Laser Beam Quality Parameters

Some parameters related to laser beam quality are given here.

1. M-square factor
This is the most widely used parameter.

M2 =

πWoΘ λ

(1)

The capital letters W_o and Θ are beam waist radius and half-width divergence respectively for a general multimode Gaussian beam (I use lower-case w_o and θ for the "imbedded" fundamental Gaussian beam [1]).

2. Beam parameter product (BPP) [2]
This parameter is defined as the product of beam width and full beam divergence:

BPP=2W0*2Θ=4M2λ/π

(2)

3. Brightness
Brightness is essentially equivalent to radiance [3], i.e., power in a unit cross-sectional area and a unit solid angle:

B =

P πW02πΘ2

=

P (M2)2λ2

(3)

References:
[1] T.F. Johnston, "Beam propagation (M²) measurement made as easy as it gets: the four-cuts method", Appl. Opt. 37, 4840 (1998).
[2] X. Gao et al., "Beam-shaping technique for improving the beam quality of a high-power laser-diode stack", Opt. Lett. 31, 1654 (2006).
[3] http://www.rp-photonics.com/brightness.html