1.1.

Research Question and Agenda

The research question is whether there is a possibility to specify a standardized material property characterization process for USP lasers. Is the approach suitable to determine the independent determination of material properties of metallic materials and are the collected material properties suitable for a calibration of a simulation?

For this purpose, the USP machining of metals is first explained by highlighting the topics of ablation model and heat accumulation. Subsequently, the state of the art will be discussed, and three recognized model approaches will be presented. Then, a procedure for the independent determination of material properties for USP machining is presented

2.1.

Ablation Model for USP Machining of Metals

During USP laser material processing, there is a strong short-term and local temperature increase in the material. Due to the inertia of the much heavier metal ions, the crystal lattice of the metal is heated much more slowly than the surrounding electron system. This behavior is described by the two-temperature model and was investigated in more detail by Luk’yanchuk et al.⁹ Only the temperature of the crystal lattice after reaching the temperature equilibrium between the electron system and crystal lattice is decisive for the material ablation behavior.¹⁰ Ablation only occurs when a threshold fluence is exceeded. The necessary fluence to ablate material is described according to Lambert’s law

$\delta$ corresponds to the effective penetration depth and can correspond to an optical or diffusive penetration depth. The scientific basis for Eq. (1) has been derived by Chichkov.¹¹ Here, $F$ refers to the fluence incorporated into the material and $\delta$ describes the optical penetration depth and is a material constant. Here, $A$ refers to the absorption coefficient. By converting to $z$, an ablation depth per laser pulse $\mathrm{\Delta }z$ can be determined, which can be divided into two different cases:¹⁰

Since the respective limiting cases rarely occur in reality it is useful to introduce an effective penetration depth ${\delta }_{\mathrm{eff}}$, which can be determined from experiments. ${\delta }_{\mathrm{eff}}$ is determined fluence-dependently in the experiment by the test series because the electronic properties can also change with the fluence. Here, the threshold fluence ($F_{\mathrm{thr}}$) describes the tipping point from which material removal is starting. Equations (3) and (4) can be summarized with the help of ${\delta }_{\mathrm{eff}}$ as follows:

2.2.

Heat Accumulation

Although the heat generation when using USP laser radiation is low compared to SP laser radiation, heat accumulation effects also occur when processing with USP lasers at medium powers $>10\mathrm{W}$.⁷ Heat accumulation effects lead to a medium-term temperature increase of the workpiece and can negatively influence the quality of the ablation process. Due to the repeated impingement of laser pulses at short time intervals on the same point on the workpiece, a significant heating can occur. Strong temperature increases can lead to thermal stress, generate melt, and finally to the destruction of the workpiece.¹²

3.1.

Determination of the Threshold Fluence

The threshold fluence is determined for different materials taking into account the system properties. The system properties are the beam guidance and shaping, as well as the wavelength and pulse duration of the laser radiation. For pulse durations $<8\mathrm{ps}$, it has already been shown that the threshold fluence is largely independent of the pulse duration.¹³ The USP laser source used in this work has a pulse duration of 900 fs. By now three different methods are known to determine the threshold fluence. B. Neuenschwander^3–5 measures the ablated volume, Liu² the bore radius and J. Hermann et al.^2,6 the ablation depth. For all approaches, the threshold fluence is considered a material-specific constant. The three approaches are now briefly presented.

3.2.

Determination of the Threshold Fluence According to Neuenschwander

Neuenschwander’s modeling approach for determining the threshold fluence aims to determine the threshold fluence computationally from an optimal ablation fluence. Neuenschwander represents the optimal ablation fluence as the most efficient fluence in terms of time and energy used. Neuenschwander establishes a relationship between the threshold fluence and the most efficient ablation fluence.

