Measurement of the waist diameter of a focused Gaussian-beam at the 1/e(sup 2) intensity, also referred to as spot size, is key to determining the fluence in laser processing experiments. Spot size measurements are also helpful to calculate the threshold energy and threshold fluence of a given material. This work reports an application of a conventional method, by analyzing single laser ablated spots for different laser pulse energies, to determine the cross-sectional area of a focused Gaussian-beam, which has a nominal pulse width of approx. 10 ps. Polished tungsten was used as the target material, due to its low surface roughness and low ablation threshold, to measure the beam waist diameter. From the ablative spot measurements, the ablation threshold fluence of the tungsten substrate was also calculated

Connell, John

Fitz-Gerald, James

Ledesma, Rodolfo

Palmieri, Frank

NASA Technical Reports Server

NASA/TM–2018-219809
Determination of Cross-Sectional
Area of Focused Picosecond Gaussian
Laser Beam
Rodolfo Ledesma and James Fitz-Gerald
University of Virginia, Charlottesville, Virginia
Frank Palmieri and John Connell
Langley Research Center, Hampton, Virginia
February 2018
https://ntrs.nasa.gov/search.jsp?R=20180001865 2019-08-30T13:05:32+00:00Z
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NASA/TM–2018–219809
Determination of Cross-Sectional
Area of Focused Picosecond Gaussian
Laser Beam
Rodolfo Ledesma and James Fitz-Gerald
University of Virginia, Charlottesville, Virginia
Frank Palmieri and John Connell
Langley Research Center, Hampton, Virginia
National Aeronautics and
Space Administration
Langley Research Center
Hampton, Virginia 23681-2199
February 2018
Acknowledgments
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Abstract
Measurement of the waist diameter of a focused Gaussian-beam at the 1/e2 intensity,
also referred to as spot size, is key to determining the fluence in laser processing
experiments. Spot size measurements are also helpful to calculate the threshold
energy and threshold fluence of a given material. This work reports an application
of a conventional method, by analyzing single laser ablated spots for different laser
pulse energies, to determine the cross-sectional area of a focused Gaussian-beam,
which has a nominal pulse width of ∼10 ps. Polished tungsten was used as the target
material, due to its low surface roughness and low ablation threshold, to measure the
beam waist diameter. From the ablative spot measurements, the ablation threshold
fluence of the tungten substrate was also calculated.
1 Introduction
The characterization of laser systems is important for understanding the effects
of the laser parameters (e.g. wavelength, pulse duration, and spot size) on the
ablation mechanisms. The ablation mechanism of a given material can occur by
photothermal, photochemical, or photophysical ablation, and generally depends on
the wavelength and pulse duration of the laser beam. Different ablation mecha-
nisms will produce different characteristics in the ablation damage, given the type
of substrate, e.g. metals and polymers. The properties of a substrate determine
how the irradiated light interacts with the surface and how the light is absorbed.
In order to compare results found in the literature, which report threshold fluences
given a specific substrate and laser characteristics, it is key to determine the spot
size and consequently, the cross-sectional area of the focused laser beam. Fluence
is an important parameter and is calculated as the amount of energy irradiated on
a surface per unit area. Several reports in the literature have addressed the deter-
mination of Gaussian laser beam spot size [1–5], even for two-dimensional energy
distribution [6].
In this work, the area of a focused Gaussian picosecond laser beam is determined
by exposure of ultraviolet single-shot laser pulses on a tungsten substrate. A con-
ventional method [3,4] is employed to measure the one-dimensional diameter of the
beam waist (1/e2) by analyzing single laser ablated spots for different laser pulse
energies. The results include the measurements of the dimensions of the ablated
craters. The ablation threshold of tungsten is determined by single-shot picosecond
laser pulses.
2 Experimental
2.1 Materials
Tungsten polycrystalline substrate (MTI Corp.) was used for the determination
of the focused laser beam area. The tungsten substrate had two sides polished,
nominal purity of 99.95%, and nominal average surface roughness of less than 30
1
A˚. The surface characteristics of the tungsten substrate provided a homogeneous
surface to clearly measure the ablated crater dimensions.
2.2 Laser Ablation
The schematic diagram of the laser system is shown in Figure 1. The single-shot
ablation was performed with a Nd:YVO4 (Atlantic 20-355, EKSPLA) laser, which
was operated at 355 nm with a nominal pulse duration of ∼10 ps. The laser beam
was focused by an f-theta lens (S4LFT6062/075, Sill Optics), with an effective focal
length of 250 mm, for a wavelength of 355 nm. The laser source operates at TEM00
beam mode. The TEM00 laser beam passes through optical components before being
focused by the f-theta lens. The laser system was assembled and calibrated by Pho-
toMachining Inc. The average laser power was measured with a thermopile sensor
(30A-BB-18, Ophir-Spiricon) and a laser power meter (Nova II, Ophir-Spiricon).
The laser ablated spots were produced by moving the XY translational stage to
expose a fresh surface after each single laser shot.
355 nm Nd:YVO4
(~10 ps)
Sample
XY Translation Stage
F-Theta Lens
Figure 1. Schematic of the picosecond laser system for ablation of the tungsten
sample.
2.3 Ablation Spot Analysis
The surface morphology analysis was performed using a JEOL JSM-5600 scanning
electron microscope (SEM) operated at an accelerating voltage of 15 kV. The di-
mensions of the ablated spots were measured by analyzing the SEM micrographs
using the image processing and analysis software ImageJ [7].
3 Results and Discussion
Figure 2 shows the SEM micrographs of the ablation craters for the pulse energies
of 5 µJ, 15 µJ, and 30 µJ. The contours of the ablated craters exhibit smooth
edges. This demonstrates that there is no thermal damage or redeposited material
around the craters. As the laser energy increases, the shape of the ablated crater
diverges from an ellipse. In addition, the absorption of the laser pulse at the center
2
increases and produces an inner crater with a more consistent elliptical shape. The
inner crater can be evidently observed in Figure 2c. The inner crater in Figure 2c
also presents smooth edges. Above 15 µJ, the craters exhibit a deformation, which
may be due to a distortion in the spatial laser energy distribution. The contours
of ablated craters exhibit effects of astigmatism, which produces an elliptical shape.
Different angles of divergence in two transverse directions cause astigmatism and
elliptical beams [8–10]. Despite the drawback of the crater shapes ablated above 15
µJ, Figure 3 shows the closest elliptical fit to the crater contours. Figure 3a shows
that the ablated crater was easily fit, however in Figures 3b and 3c, the elliptical fits
became more challenging. From the elliptical fit (red contour) shown in Figure 3,
consider D1 as the minor diameter (green chord) and D2 the major diameter (yellow
chord).
Figure 2. SEM micrographs of craters ablated at a) 5 µJ, b) 15 µJ, and c) 30 µJ.
Figure 3. SEM micrographs with measurements of the elliptical fits to ablated crater
contours, a) 5 µJ, b) 15 µJ, and c) 30 µJ. The green chord is the minor diameter,
and the yellow chord is the major diameter.
Theoretically, the diameter of an ablated spot can be calculated by [11]:
D2 =
D20
2
ln
(
E
Eth
)
(1)
where D is the diameter of the ablated crater, D0 the diameter at the Gaussian
beam waist, E the irradiated pulse energy on the material, and Eth the ablation
threshold of the material. The optical diameter D0 represents 1/e
2 of the intensity
peak value. Within the circle of radius w(z), 86% of the laser beam power is carried.
At the waist, z = 0, the radius is w(0) = D0/2.
3
From the SEM micrographs, it is clear that the Gaussian beam distribution is
two-dimensional. Considering the minor diameter axis to be x and the major axis
to be y, the two-dimensional Gaussian intensity (irradiance) at the beam waist is
given by:
I(x, y) = I0 exp
(
− 2x
2
w20x
)
exp
(
− 2y
2
w20y
)
(2)
where I0 is the peak intensity at the center of the beam and w0 is the Gaussian
beam radius, at which the intensity drops to 1/e2 of its peak intensity. The peak of
the two-dimensional Gaussian function occurs when both radial positions, x and y,
are on the center axis of the beam, i.e. (x, y) = (0, 0).
Figure 4 shows the single-shot laser ablation threshold measurements of tungsten.
Each data point is an average of three measurements, and the error bars indicate 1σ
standard deviation. The logarithm of the ratio of E to Eth is linearly proportional
to D2. From the logarithmic fit to D1, Eth,1 = 0.34 µJ. Likewise, for D2, Eth,2
= 0.8 µJ. Since the threshold for D1 is smaller than that for D2, D1 is used to
determine the ablation threshold energy, Eth, needed to produce ablation damage
on the tungsten substrate. Therefore, D0 = D1 = 2w0x. Consequently, Eth = Eth,1
= 0.34 µJ.
10 1 100 101 102
 / D V H U  S X O V H  H Q H U J \    - 
 
   
    
D
  V
 T X
 D U
 H G
  
 P
2  
y1 = 114.3ln(x) + 123.3
y2 = 247.3ln(x) + 61.7
 ' L D P H W H U  
 ' L D P H W H U  
 / R J D U L W K P L F  I L W
Figure 4. Single-shot laser ablation threshold measurements of tungsten. Diameter
1 is referred to as D1, the minor diameter, and Diameter 2 is referred to as D2, the
major diameter.
Figure 5 shows the linear relationship between ln (E/Eth) and D
2, according to
Eq. 1. From Eq. 1, the one-dimensional optical diameter of the Gaussian beam can
be determined when D = D0, and consequently E/Eth = e
2. Considering the minor
diameter, when D1 = D1,0 = 15.1 µm, E1 equals 2.5 µJ. Now, calculating for D2
at E1 = 2.5 µJ yields D2 = 16.8 µm. The cross-sectional area A of the focused
elliptical laser beam is calculated as:
A =
(pi
4
)
D1D2 (3)
4
           
ln(E/Eth)
 
   
    
D
  V
 T X
 D U
 H G
  
 P
2  
 ' L D P H W H U  
 ' L D P H W H U  
 / L Q H D U  I L W
Figure 5. Linear relationship between ln (E/Eth) and D2, according to Eq. 1.
Therefore, the elliptical area A is 1.99 × 10−6 cm2. By knowing the focused
laser beam area, the average fluence F can be calculated as:
F =
E
A
(4)
and the peak fluence as:
F =
2E
A
(5)
Thus, the threshold fluence of the tungsten substrate using the ∼10 ps focused
laser beam is 0.17 J/cm2. This fluence threshold is similar to other values found in
literature [12–15].
4 Conclusions
The one-dimensional spot size of the Gaussian beam at the waist was determined.
The ablated spots were generated using single laser pulses focused on a tungsten
substrate. The focused Gaussian beam generated ablative damage in an elliptical
shape. Thus, the Gaussian beam was represented with a two-dimensional spatial
distribution. The minor diameter of the elliptical fit of the ablated crater contour
was used to determine the energy and fluence thresholds. Using picosecond pulses,
the threshold energy of tungsten was found to be 0.34 µJ, and the cross-sectional
area of the focused elliptical laser beam was determined as 1.99 × 10−6 cm2. Thus,
the threshold fluence was calculated to be 0.17 J/cm2.
References
1. Winer, I.: A self-calibrating technique measuring laser beam intensity distribu-
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5
2. Mauck, M.: Knife-edge profiling of Q-switched Nd:YAG laser beam and waist.
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CRC Press, 2015, pp. 1–15.
11. Haskal, H.; and Rosen, A.: Power and focusing considerations for recording with
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12. Preuss, S.; Demchuk, A.; and Stuke, M.: Sub-picosecond UV laser ablation of
metals. Appl. Phys. A, vol. 61, 1995, pp. 33–37.
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6
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Determination of Cross-Sectional Area of Focused Picosecond Gaussian
Laser Beam
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Rodolfo Ledesma, Frank Palmieri, James Fitz-Gerald, and John Connell
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NASA Langley Research Center
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14. ABSTRACT
Measurement of the waist diameter of a focused Gaussian-beam at the 1/e2 intensity, also referred to as spot size, is key to
determining the fluence in laser processing experiments. Spot size measurements are also helpful to calculate the threshold
energy and threshold fluence of a given material. This work reports an application of a conventional method, by analyzing
single laser ablated spots for different laser pulse energies, to determine the cross-sectional area of a focused Gaussian-beam,
which has a nominal pulse width of ∼10 ps. Polished tungsten was used as the target material, due to its low surface
roughness and low ablation threshold, to measure the beam waist diameter. From the ablative spot measurements, the
ablation threshold fluence of the tungten substrate was also calculated.
15. SUBJECT TERMS
Gaussian beam, Spot size, Picosecond, Laser ablation, Scanning electron microscopy
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Determination of Cross-Sectional Area of Focused Picosecond Gaussian Laser Beam

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