*2.1. Opto-Mechanical Set-Up*

The "POLAR" laser polishing machine (Figure 1a) is a prototype and was set up by Fraunhofer ILT (Aachen, Germany) and Maschinenfabrik Arnold (Ravensburg, Germany) as part of a publicly funded project. The mechanical basis for this machine was a 5-axis

milling center C600U from Hermle (Gosheim, Germany), in which an optical set-up for laser materials processing was integrated (Figure 1b).

**Figure 1.** (**a**) Photo of processing chamber and optics box of the POLAR machine, and (**b**) schematic of the optical set-up and beam path.

A diode-pumped Yb:YAG disk laser (TruMicro 7051, Trumpf GmbH, Ditzingen, Germany) was used in the POLAR machine for the experimental investigation. The maximum average laser power of the TruMicro 7051 is approximately *PL*,*max*,*TM* = 550 W at *λem* = 1030 nm for pulse repetitions rates between *fP* = 5 and 20 kHz. In the pulsed mode, Q-Switch controlled laser pulses were generated with pulse durations ranging from *tP* = 1 μs to approximately 3 μs, which strongly depends on laser power. The square laser beam results from an optical transport fiber with a square, step-index fiber core and edge lengths of *dfiber* = 100 μm, which was projected onto the work piece. Different laser beam dimensions were achieved by means of a zoom telescope, which offers a 20 mm beam aperture and enables continuous magnification in the range from approximately 0.2–1.8. A laser scanning system from Scanlab AG (Puchheim, Germany) consisting of a VarioScan 30, a HurryScan 25, and an f-theta objective (focal length 420 mm) was used for fast laser beam deflection. Additionally, a laser power attenuator was part of the optical set-up, so that the TruMicro7051 was operated at maximum laser power and the laser power attenuator was used to control the laser power on the workpiece. This was done to maximize the pulse stability of the laser beam source and achieve a fixed pulse duration of approximately *tP* = 1.2 μs for all laser powers and laser beam sizes. Laser polishing took place in an approximately 200 L process chamber using a closed-loop control to adjust and stabilize the residual oxygen content.

### *2.2. Intensity Distribution and Laser Beam Characteristics*

An optical delivery fiber with a square step-index fiber core (100 μm × 100 μm) was used for beam guidance, delivery, and shaping of the intensity distribution. Using a continuous zoom telescope, three different dimensions of the intensity distribution were realized and measured by a so-called "MicroSpotMonitor" (Primes GmbH, Pfungstadt, Germany). The "LaserDiagnoseSoftware v2.98" (Primes GmbH, Pfungstadt, Germany) (LDS) was used to analyze beam caustic and particularly intensity distribution in the focal plane (Figure 2).

**Figure 2.** Normalized intensity distribution of square laser beams in their focal plane with side lengths of (**a**) 100 μm (Q100), (**b**) 200 μm (Q200), and (**c**) 400 μm (Q400).

Figure 2 shows intensity distributions for three laser beams with a square basis and side lengths of 100 μm, 200 μm, and 400 μm, respectively. In the following, these will be referred to as Q100, Q200, and Q400. Based on 86% energy inclusion, the LDS analysis delivers the following laser beam characteristics for Q100, Q200, and Q400 (Table 1). Furthermore, a square asymmetric super Gaussian distribution was fitted to the measured intensity distribution Equation (1) [49].

$$I(x,y) = I\_0 \cdot \mathcal{e}^{-2\left(\left(\frac{x}{\pi}\right)^M + \left(\frac{y}{\pi}\right)^M\right)^N} = I\_0 \cdot \mathcal{e}^{-2\left(\left(\left(\frac{x}{\pi}\right)^M + \left(\frac{y}{\pi}\right)^M\right)^M\right)^{NM}}.\tag{1}$$


**Table 1.** Tabular overview of laser beam characteristics.

The main characteristics are the beam diameter *a* and the numerical parameters *M* and *N*·*M*. A larger parameter *M* represents an intensity distribution closer to a square shape, while a larger product of *N*·*M* represents an intensity distribution closer to a top-hat shape.