Figure 2 illustrates the removal behavior of stainless steel according to Neuenschwander. In Fig. 2(a), the removal rate of stainless steel in ${\mathrm{mm}}^3/\min$ is plotted against the repetition rate in MHz regime for different laser powers used. Figure 2(b) shows the removal rate of stainless steel per average power in ${\mathrm{mm}}^3/(\min \times \mathrm{W})$ plotted against the pulse peak fluence as a multiple of the threshold fluence. The removal rate per average power indicates the ratio of volume removed to the average power and process time and can thus be regarded as the ablation or removal efficiency. The fluence at the local maximum of the right graph is called the most efficient fluence ($F_{\mathrm{eff}}$). The fluence at which the removal efficiency intersects the $X$-axis is called the threshold fluence ($F_{\text{thr}}$). Equation (6) represents the mathematical relationship for a Gaussian beam between ${\mathrm{F}}_{\text{thr}}$ and ${\mathrm{F}}_{\text{eff}}$, which was determined by a working group led by Neuenschwander and confirmed experimentally^4,14

Fig. 2

(a) stainless steel removal rate for different repetition rates and (b) stainless steel removal rate per average power.¹⁴

This relationship allows to determine the threshold fluence without using fluences in the order of $F_{\mathrm{thr}}$. One advantage of the Neunschwander method is that it is not necessary to determine an ablation threshold in the vicinity of the threshold fluence with optical measuring systems. For this reason, different methods for determining the threshold fluence are analyzed (Sec. 4.1) A similar relationship like Eq. (6) was previously described by Raciukatis¹⁵ with the aim of increasing the ablation efficiency.

3.3.

Determination of the Threshold Fluence According to Liu

Liu developed a method as early as 1982 that makes it possible to determine the threshold fluence of Gaussian beam profiles. The threshold fluence is determined with knowledge of the intensity or fluence distribution and the measured radius of the ablated circular shape by using a Gaussian beam profile in the workpiece. Equation (7) shows the function of the fluence distribution as a function of the ablation radius $r$²

3.4.

Determination of the Threshold Fluence According to Hermann

Hermann establishes a linear relationship between the ablation depth per laser pulse and the natural logarithm of the fluence. With the help of this linear relationship, the threshold fluence can be determined. Figure 3 shows the averaged ablation depth over the logarithmically plotted fluence using Hermann’s method.⁶

Fig. 3

Ablation depth plotted against fluence according to Hermann. Measurement data points are shown in blue, regression line in red; USP laser with 100 kHz and 900 fs; $19\text{-}\mu \mathrm{m}$ focus diameter.

The logarithmic representation of the fluence on the $x$-axis results in a linear increase in the average ablation depth. By extrapolating the regression lines to the $x$-axis, the threshold fluence can be determined, which is in the range $\ge 0\mathrm{J}/\mathrm{c}{\mathrm{m}}^2$ at the intersection of the regression lines with the $x$-axis. By transforming Eq. (8) to ${\delta }_{\mathrm{eff}}$ and using the slope of the regression line by means of a gradient triangle, the effective penetration depth can be represented as follows:

3.5.

Angle Dependent Absorption Coefficient

The pulse energy deposited into the material and thus the ablation behavior is significantly dependent on the absorption coefficient. A change in the angle of incidence of the laser beam also changes the absorption coefficient. Figure 4 shows the absorption coefficient as a function of the angle of incidence qualitatively for iron.¹⁶

Fig. 4

Angle of incidence dependent absorption coefficient of iron for parallel, perpendicular, and circular polarization.

At an angle of incidence of zero degrees, all polarization types are absorbed equally. The orange curve (squares) represents the absorption coefficient for parallel polarization as a function of the angle of incidence. The blue curve (dots) represents the absorption coefficient for perpendicular polarization as a function of the angle of incidence. The green curve describes the absorption coefficient for circular polarization and is the superposition of the two curves blue and red. Thus, during USP processing geometries with resulting tapers occur as a function of the angle of incidence of the laser radiation and the ablated depths. The degree of absorption depends on polarization and inclination angle. Even without taking multiple reflections into account, this observation explains why drilled holes are not the best choice to determine ablation thresholds. The determined ablation thresholds will depend on the geometrical shape of the drilled hole. The perpendicular polarized laser radiation is better absorbed with an increasing angle of incidence, as can be seen in Fig. 4, and the material is thus stronger ablated in the direction of the perpendicular polarization.

4.1.

