Non-Diffractive Bessel Beams for Ultrafast Laser Scanning Platform and Proof-Of-Concept Side-Wall Polishing of Additively Manufactured Parts

2.1. Bessel Beam and Its Self-Healing Property under Particle Obstruction

An ideal zeroth-order Bessel beam is defined as the beam whose electric field (E) is explicitly described by the zeroth-order Bessel function of the first kind ($J_0$) [37,38]:

where $A_0$ is the amplitude of the electric field; $k_z$ and $k_r$ are longitudinal and radial wavevectors, with $k=\sqrt{k_z^2+k_r^2}=2\pi /\lambda$ is the wavenumber in air at the wavelength $\lambda$; z, r, and $\varphi$ are the longitudinal, radial, and azimuthal components, respectively.

The beam transversally appears in the form of a maximum intensity central lobe, surrounded by an infinite series of concentric rings with lower intensity. Its formation is considered to be a result of the interference of plane waves whose wavevectors belong to a conical surface. Experimental Bessel beams carry a definite amount of energy due to the finite extension of optical systems and use of practical beams.

In practice, the generation of Bessel beams can be realised by several methods: annular slit method [39], SLM based method [40,41], optical fibers [42,43], and axicons [28,29,30,44].

In our work, a high quality axicon or conical lens is chosen as an efficient way for generating the so-called Bessel–Gaussian (BG) beam. When collimated Gaussian laser beams pass though an axicon with a refractive index n and a base angle $\alpha$, they deviate with an angle $\theta =arcsin(nsin(\alpha \left)\right)-\alpha$ to the optical axis (Figure 1a). The conical intersection of wavefronts upon propagating through the axicon creates an interference pattern which is characterised as the zeroth-order Bessel beam with the conical half-angle $\theta$. The transverse profile of the beam comprises a bright central core that is surrounded by concentric rings (Figure 1a). The full width/diameter of the central lobe (2${\omega }_b$) can be determined by the first zeros of the Bessel function [37]:

The beam central lobe has the highest intensity and it does not spread within the non-diffractive propagation (Bessel zone). The length of the Bessel zone $z_b$ can be approximated from the wavevectors of the Bessel beam propagating in the conical pattern [45]:

where $D_0$ is the diameter of the incident Gaussian beam. At any specific transverse plane within the Bessel zone, the energy density in the central lobe will originate from a corresponding ring in the initial Gaussian distribution that is refracted by the axicon on this area. The peak fluence of the central lobe ($F_b$) can be approximated by its energy $(2{\omega }_b/D_0)E_{in}$ distributed over the surface area $\pi {\omega }_b^2$ [29]:

where $E_{in}$ is the Gaussian input energy. The peak fluence can be expressed as a function of the half conical angle $\theta$:

In comparison to the conventional Gaussian beam which is generated by a focusing lens (Figure 1b), the Bessel beam offers a significantly longer (typically one order of magnitude longer) depth of focus than the Gaussian counter part with a similar beam diameter (2${\omega }_g\sim 2{\omega }_b$). In the Gaussian setup, the elongation of the depth of focus ($z_g$ = 2 × Rayleigh range) would require lenses with long focal length, and incident beams with small beam diameter. This classic configuration has a limited extent and unwantedly makes the focused beam having a large beam diameter, which, in turn, limit applications on processing objects with small features. In this matter, the Bessel configuration could ideally offer the beam with a long depth of focus, while maintaining a small beam diameter.

The Bessel self-reconstruction property has not been reported in the harsh and dusty AM context, despite it being demonstrated in various studies [46,47,48]. In order to demonstrate the interest of the unique Bessel self-reconstruction property for laser processing in the AM environment, the propagation of beams through an obstruction created by a cloud of metallic particles was investigated. The experiment was conducted by a beam-profiling setup as illustrated in Figure 1c. The metallic particles with the size ranging between 5 and 45 $\mathsf{\mu }$m were immobilised on a glass slide and covered ∼50% of its transmissive window (Figure 1c inset). The obstruction resembles the SLM manufacturing environment in which the presence of suspending metallic particles is inevitable. The beam transverse profiles after passing through the particles-immobilised glass slide (obstacle) were collectively recorded by the imaging system, which consists of an objective 50x, a lens f-100 mm and a CCD camera. The obstacle was placed at different positions ($\Delta$z) with respect to a starting point (the reference plane) of the focused beams. The profiles of both Bessel and Gaussian beams were studied under the same obstructed conditions for a fair comparison.

