THORLABS M2MS, Operating Manual

Page: 133 / 167

BP209 Series 7 Operation Instructions
Rev: 8.1, 14-Feb-2022 © 2022 Thorlabs Page 131
For mode mixture (MM) beams, i.e. beams which feature higher order modes than just the
fundamental mode TEM
00
, the product of beam diameter and divergence increases by a factor
of M².
Finally, the times-diffraction-limit factor M
2
is calculated by
The Rayleigh Length is now given by
The reciprocal of the times-diffraction-limit factor M
2
is called the beam propagation factor or
beam quality K.
The following table illustrates the differences between a perfect Gaussian beam and non-per-
fect beam.
Parameter Gaussian Beam Mode Mixture Beam
Times-diffraction-limit factor M
2
1 > 1
Beam propagation factor = Beam quality K 1 < 1
Beam waist for given lens minimal larger
Divergence angle
q
at given beam waist d
0
narrow wider
Reasons for Non-Ideal Gaussian Beam with M
2
> 1
Using a Gaussian beam is preferred because of its minimum divergence angle and the ability to
achieve the minimal focus diameter. Differences to Gaussian shape can be due to
·
existence of higher order modes
·
amplitude and phase distortions due to inhomogeneous gain medium in lasers
·
presence of extraordinary beams
These distortions lead to a larger beam waist compared to Gaussian beams when the same
focal lens is used. This results in a lower maximum achievable power density in the focal point.
Comparison of Propagation Between Fundamental Mode TEM
00
(Ideal Gaussian beam)
and Mode Mixture Beams
With a given divergence angle (i.e. knowing the focal length of the lens), the fundamental mode
alone produces the theoretically smallest possible beam waist (green curve). If beam quality
worsens (red curve), the beam waist increases. If divergence is fixed, beam waist increases
linearly by the factor M
2
compared to the underlying Gaussian.