Test Series 1: Identifying the Threshold Fluence

The objective of the first test series (T1) is to determine the threshold fluence by a purely visual evaluation of qualitative ablation phenomena of the structured workpiece. Literature indicates that the threshold fluence of stainless steels for processing with USP lasers is in the range of 60 to $100\mathrm{mJ}/\mathrm{c}{\mathrm{m}}^2$.⁴ To determine the threshold fluence within the scope of this research the fluence is varied both above and below the known 60 to $100\mathrm{mJ}/\mathrm{c}{\mathrm{m}}^2$. The measured average power is used to determine reasonable intervals over which the fluence can be varied in small steps. During the examination, attention is paid to when there is no ablation of the workpiece while the average power or the laser pulse energy is increased between two successive reference positions. In case there is visually recognizable ablation, the fluence at which ablation phenomena can be detected is subsequently referred to as the threshold fluence or ablation threshold.

To detect the threshold fluence, the workpiece is first machined by point geometries with multiple laser pulses. It is comparable to a percussion drilling process and Liu’s approach to determine the threshold fluence (Sec. 3.3). When analyzing the experimental variation of the point geometries, it becomes apparent that a change in appearance hereinafter referred to as “modification” of the material surface can already be seen at a fluence of $25\mathrm{mJ}/\mathrm{c}{\mathrm{m}}^2$. In addition, it can be shown that the occurrence of the modification is dependent on the number of laser pulses applied to the workpiece. Figure 8 shows an example of a digital microscope and SEM image of the variation of fluence and number of laser pulses using point structures. A test matrix for ${10}^2$ to ${10}^5$ applied laser pulses at different fluences at a repetition rate of 100 kHz is illustrated in Fig. 8(a). Each combination of fluence and number of laser pulses is patterned and framed five times side by side on the workpiece to highlight the homogeneity of its appearance for visual evaluation. The green line subsequently inserted in Fig. 8(a) marks the limit from which combination of fluence and number of laser pulses lead to a modification of the surface. It is obvious that with different numbers of laser pulses, a modification occurs at different fluence. This procedure, as shown in Fig. 8(a), is similar to Liu’s method of elevation the threshold fluence. According to Liu’s approach, a modification can apparently be mistaken for an ablation. The difference between a modification and an ablation can only be inadequately assessed by a digital microscope. Therefore, the authors assume at this point that this behavior can be attributed to the incubation effect described in literature. SEM images are able to provide a clear distinction and distinguish a first ablation result from a ripple-based modification.

Fig. 8

Variation of fluence and laser pulse number for detection of $F_{\mathrm{mod}}$ at $f_{\mathrm{rep}}=100\mathrm{kHz}$ (a) and point structuring of the workpiece surface at $56\mathrm{mJ}/\mathrm{c}{\mathrm{m}}^2$ and $f_{\mathrm{rep}}=100\mathrm{kHz}$ (b). Comparison of $F_{\mathrm{mod}}$ at different repetition rates with varying fluence and number of applied laser pulses (c).

The ablation threshold for a fixed combination of material and USP laser can be assumed as a constant value in $\mathrm{J}/\mathrm{c}{\mathrm{m}}^2$. The present findings suggest to define a “modification threshold,” which is the fluence threshold where modifications but no ablation of the material can be observed, see Fig. 8(a). When the fluence in combination with the number of applied laser pulses is sufficient to produce a visible modification of the workpiece surface, as shown in Fig. 8(b), the fluence leading to this first-ever modification will be referred to as the modification threshold ($F_{\mathrm{mod}}$) in the rest of this paper. Figure 8(c) compares the modification thresholds of structured point geometries at different repetition rates. It can be seen that the modification threshold for point geometries is dependent on the number of laser pulses applied and not on the used repetition rate. Thus, the incubation effect is not related to the ablation threshold, but to the changing modification threshold. We observe a change in the modification threshold with the number of pulses but the ablation threshold does not change with the number of pulses. The conclusion that the modification threshold is independent of the repetition rate in a frequency range from 0.6 to 600 kHz can thus be drawn, whereby the fluctuations shown between the different repetition rates are probably due to surface contamination or material defects. At this point, however, the behavior of the modification threshold is not investigated further, since the objective is to determine the ablation threshold.

To better illustrate the difference between modification and ablation, the point geometries are replaced by squares, since a clear differentiation of the modification and ablation areas is possible due to the larger machinable area on the workpiece surface. For this purpose, $432\times {10}^6$ laser pulses were applied over the entire square with an edge length of $200\mu \mathrm{m}$. To reduce the time required for the number of laser pulses applied the line spacing is set to $1\mu \mathrm{m}$, the repetition rate to 600 kHz and the feed rate to $100\mathrm{mm}/\mathrm{s}$. This results in a pulse overlap of 90%. For square structuring, ablation first occurs at a fluence of $65.5\mathrm{mJ}/\mathrm{c}{\mathrm{m}}^2$ in combination with $3\times {10}^6$ applied laser pulses per focal area. For USP processing of the workpiece with a fluence of $49.4\mathrm{mJ}/\mathrm{c}{\mathrm{m}}^2$, no ablation can be demonstrated [Fig. 9(a)], which is why the ablation threshold must be in the range $49.4<{\mathrm{F}}_{\mathrm{t}\mathrm{hr}}\le 65.6\mathrm{mJ}/\mathrm{c}{\mathrm{m}}^2$. The comparison of the ablation with point and square texturing illustrates that both surface textures exhibit ripples [Figs. 9(c) and 9(d)] and that a modification region forms around the area of ablation [Figs. 9(c) and 9(d)]. The ripples seen in the square texturing are more concise than those in the point texturing and can be more clearly interpreted as ablation due to the larger textured area. Accordingly, only appearances of larger structures like square structures should be used to determine the threshold fluence. The smallest fluence leading to ablation is observed for point structuring in Fig. 9(c) at $56\mathrm{mJ}/\mathrm{c}{\mathrm{m}}^2$, which lies in the previously determined interval [Figs. 9(a) and 9(b)] of the threshold fluence of $49.4<{\mathrm{F}}_{\mathrm{t}\mathrm{hr}}\le 65.6\mathrm{mJ}/\mathrm{c}{\mathrm{m}}^2$. It is shown that the ablation threshold is independent of the number of laser pulses.

Fig. 9

Differentiation of (a) modification and (b) ablation for structuring the workpiece surface with squares at $f_{\mathrm{rep}}=600\mathrm{kHz}$ and differentiation of ablation between point and square structuring of the workpiece surface for (c) $f_{\mathrm{rep}}=100\mathrm{kHz}$, and (d) $f_{\mathrm{rep}}=600\mathrm{kHz}$.

4.2.

Test Series 2: Identifying the Most Efficient Fluence

From literature, it is known that an efficiency maximum occurs at the pulse peak fluence ($F_{\mathrm{eff}}$) which can be simply described by the product of the threshold fluence ($F_{\mathrm{thr}}$) and Euler’s number.⁴ The experiments are varied in the interval from $3\times F_{\mathrm{thr}}$ to $13\times F_{\mathrm{thr}}$ to map the theoretical efficiency maximum at a factor of $e^2\approx 7.39$ in the center of the fluence interval to be investigated. An important material and model property for laser material processing is the effective penetration depth of the laser radiation into the workpiece. The effective penetration depth can be determined from the values of $F_{\mathrm{thr}}$, the fluence used and the ablation depth per pulse, e.g. Eq. (5).

In Fig. 10 the mean value of the ablation volume per pulse and pulse energy per fluence (according to Neuenschwander) and the mean value of the ablation depth per fluence are plotted for the structured squares with 566 LpF. The average ablation depth increases almost linearly with increasing fluence (red). The ablation efficiency increases with increasing fluence (blue) in the range from 0 to $0.5\mathrm{J}/\mathrm{c}{\mathrm{m}}^2$. The efficiency maximum can be confirmed at a factor of $e^2\times F_{\mathrm{thr}}$ if the ablation threshold is determined visually. The effective penetration depth is calculated using the measurement points shown in Fig. 10 and the previously mentioned simulation of the USP machining process.¹ The effective penetration depth can be determined by the known ablation depth and the threshold fluence by using the simulation model¹ or the virtual volume method. The virtual volume method will be described in Sec. 4.3. Using the determined ablation threshold the simulation calculates the ablation structure for different penetration depths. By comparison with the experimental results, the penetration depth can be determined as function of the fluence. The resulting effective penetration depth in fluence range (0 to $0.5\mathrm{J}/\mathrm{c}{\mathrm{m}}^2$) lies in the interval of $5.7\mathrm{nm}<{\delta }_{\mathrm{eff}}<11.2\mathrm{nm}$ (Fig. 10).

Fig. 10

Hermann and Neuenschwander graphs for different laser structured square cross section (like shown in Fig. 7) with 566 laser pulses per focal area. For the statistical purposes, six squares each with the same process parameters have been produced and measured.

Fig. 11

Ablation depth and Neuenschwander plots for squares with 45 laser pulses per focal area at $f_{\mathrm{rep}}$ 100 kHz.

4.3.

Test Series 3: Identifying the Impact of Higher Fluences

The objective is to conduct the characterization of the material properties of stainless steel at higher fluences. Therefore, fluences from 1.76 to $24.8\mathrm{J}/\mathrm{c}{\mathrm{m}}^2$ are investigated. It is intended to generate an understanding of the influence of comparatively high fluences for high-precision micro and nano structuring. To obtain meaningful microscopy images, the number of laser pulses used will be reduced, since measuring ablation depths $>30\mu \mathrm{m}$ for $200\times 200\mu \mathrm{m}$ cavities with the VHX-5000 digital microscope can lead to under-exposure of the ablated area and thus to measurement inaccuracies. Squares are structured with an applied number of laser pulses per focal area (LpF) in an interval of 20 to 200.

The average ablation depth increases almost linearly with increasing fluence (red). In contrast, the ablation efficiency decreases exponentially with increasing fluence (blue). This suggests that the efficiency maximum is between 0.5 and $1.76\mathrm{J}/\mathrm{c}{\mathrm{m}}^2$. The ablation for higher fluences drops nearly by a factor of 3.

In the following, the surface roughness of the manufactured cavities is investigated and presented as a function of fluence. At this point, it can also be seen that from about $12\mathrm{J}/\mathrm{c}{\mathrm{m}}^2$ (Fig. 11), the surface roughness due to USP processing becomes worse than the initial surface roughness of the stainless steel foil. Measurement point 4, shown in Fig. 12(a), is the first measurement point in Fig. 12(b) to show the noticeable trend where the determined standard deviation significantly exceeds the waviness of the original material.

Fig. 12

(a) Mean ablation depth for 113 applied laser pulses per focal area in relation to the applied fluence. (b) Standard deviation of the ablation depth of six structured squares each with 113 applied laser pulses per focal area in relation to the line roughness of 320 nm ($\pm 160\mathrm{nm}$). LSM measurement of the line roughness of the initial surface of the workpiece used. (c) The absolute difference is $0.325\mu \mathrm{m}$ and can be specified as $+/-0.160\mu \mathrm{m}$.

Figure 12(a) shows the course of the ablated depth-averaged from six square patternings with 113 LpF over the fluence. Figure 12(b) shows that the standard deviations of these measured average ablation depths are greater than the determined line roughness of 325 nm ($\pm 160\mathrm{nm}$) shown in Fig. 12(c). Due to the use of high fluences, temperature-related influences during machining cannot be excluded. The formation of CLPs is made possible by high fluences. CLPs are demonstrably caused by excessive thermal stress on the component during machining.⁸ Due to temperature-related influences, the theoretically determined effective penetration depth may deviate from the one obtained from test series 2.

Using the ablation cross-sections of the machined squares, the effective penetration depth is determined mathematically based on the depth present at the center of the structure. For a fluence of up to $1\mathrm{J}/\mathrm{c}{\mathrm{m}}^2$, the effective penetration depth is circa $5.7\mathrm{nm}<{\delta }_{\mathrm{eff}}<11.2\mathrm{nm}$ and for a fluence of about 2 to $25\mathrm{J}/\mathrm{c}{\mathrm{m}}^2$ it is $8\mathrm{nm}<{\delta }_{\mathrm{eff}}<19.4\mathrm{nm}$. The ablation efficiency maximum is approximately located at a fluence of $0.5\mathrm{J}/{\mathrm{cm}}^2$ [Fig. 13(b)]. The relationship between the fluence and the threshold fluence, known from the literature, is described by Eq. (6). With the determined threshold fluence of $65.6\mathrm{mJ}/\mathrm{c}{\mathrm{m}}^2$, the ablation efficiency maximum is calculated to be $0.485\mathrm{J}/\mathrm{c}{\mathrm{m}}^2$. This almost agrees with the result from test series 2 for a fluence of $0.5\mathrm{J}/\mathrm{c}{\mathrm{m}}^2$. The asymptotic course of the ablation efficiency for a fluence of up to $25\mathrm{J}/\mathrm{c}{\mathrm{m}}^2$ is shown in Fig. 13(b). The mean depth of the cross section can be used to define a virtual volume of material ablation [Fig. 13(a)]. Multiplying the mean ablation depth by a virtual two-dimensional area of any size gives a virtual ablation volume of the square structuring. The number of laser pulses applied to the total virtual ablation volume can be calculated from the feed rate, repetition rate, track spacing, and edge lengths of the virtual area under consideration. Subsequently, the required virtual ablation volume per laser pulse and pulse energy can be determined. In addition, the mean value of the virtual ablation volume and its standard deviation are computed. In this work, the collected mean values and standard deviations were composed of the measurement data of six structured squares each with processing parameters kept constant

Fig. 13

Graphical approach to illustrate the procedure used to determine the ablation efficiency. (a) The approach is newly introduced and will be named as a “model of the virtual volumes” based on the presented procedure of this work. (b) Cumulative course of the ablation efficiency over the investigated fluence interval from 0 to $25\mathrm{J}/\mathrm{c}{\mathrm{m}}^2$.

4.4.

Test Series 4: Determination of the Absorption Coefficient

In test series 4, the absorption coefficient of the stainless steel workpiece will be determined. The optical properties can be determined by comparison with simulation using Fresnel’s equations to describe angle-dependent absorption. Here, structured squares with a specified edge length of $50\mu \mathrm{m}$ are machined and measured. A linearly polarized laser beam is now used to determine the absorption dependence. Figure 14(a) shows how a $\lambda /2$ plate varies the polarization by rotation and how this affects the resulting geometry of the ablated structure. Figure 14(b) and 14(c) show an SEM image and a simulated 3D model of the ablation of a square structure. On the workpiece surface, the machining strategy is identical in both cases only the linear polarization direction is changed by $\sim 45\mathrm{deg}$ perpendicular to the incident laser beam. In the SEM and simulation images, it can be seen that the perpendicular edges of the “square” have different lengths. Since perpendicular and parallel polarization produce different degrees of absorption at incident angles between 0 deg and 90 deg and the edges of the squares show a taper, the length and width of the squares change. They change with the set angle of rotation of the $\lambda /2$ plate which affects the orientation of the linear polarization [compare Fig. 14(a)]. The workpiece is more ablated in the direction of the $p$-polarization (compare Fig. 4). This is shown in Figs. 14(b) and 14(c) for two different orientations of the polarization.

Fig. 14

(a) Influence of the angle of rotation of the $\lambda /2$-plate on the degree of ablation of the workpiece with a square structure. (b) and (c) Two different 3D model of square structure and SEM images to prove the influence of the polarization direction.

From the aforementioned change in length and width, the angle-dependent absorption coefficient of the stainless steel workpiece can be determined for a given rotation angle of the $\lambda /2$ plate. The green dashed areas in Fig. 14(a) represent the geometries that are scanned on the workpiece surface with the scanning system. The black areas represent the geometries that are generated due to different degrees of absorption on the workpiece surface. As the angle of rotation of the $\lambda /2$ plate changes and thus the orientation of the linear polarization of the laser beam the structured geometry changes in width and length. Previously used material thickness of $200\mu \mathrm{m}$ proves to be unsuitable for the next step of this test series. So a workpiece with a thickness of $25\mu \mathrm{m}$ of the same material is used. To prevent measurement inaccuracies, several squares with the same polarization orientation are patterned through a $25\mu \mathrm{m}$ stainless steel foil. A rotation of the $\lambda /2$ plate by 10 deg corresponds to an optical rotation of 20 deg. To realize an optical rotation of 180 deg, the polarization orientations of the $\lambda /2$ plate are divided by steps of 10 deg per step in a range from 0 deg to 90 deg. Diffraction effects can occur during microscoping, which are manifested by blurring at the edges of the surface patterning to be measured. To avoid diffraction effects during microscoping, the square tapers on the back of the specimen are measured with incident top light. The taper angle of the square edges depends on the fluence used, therefore, two different fluences of 1.8 and $4.2\mathrm{J}/\mathrm{c}{\mathrm{m}}^2$ will be investigated.

For the purpose of this study, taper is only of secondary importance. In the following, the length and width differences are evaluated. Figure 15 shows the length and width variation at different rotation angles of the $\lambda /2$ plate and the maximum length and width difference in each case. In Fig. 15(a), the course of the length and width change for $1.8\mathrm{J}/\mathrm{c}{\mathrm{m}}^2$ and Fig. 15(a) for $4.2\mathrm{J}/\mathrm{c}{\mathrm{m}}^2$. From the amplitudes of the respective plots, conclusions can be drawn about the absorption coefficient of the combination of workpiece and USP laser used. In addition, it can be observed that the squares are more strongly ablated in length (blue line) than in width (red line) by about $1.5\mu \mathrm{m}$. This may be due to an elliptical raw beam or an alignment error of the laser beam. The half-length or half-width differences are defined as amplitudes. Taking into account the standard deviation for both plots the amplitudes are $\sim 2.7\pm 0.2\mu \mathrm{m}$ big.

Fig. 15

Influence of the rotation angle of the $\lambda /2$-plate on the length and width of a structured square at a fluence of (a) $1.8\mathrm{J}/\mathrm{c}{\mathrm{m}}^2$ and (b) $4.2\mathrm{J}/\mathrm{c}{\mathrm{m}}^2$.

With the amplitude of the width or length change depending on the angle of rotation of the $\lambda /2$ plate the absorption coefficient at perpendicular angle of incidence (0 deg) can be calculated to $\sim 0.7$. This is shown in Fig. 16. From the aforementioned change in length and width (compare Fig. 15), the angle-dependent absorption coefficient of the stainless steel workpiece can be determined for a given rotation angle of the $\lambda /2$ plate.

Fig. 16

Angle of incidence-dependent absorption coefficient of stainless steel.

4.5.

Optimization of the Ultrashort Pulsed Ablation Process Using a Simulation Model

This chapter is brief, as it is already described in more detail in the previous paper.¹⁷ The presented procedure can be used to determine the material properties of metals such as stainless steel (material number: 1.4301) for application in USP laser surface structuring. The results from test series 1 to 4 can be used to calibrate a simulation model.¹

Thus, a time-efficient machining process can be determined in advance by presimulation. With the help of the three material properties determined in this work (threshold fluence, effective penetration depth, and absorption coefficient), the ablation behavior of metallic workpieces during USP machining can be simulated. The machining parameters relevant for the material ablation behavior (repetition rate, feed rate, path planning, pulse energy, focus diameter, and wavelength) depend on the combination of the workpiece, machining system, and USP laser used and are transferred to the simulation. So the USP machining process can be simulated and the simulated material ablation result can be visualized. Figure 17 shows an exemplary comparison of the real USP machining process with those from the calibrated simulation. The ablation result by USP machining of the workpiece is shown in the left image of Fig. 17 by means of a microscope image with a colored height scale. The right image of Fig. 17 shows the simulated result.

Fig. 17

Comparison of an ablation result in USP machining with a simulation.