*4.4. Critical Wavelength/Frequency*

The critical wavelength or critical frequency was almost the same for all laser beam sizes. This underscores the importance of the pulse duration and that the laser beam size is of secondary importance. However, the laser beam dimensions are assumed to be at least twice as large as the critical wavelength. The critical wavelength for Q100 and *F* = 12 J/cm<sup>2</sup> is of special interest since a change to a continuous process is assumed. In a continuous remelting process, melt duration is typically approximated by the interaction time of the laser beam and material [39], which is typically calculated by *tint* = *dL*·*vscan*<sup>−</sup><sup>1</sup> and is approximately *tint* = 0.5 ms for Q100. This is two orders of magnitude larger than the pulse duration (*tP* = 1.2 μs), but the critical wavelength was not significantly increased to more than 80 μm (in comparison to Q200 and Q400). This is a little bit surprising, but in this case, the critical wavelengths are presumably strictly limited by the laser beam dimensions, since no roughness with larger dimensions than the laser beam can effectively be smoothed in cw laser polishing. Additionally, melt pool disturbances due to the partial evaporation and dissolution of chromium carbides counteract a more effective smoothing. This is particularly imminent for Q200 and Q400, where also a continuous remelting process is assumed for high fluences of *F* > 10 J/cm2. This critical wavelength is not only further increased but even reduced, since the process-inherent formation of surface structures, e.g., ripples or boundary lines at the edges of the laser tracks, counteracts the smoothing effect of surface remelting.

### *4.5. Laser Polishing Fluence and Area Rate*

Another important result of this study is that the laser polishing fluence decreases for larger laser beam dimensions (Figure 11a). A possible explanation results from an energetic point of view. At fixed laser fluence, a larger laser-irradiated area absorbs more laser energy in total. An increase in absorbed energy not only results in larger melt pool dimensions but also in longer melt durations. Additionally, temperature gradients in larger melt pools are less steep, and thus, cooling to ambient temperature takes longer. Particularly for multipulse processing, this has several consequences. Firstly, if the temporal distance between subsequent laser pulses is the same as for smaller laser beam dimensions, heat accumulation is more pronounced due to larger energy input per pulse and smaller temperature gradients in the melt pool. Heat accumulation not only leads to a reduction in the threshold fluence for laser ablation [57] but also to a reduction in laser polishing fluence [18]. Secondly, particularly noteworthy at this point is that the overall energy input for a larger laser beam size is reduced. This prevents the global heat accumulation of the whole sample and should reduce thermal effects such as distortion and deformation. Since the laser polishing fluence is reduced and local heat accumulation is increased for larger laser beams, locally induced thermal stresses should also be reduced [63]. Based on the insights of Spranger at al. [64], one could also assume that the very high cooling rates lead to a very fine microstructure in each case; however, this was not particularly investigated in this study.

The results already show that larger laser beam sizes lead to higher area rates without increasing the resulting surface roughness if the number of remelting cycles is kept constant (Figure 11b). In principle, the influence of laser beam dimensions *sL*2, repetition rate *frep*, and number of remelting cycles *n* on an achievable area rate *AR* can be discussed based on Equation (3).

$$A\_R = \frac{s\_L^2 \cdot f\_{\rm rep}}{n};$$

$$\text{with } n = \frac{s\_L^2}{\text{d}x \cdot dy}; \text{ } s\_{L,\text{max}}^2 = \frac{E\_{P,\text{max}}}{\text{F}\_{\rm pvl}}; \text{ } P\_{L,\text{max}} = E\_{P,\text{max}} \cdot f\_{\rm rep,max}$$

The maximum area rate *AR* is the product of the remelted area per pulse (*A* = *sL*2) and the pulse repetition rate *frep* divided by the number of remelting cycles per spot *n* (effectively resulting from pulse and track overlap). Thus, for example, the side length *sL* of a square laser spot has a quadratic effect on the area rate *AR*. However, the required pulse energy *EP* scales almost linearly with the remelted area *A* (*EP* ~ *A*). Increasing the pulse frequency leads to a linear increase in the area rate. Therefore, preferably, the dimensions of the focused laser beam should be maximized if the pulse repetition rate is crucially limited. The maximum laser beam dimensions depend on the available maximum pulse energy *EP,max* and on the laser polishing fluence *Fpol*. In turn, the laser polishing fluence *Fpol* tends to decrease with increasing dimensions of the laser beam (Figure 11a). Furthermore, the maximum pulse frequency depends on the maximum available laser power *PL,max* at maximum pulse energy *EP,max*. Applied specifically to LμP, and taking into account this and other studies on LμP, a reasonably achievable area rate can be estimated for a commercially available laser system. In this work, a spot on the surface was remelted on average approximately *n* = 100 times. However, typically, only approximately *n* = 20 remelting cycles are required to achieve a minimal surface roughness in LμP of steels [18,27]. Using the example of a commercially available laser system (e.g., IPG YLPN-HP *tP* = 120 ns, *PL,max* = 5 kW; *EP,max* = 100 mJ; *frep,max* = 50 kHz), a realistic area rate can be estimated. The selected laser beam source already provides a square fiber cross-section. The maximum pulse energy of approximately *EP,max* = 100 mJ enables a laser focus with an area of *sL*<sup>2</sup> = 20 mm<sup>2</sup> at a required laser polishing fluence of approximately *Fpol* = 5 J/cm2. The maximum pulse frequency of the laser system is 50 kHz, so that a maximum laser power of *PL,max* = 5 kW is available. Thus, considering *n* = 20 remelting cycles per spot, area rates of up to *AR* =3m2/min might be achievable. Area rates of this order of magnitude are already remarkably interesting for industrial applications, even for large-area polishing of flat components.

Larger laser beam dimensions lead to larger area rates with reduced energy input, since the required laser polishing fluence decreases (Figure 11). If high spatial resolution is of secondary importance in LμP and large pulse energies are available, then large area rates are easily achievable. However, a similar effect of decreasing laser polishing fluence was observed for high pulse frequencies [18]. Thus, an increase in pulse frequency also leads to a reduced laser polishing fluence and to a reduction of the overall irradiated laser energy. Which effect outweighs the other cannot be said without further studies, but both ways—increasing single pulse energy and increasing pulse repetition frequency, respectively—are viable ways to significantly increase the area rate in LμP. Since the product of single pulse energy *EP* and pulse frequency *frep* equals the average laser power *PL*, Equation (3) can be boiled down to a simple dependency *AR* ~ *PL,max*, which is valid for many laser-based processes. The area rate in LμP basically scales linearly with the average laser power of the laser beam source. Nonetheless, there are limits to consider regarding the maximum single pulse energy (regarding damage thresholds of optical components etc.), pulse duration (maximum pulse peak power), and maximum pulse repetition frequency (maximum deflection speed of laser scanning systems, etc.).

As a visual conclusion of the discussion, Figure 14 shows the laser-polished surface with the lowest roughness achieved in this study (Figure 14b) compared to the initial surface roughness (Figure 14a). A considerable reduction in surface roughness and a particular increase in gloss are the obvious results displayed in these micrographs.

**Figure 14.** Micrographs of (**a**) initial surface roughness in comparison to (**b**) laser-polished surface with lowest surface roughness (Q400, *F* = 8 J/cm2).
