THORLABS M2MS, Operating Manual

Page: 132 / 167

BP209 Series 7 Operation Instructions
Page 130
21424-D02
7.2.9 M² Theory
The diameter d(z) of a focused laser beam increases with distance z from its waist position and
can be calculated as follows:
with
d
0
Waist Diameter
z
R
Rayleigh Length
l Wavelength
In this equation it was assumed that the waist location is at zero. Otherwise z has to be
replaced with (z-z
0
)
The Rayleigh Length z
R
determines the distance from the beam waist to the position where the
beam diameter has increased by a factor of Ö 2 = 1.41 compared to the minimum diameter at
the waist.
From the equation for d(z) it can be seen that the beam diameter increases linearly with z in the
far field ( z >>z
R
). The full divergence angle Θ can be calculated by
For laser beams with fundamental mode TEM
00
(Gaussian Beam shape) it can be theoretically
shown that the Rayleigh Length is given by
Thus the product of the minimum diameter of a Gaussian beam (at waist) and the divergence
angle
(AKA 'Beam Parameter Product', BPP) is constant for a given wavelength: