In the production and use of lasers, it is inevitable to involve the detection and characterization of beam quality. M2 and BPP are the two most commonly used physical quantities that express the quality of laser beams. M2 and BPP are derived based on the same physical concept, so they can be converted to each other.
The reason why the beam quality is important is that it is a key physical quantity to judge the quality of the laser and whether it can be laser precision processed. For many kinds of single-mode output lasers, high-quality lasers usually have high beam quality, corresponding to Very small M2, such as 1.05 or 1.1. And the laser can maintain a good beam quality throughout its service life, and the M2 value is almost unchanged. For laser precision machining, a laser beam with high beam quality is more conducive to shaping, thereby performing flat-top laser machining without damaging the substrate and without thermal effects. In actual use, when marking laser specifications, M2 is mostly used for solid-state lasers and gas lasers, while BPP is mostly used for fiber lasers.
How to calibrate the quality of the beam? The beam quality describing the laser is usually expressed by two parameters: BPP and M². M² is also often written as M2, which can be read as M squared or M2. The following figure is the longitudinal distribution of the Gaussian beam, where the beam waist radius W and the far field divergence angle half angle θ.
BPP (Beam Parameter Product) is defined as beam waist radius × far field divergence angle
BPP=W × θ
Half-field divergence angle of Gaussian beam:
θ0=λ / ΠW0
M²: the ratio of the beam parameter product to the beam parameter product of the fundamental mode Gaussian beam:
M2=（W×θ）/（W0×θ0）=BPP /（λ/Π）
It is not difficult to find from the above formula, where BPP has nothing to do with the wavelength, and the M² factor is also related to the laser wavelength. They are mainly related to the laser cavity design and assembly accuracy.
The value of the M² factor is infinitely close to 1, indicating the ratio of real data and ideal data. When the real data is closer to the ideal data, the beam quality is better. That is, when the M² factor is closer to 1, the beam quality is better, corresponding The smaller the divergence angle.
For the analysis of beam quality, it mainly depends on the beam analyzer for measurement. The beam quality analyzer can make accurate measurements, but the use of a spot analyzer requires complex operations, collecting laser cross-section data from different positions, and then synthesizing M² data through the instrument's built-in program. If there are operational errors or measurement errors during the sampling process , You cannot measure and analyze the value of M². For high-power measurement, a complex attenuation system is required to keep the laser power within the measurable range to avoid damage to the detection surface of the instrument due to excessive power.
According to the above figure, the fiber core and numerical aperture can be estimated. For fiber lasers, the beam waist radius ω0=fiber core diameter/2=R, θ=sinα=α=NA (fiber numerical aperture)
It can be concluded from this:
The smaller the BPP, the better the laser beam quality.
For 1.08um fiber laser, single fundamental mode M2=1, BPP=λ/Π=0.344 mm mrad
For 10.2um CO2 laser, single fundamental mode M2=1, BPP=3.38 mm mrad
Assuming that the two single fundamental mode (or multimode M2 is the same) lasers after focusing, the divergence angle is the same, then the focal diameter of the CO2 laser is 10 times that of the fiber laser.
The closer M² is to 1, the better the beam quality of the laser.
When the laser beam is in a Gaussian or near-Gaussian distribution, the closer the M² factor is to 1, the closer the actual laser is to the ideal Gaussian laser, and the better the beam quality.