In the case of Bessel configuration, the Bessel beam was initially generated by focusing an incident pulsed laser beam (1 kHz, 200 fs, 800 nm) with a diameter of 4 mm through an axicon with $\alpha =5^{\circ }$. The generated beam was further demagnified through a telescopic afocal arrangement (lens1: 100 mm and lens2: 75 mm); giving a better adjustment of the Bessel beam parameters, i.e., a half conical angle $\theta$ = $3^{\circ }$, a central lobe 2${\omega }_b$ = 11 $\mathsf{\mu }$m, and a Bessel length $z_b$ = 34 mm (Figure 2a). The choice of axicon and lenses was made for the purpose of producing the Bessel beam with the Bessel length staying within our measureable tool (<50 mm), and a beam diameter large enough for comparison with a Gaussian counter part. Transverse profiles of the laser beams were individually captured at different positions with respect to the reference plane. Therefore, it is possible to construct 3D images of the beam profile by stacking those individual transverse images together. The stacked profile of Bessel beam shows a bright central lobe and surrounding rings. The central lobe diameter seems to exhibit a negligibly small variation (below 4 %) along the Bessel length, which could be attributed to a small divergence of the incident Gaussian beam as well as the imperfect tip of the conical lens [49]. The Bessel beam quality can be improved while using a spatial filter and/or using reflective axicon elements.

The Bessel self-healing behaviour is evidently confirmed by the reconstructed beam profile presented in Figure 2b, in comparison with the original profile without obstacle in Figure 2a. It is noted that the experiment was focused on the self-reconstruction of the beam central lobe. In the particular case, when the obstacle was placed at $\Delta$z = −0.5 mm before the reference plane, the Bessel beam did not suffer from the obstruction. Figure 2c shows longitudinal and transverse cross-section of the original Bessel beam vs its self-reconstructed profile. The self-reconstructed beam sustained a good profile, except a small decrease of <10 % in its peak intensity along the central region (Figure 2c). A closer look to the evolution of the self-reconstruction ($\Delta$z = 2 mm) is additionally illustrated in Figure 3a, where the obstruction clearly occurred at the position 2 mm (Inset shows the image with an additional background light for better visualisation). The beam started to reconstruct itself at the position 2.2 mm, which is just 0.2 mm after the obstruction. The beam reconstruction mechanism is described in a simplified schematic (Figure 3b), where the length of the beam disrupted shadow is approximately the distance to which the beam starts reconstructing. The length can be geometrically estimated, depending on the beam conical angle, size, and location of the obstacle [37]. Particularly, in the presence of 4–45 $\mathsf{\mu }$m particles, the shadow length is approximated within a range between 0.2 mm and 1 mm. Similar self-reconstructed results were observed when the obstacle was placed at $\Delta$z = −6, −3, −2, −1, −0.5, 0, 0.5, 1, 2, 3, and 6 mm planes with respect to the reference plane of the Bessel beam (data not shown for the sake of brevity).

