Gentec-EO Beamage-M2 - Manual (Page 10)

Beamage-M 2 User Manual Revision 2.0 10
2.
Theory
2.1. Understanding the M 2 Factor
The M 2 factor, which is unitless, can be considered as a quantitative indicator of laser beam quality. It indicates
the deviation of the measured beam from a theoretical Gaussian beam of the same wavelength. It can
mathematically be defined as the ratio between the Beam Parameter Product (beam waist radius w
0
multiplied
by divergence half-angle θ) of the measured beam with the theoretical Gaussian beam. Thus, for a single mode
ideal TEM
00
theoretical Gaussian beam, the M 2 factor is exactly one. Since an ideal Gaussian beam diverges more
slowly than any other beam, the M 2 value is always greater than one. An M 2 value very close to 1 indicates an
excellent beam quality. This is associated with a low divergence and a good ability to focus. Multimode lasers
have higher M
2 factors.
2.1.1. Propagation Parameters
In the following equations, ‘’th’’ refers to theoretical values and ‘’exp’’ to experimental or real values.
The beam waist is defined as the location along the beam propagation axis where the beam radius reaches its
minimum value (see Figure 2-1). For a theoretical Gaussian beam, the beam radius w
th
(z) at any position z along
the beam axis is given by the following equation:
Where λ is the laser wavelength and w
0th
the theoretical beam waist radius.
As depicted by Figure 2-1, the theoretical Rayleigh length Z
Rth
is the distance (along the propagation axis)
between the beam waist and the position where the beam radius is times larger than the beam waist
(doubled cross-section).
Figure 2-1 Beam Propagation Diagram
Mathematically, it is given by the following equation: