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Chapter 5 M
2
Tutorial and Theory
Introduction to M
2
5.1
The M
2
model is the accepted standard for characterizing the general performance (or “quality”) of a laser
beam. This one quantity, in each of the two orthogonal propagation planes, ties together the three interrelated
beam parameters of beam waist width, divergence, and Rayleigh range. This measurement is based on how a
real laser compares to a single mode beam. A single mode beam (referred to as the fundamental mode or
TEM
00
) has an M
2
value of 1. Beams of higher order mixed modes have an M
2
value greater than 1.
The M
2
value for a given laser beam is derived from propagation theory and is referred to as the “beam
propagation ratio.” One practical consequence of the M
2
definition is that a beam with an M
2
value of 1 can be
focused to a minimum spot diameter, whereas beams of higher M
2
values focus to larger spot diameters in
proportion to the M
2
value. For example, a beam with an M
2
value of 2 will have a minimum focus spot 2 times
as large as a Gaussian beam of M
2
= 1. Thus, knowledge of the M
2
value can provide meaningful information
about lasers, especially if their application involves small focused spot sizes.
A second notation for beam quality has also been adopted. It is referred to as the Beam Propagation Factor
(K) where: K = 1/M
2
. And a third representation called the Beam Parameter Product (BPP) has come into use,
where: BPP = M
2
λ/
π
. BeamSquared calculates and reports all three values.
For the remainder of this discussion we will only refer to the M
2
form.
The International Organization for Standards (ISO) subcommittee on electro-optical systems has created a
standard for test methods relating to the measurement of laser beam parameters. BeamSquared employs
algorithms that conform to the methods described in the ISO 11146-1 and 11146-3:2005(E) procedures.
Copies of the measurement standard can be procured from ISO.
ISO 11146-1 describes the method for characterizing stigmatic and simple astigmatic beams. BeamSquared is
designed to measure these types of lasers.
ISO 11146-2 details the method for characterizing general astigmatic beams (twisted beams). BeamSquared is
not capable of measuring this class of laser.
ISO 11146-3 describes general measurement methods.
M
2
< 1 5.2
It has been suggested that if the M
2
results are computed to be less than one an M
2
= 1.0 should be displayed
as the answer. The BeamSquared algorithms use the input settings and collected data points to make all
calculations. No attempt is made to change or conceal data. This is done to provide useful information to the
user and may indicate an error in the setup or input values.
There are two common occurrences when M
2
results are less than one. The first and most common is an
incorrect wavelength entry. The wavelength can be corrected in the Results Window Settings (see section
3.7.5.1).
The second main cause for M
2
results less than one is due to nominal accuracy tolerances. These are normal
and expected. Within the measurement tolerance, results can vary ±5%. Here the M
2
is likely to be between
0.99 and 0.90.