For comparison, the Gaussian beam was separately evaluated in the same particle obstruction, using an objective 4x, NA 0.1, which gives the focused beam diameter 2${\omega }_g$ = 11 $\mathsf{\mu }$m relatively similar to its theoretical calculation, and comparable with the central lobe diameter of the presented Bessel beam. A small aberration (ring shadow) can be seen in the Gaussian beam profile (Figure 4a). This is a common effect that is caused by the finite aperture of the incident beam. The Gaussian beam is characterised with a short depth of focus/confocal region $z_g$ = 0.24 mm, measured where the beam intensity drops by a half. This measured value is slightly smaller that its theoretical calculation, which is attributed to the laser beam quality factor M${}^2\approx$ 1.33. The short confocal region of the Gaussian beam evidently exhibits its limit over the long non-diffractive Bessel length $z_b$ = 34 mm. Concerning the beam profile after passing through the obstacle (particularly placed at $\Delta$z = −0.5 mm), the result shows a distorted form of the beam (Figure 4b). The distorted beam experienced a large drop of its intensity down to ∼20% (Figure 4c). Similar distortions were recorded when the obstacle was placed at $\Delta$z = −6, −1, −0.5, and 0 mm with respect to the reference plane of the Gaussian beam (data not shown for the sake of brevity).

The experimental results of both Bessel and Gaussian beams were in a good agreement with numerical simulation (see Appendix: Figure A1 and Figure A2). The successfully demonstrated advantages of the Bessel beam properties open great potential for the Bessel configuration to be applied in large-scale processing.

2.2. Bessel Beam Scanning Platform

The previous demonstration of the Bessel beam for its beneficial diffraction-free depth of focus and self-reconstruction property, along with its efficiency for surface ablation [50], have drawn the attention for its adaptation into a large-scale laser processing platform, i.e., a scanner. Despite the Bessel beam-scanner integration being demonstrated for microscopy [51,52], coupling of a high power Bessel beam to a large-scale scanner for machining has not yet been done. In this approach, the Bessel beam scanning platform was realised by combining an axicon with a telescopic afocal arrangement in which one of the lenses, i.e., lens2 was a f-theta lens of a Galvano scanner (Figure 5). The setup was additionally equipped with a telescope which helps tuning the incident beam size, and accordingly adjusting the Bessel length. The particular axicon was used with a base angle $\alpha$ = $5^{\circ }$, in combination with a 4 mm diameter incident beam, resulting in the initial Bessel beam with a half conical angle $\theta$ = ${0.25}^{\circ }$, a central core diameter 2${\omega }_b$ = 102 $\mathsf{\mu }$m, and a Bessel length $z_b$ = 458 mm. After demagnification from the telescopic system: the lens1 F1 = 350 mm and the f-theta lens F2 = 88 mm, the final Bessel beam was characterised with $\theta$ = $1^{\circ }$, 2${\omega }_b$ = 26 $\mathsf{\mu }$m, and $z_b$ = 29 mm. It is noted that the choice of the axicon and lenses was taken when considering the production of a beam central lobe diameter comparable with its Gaussian counter part, and a well fit of the intermediate incoming Bessel ring to the entrance aperture (3 mm diameter) of the scanner head. The size of the intermediate Bessel ring is critical to adapt in most of the cases, which requires a combination of an axicon to telescopic afocal systems, particularly when the beam encounters a small aperture.

The beam quality is transversally characterised within the scan field of 35 × 35 mm${}^2$) in order to examine the stability of the Bessel beam formation through the scanner. The scanner head allows for the beam to move to different zones from the centre to the furthest corner of the scan field (Figure 5 red point) where its profile is captured by the imaging beam profiler.

The resulted profile of the Bessel beam through the scanner, along with its central lobe diameter are illustrated as a function of the distance from the centre to corner of the scan field (Figure 6). Quantitatively, the beam appears to have a small variation in its lobe diameter along the field extent (Figure 6 Square-symbol graph). This is in a good agreement with values from the datasheet provided for a classic Gaussian configuration (Figure 6 Circle-symbol graph). In the datasheet graph, the diameter variation was adapted to the percentage unit, since its original data were provided for a different beam size. Concerning the beam spot distribution or the beam symmetry over the scan field, little degradation of the profile was observed at the furthest extent (25 mm from the scan field centre). The slight shape distortion of the beam is related to the telecentricity of the F-theta lens, which similarly occurs to the Gaussian configuration. The results were well in line with another independent experiment on a Gaussian beam profile while using the same f-theta lens conducted on the same scanner. Bessel and Gaussian beams both resulted in the same propagation axis, regardless of the position of the beams within the scan field.

