THORLABS BC106-UV, Operation Manual

Page: 144 / 167

© 2011 Thorlabs
142 Thorlabs Beam 4.0
6.7
M² Theory
The diameter d(z) of a focused laser beam of fundamental modeTEM
00
increases
with distance z from its waist position.
with
d
0
waist diameter
z
R
Rayleigh length
wavelength
This formula is simplified. If the waist position z
0
is not zero, z has to be replaced
with (z-z
0
).
d
0
d
0
* 2
z
R
z
0
z
M
2
= 1
Fundamental
mode TEM
00
Focusing lens
Rayleigh length
d(z)
The Rayleigh length z
R
is defined by
and determines the distance from the beam waist where the beam diameter has
increased by a factor of 2 = 1,41 compared to the minimum diameter at the waist.
This formula is valid for a Gaussian beam.
In the far field, (z >> z
R
) beam diameter increases linearly with z which gives a
constant divergence angle in the far field.
The product of min. beam diameter at waist and divergence angle d
0
* is constant
for a given wavelength.