or scanning-slit profiler at multiple positions within the beam after focusing it with a lens of high optical quality and known focal length.