It is worth noting that the given Bessel beam has the central lobe diameter (26 $\mathsf{\mu }$m) comparable with a Gaussian beam diameter (27 $\mathsf{\mu }$m) while using the same f-theta lens, whereas its depth of focus is proven to be >1 order of magnitude longer than the Gaussian counter part (29 mm as compared to 2 mm). By optimising the choice of the axicons and lenses, the platform can be further adjusted in order to produce the beam with a smaller diameter while maintaining its beneficial long depth of focus. There have been reports of taper-like shapes being produced during ultrafast laser processing, which limits the surface enhancement of the processed material. Therefore, the smaller-diameter beam is desirable for minimising its taper effect. While this is challenging for a classic Gaussian beam setup, the Bessel beam configuration can come in as a better alternative.

2.3. Side-Wall Polishing with Bessel Beam

As a proof of concept, the Bessel beam scanning platform was further used in order to showcase the Bessel beam advanced capacity for side-wall polishing on an additively as-fabricated workpiece (Figure 7). The experiment was performed with the laser Legend Elite from Coherent Inc, using optimised parameters: linear polarisation, repetition rate 2 kHz, pulse duration 100 fs, and peak fluence ∼1 J/cm${}^2$. These optimised laser conditions were chosen from [50], towards producing optimal ablation efficiency and effective roughness improvement of the ablated surface.

The dynamic ablation was processed on the sample edge by setting the scanner to move in raster scanning trajectories (Figure 7a). The laser path is translated in the x-axis direction, and consecutively shifted in the y-axis direction. The pulse-to-pulse overlap in x-axis depends on the scanning speed, the beam spot size, and repetition rate of the laser, while the y-axis overlap depends on the spacing shift between the consecutive scanning lines. In this demonstration, the overlaps in x-axis and y-axis were kept the same at 97%, towards the optimisation of the laser-polishing quality. It is noted that the laser translation was started from a position outside of the sample edge, and then y-shifted toward the sample bulk. After 20 iterative scans, the ablated and polished part at the edge of the LPBF-fabricated sample was qualitatively characterised by a microscope, showing evidence of visually reflective surface (Figure 7b). The polished region appears to split the white light illumination into red green blue (RGB) color (the blue was shown in the image). It is a result of the reflection grating by sub-micro grooves which were formed under raster scanning of the laser beam. For a quantitative characterisation, the laser-polished part is further measured for its side-wall roughness (Ra). The result reveals a roughness reduction of the LPBF-fabricated sample from its original side-wall roughness Ra of 10 $\mathsf{\mu }$m to Ra of 1 $\mathsf{\mu }$m (Figure 7c).

It can be noticed that the 0.3 mm polished depth was achieved (Figure 7c), but it can be extended following longer scanning time/cycles. However, achieving a long-depth polishing is not the scope of the paper. It is also pertinent to mention that the Rayleigh length of the Gaussian beam using the same F-theta lens is 1.3 mm, which is above 0.3 mm. Thereby, the polishing on 0.3 mm depth is also possible with the ex-situ Gaussian configuration. However, in the harsh AM environment, the Gaussian beam is much more sensitive to obstacles (inherent suspending particles), whereas the Bessel beam can self-reconstruct.

The Bessel beam scanning platform effectively demonstrated its proof-of-concept side-wall polishing and additionally promises its potential for re-dimensioning over-sized AM parts. It lays a foundation for the ultimate use of this beam engineering solution in a hybrid AM machine [16]. The hybrid AM machining is an inline process in which each AM layer can be immediately treated, prior to the next AM layer to be built, with a contour of ultrafast Bessel beam scanning. It allows for direct dimension controlling and polishing of the current AM layer’s sidewall. Therefore, the resulting AM parts do not require additional surface post-processing steps.