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Section 5:
Laser Beam Shaping
Overview
Example of beam shaping for TEM00 Laser
Spot Diameter
1.2
1
0.8
0.6
Heating
Energy
Gaussian
Superfluous
Energy
Top-Hat
Ablation
Threshold
1.2
1
0.8
0.6
Intensity (a.u.)
Spot Diameter
Figure 5.2: Beams with Gaussian profi les are less effi cient than those
with fl at top profi les in laser ablation applications because of both a
large beam area with superfl uous energy higher than the required ablation
threshold and energy lower than the threshold in the outer regions
of the Gaussian profi le
A laser beam shape is typically defi ned by its irradiance distribution and
phase. The latter is essential in determining the uniformity of a beam
profi le over its propagation distance. Therefore, beam shapers are designed
to redistribute the irradiance and phase of an optical beam to
attain a desired beam profi le that is maintained along the desired propagation
distance. Common irradiance distributions include Gaussian, in
which irradiance decreases with increasing radial distance, and fl at top
beams, also known as top hat beams, in which irradiance is constant
over a given area (Figure 1). A detailed description of Gaussian beam
propagation can be found in Section 2 on pages 8-11 and information on
quantifying the quality of a laser’s irradiance distribution can be found
in Section 4 on pages 13-15.
Some applications benefi t from beam profi les diff erent from that of the
laser source, which is typically Gaussian. For example, fl at top profi les
are advantageous in applications such as certain materials processing
systems because they often result in more accurate and predictable cuts
and edges than Gaussian beams (Figure 5.2). However, introducing a
beam-shaping optics increases system complexity and cost.
Beam shaping modifi es the properties of light at their most fundamental
level and its effi ciency is determined by Heisenberg uncertainty principle
on time-bandwidth:1
x represents position and v represents momentum. The uncertainty principle
adds some limitations to the design of beam shapers. For example,
for a design with very well-defi ned position, the spatial frequencies
become less defi ned. Applying the uncertainty principle to diff raction
theory, i.e. the Fourier transform relation in the Fresnel integral, a characteristic
parameter β is obtained:
where ro is the input beam half-width, ri is the output beam half-width,
C is a constant, λ is wavelength, and z is the distance to the output
plane. The value of β is very important when designing or considering
a beam shaping application since larger values correspond with better
beam shaping performance. For example, for β<4, the beam shaper
will not produce acceptable results for essentially any laser application,
while a 16<β>16 would provide low performance. Hence, for optimal
performance, experimental conditions that lead to β>16 should
be employed. This formula implies that it will be more straightforward
to design beam shapers for larger beams, shorter wavelengths, and
shorter focus distances.
Section 5.1: Refractive Beam Shaping
In low-performance systems where cost is a driving factor, Gaussian
beams may be physically truncated by an aperture to form a pseudo-fl at
top profi le. This is ineffi cient and wastes the energy in the outer regions
of the Gaussian profi le, but it minimizes system complexity and cost.
0.4
-6 -4 -2
X, mm
0.2
0
0 2 4 6
0.4
-5 -4 -3
X, mm
0.2
0
-2 0 2 3 4 5
Input
TEM00
Output
Flat-top
Figure 5.1: For a Gaussian beam profi le (left), irradiance decreases with
increasing distance from the center according to a Gaussian equation.
For a fl at top beam (right), irradiance is constant over a given area.
5.1
5.2