Two basic means are used for defining beam widths according to ISO11145 [
7]. One is encircled power (energy) width of the smallest slit transmitting
u% of the total beam power (energy) in two preferential orthogonal directions
x and
y, which are perpendicular to the beam axis. The other is second moment of power (energy) density distribution function. In practice, in order to increase the mode volume to achieve high power, an unstable resonator structure is often used to achieve multi-mode output. IEC60825-1 [
8] also makes provisions for the definition of beam widths. It is defined as the beam diameter
du at a position in space is the diameter of the smallest circle which contains
u% of the total laser power (energy). It is also pointed out that the second moment diameter definition is not used for beam profiles with central high irradiance peaks and a low level background, such as produced by unstable resonators in the far field: the power that passes through an aperture can be significantly underestimated, when using the second moment and calculating the power with the assumption of a Gaussian beam profile. That is to say that
M2 is inappropriate to evaluate beam quality in the field of industrial manufacturing. Evaluating beam quality in terms of
M2 for a high power laser with an unstable resonator may inaccurately estimate the ability of the laser system to accomplish its intended mission. In fact, it is extremely difficult to acquire the precision mode content and density distribution function. As to the definition of
Kf and
M2, the former is a product, the later is a ratio.
M2 includes the factor of wavelength. Beam quality with various wavelengths may be significantly different even if with same value of
M2. In fact, the primary factor that determines performance of a laser system is the encircled power or energy in a small region around the focal spot. We recommend that
Kf is the appropriate measure of beam quality because it is directly related to the mission objectives.