# Customized flipped quasi-Bessel beams for infrared ultrafast laser drilling through scattering FR4 composite

P Sopeña, N Sanner

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P Sopeña, N Sanner. Customized flipped quasi-Bessel beams for infrared ultrafast laser drilling through scattering FR4 composite. Optics and Laser Technology, 2025, 192, pp.114037. 10.1016/j.optlastec.2025.114037. hal-05326595

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Submitted on 22 Oct 2025

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Full length article

# Customized flipped quasi-Bessel beams for infrared ultrafast laser drilling through scattering FR4 composite

P. Sopeña* ID, N. Sanner ID

Aix-Marseille Université, CNRS, LP3 UMR 7341, 163 Av. Luminy, 13009 Marseille, France

## ARTICLE INFO

### Keywords:

- Laser processing

- Laser drilling

- Bessel beam

- Scattering material

- FR4 fiberglass epoxy

## ABSTRACT

The light-scattering behavior of heterogenous transparent materials impedes the proper propagation of laser beams, affecting the formation of a precise below-surface focal spot and, therefore, their processing with ultrafast laser beams. In this work, the interest of using and customizing non-diffractive Bessel beams as a solution to mitigate in-volume propagation scattering losses during bulk laser processing of a composite material is investigated. For this purpose, we assess the compensation ability on the ultrafast laser drilling performance of holes through a translucent fiberglass epoxy resin (FR4) substrate, a material of interest for printed electronic circuits. Using simple optical elements like axicons and lenses, customized regular and flipped quasi-Bessel beams are generated, which respectively show decreasing or growing on-axis intensity profiles. Their performance to drill through-holes in a 200-µm thick FR4 substrate is systematically investigated using different pulse numbers and energy. The interest of sample-long flipped-profile Bessel beams is shown, obtaining repeatable through-holes between 10 and 95 µm wide, a lower drilling energy threshold, and a reduced heat-affected zone around the holes. These results demonstrate the benefit of adapted beam shaping as a solution to mitigate scattering during laser processing of heterogeneous materials, unveiling a new range of accessible materials and potential applications by ultrafast laser processing.

## 1. Introduction

Ultrafast lasers delivering pulses in the pico- and femtosecond regime are widely employed in laser processing [1,2]. In the case of transparent materials, the high intensity of tightly focused ultrashort pulses allows triggering nonlinear multiphoton absorption, offering both surface and volume processing capabilities when surpassing the modification fluence threshold [3]. This is particularly interesting as it allows to locally process all kinds of materials with high precision and reproducibility. In this context, several demonstrations have been performed such as waveguides in dielectrics [4], optical elements in semiconductors [5], laser welding of transparent materials [6], and 3D-writing of polymers [7], in application fields ranging from electronics to biology [8,9].

Taking a closer look at the materials properties, one realizes that most of the studies are performed on homogeneous materials, where light propagates with minimal scattering, diffraction, or nonlinearities. Therefore, when a beam is focused inside the bulk of the material, a well-defined focal spot is mostly achieved. However, in some ceramic,

polymer, semiconductor or composite materials that exhibit polycrystalline, granular or heterogenous inner structure, it is very unlikely or impossible to obtain a precise focal spot and, in turn, volume modification due to scattering [10]. For instance, this was observed in transmission laser-welding of polycrystalline ceramics [11], where the refractive index mismatch of the embedded pores within the sintered ceramic lead to light scattering, limiting laser welding to depths of < 1 mm.

In such complex media, wavefront shaping solutions have been proved to be efficient for imaging purposes [12]. However, applying the same strategy to laser processing would require to be specifically adapted to each point and material. A more universal and straightforward approach to reduce the detrimental scattering effects would be employing a beam that experiences less diffraction effects as it propagates. A first option could be to use wavelengths in the mid-infrared (IR) and ideally far-IR, which are naturally less prone to suffer from scattering than visible ones. Another solution is to opt for a naturally robust beam shape, like Bessel beams [13]. This type of beam is known to be "non-diffracting", since it exhibits an extended focal region, with a

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: pol.sopena-martinez@univ-amu.fr (P. Sopeña).</footnote>
quasi-constant intensity over a length that exceeds by several orders of magnitude the Rayleigh length of a Gaussian beam. Thanks to their long 'focal zone', they offer the capability of machining ultradeep holes while avoiding translating the workpiece along the laser axis (z). It results in a simple, fast and efficient process, also releasing the constraints on the accuracy/tolerance of positioning of the sample. In the context of processing transparent materials, Bessel beams have unlocked several challenges, amongst which: processing ultradeep high-aspect-ratio channels within one single laser shot [14], cutting centimetric-thick samples without moving longitudinally the workpiece [15], fabricating nanophotonic nanovoid structures inside silica glass [16], or writing of biomimetic antireflective structures on MgF₂ [17].

Additionally, Bessel beams provide the crucial advantage of self-reconstruction after an obstacle on its beam path. This arises from the optical formation mechanism of the beam, which is –unlike Gaussian beams– fundamentally formed by the interference of a set of conical plane waves around the laser axis that distributes uniformly the energy all along the non-diffracting beam length. This has been proven to be efficient for providing quasi-uniform lightning for biological imaging in non-homogeneous media [18] or material processing [19]. For through-processing of complex materials with scattering properties, this specific ability seems highly relevant to deliver and distribute the laser energy along the full material thickness. In this regard, in this work we implement this option as well as full customization of the Bessel beam properties (length and on-axis profile), in order to exploit every laser photon and reduce intensity losses with depth due to scattering.

All machining experiments are performed on the composite material 'flame retardant 4' (FR4), one of the most widely used substrates for printed circuit boards (PCB). The composite structure of FR4, composed of a mesh of micrometric glass fibers embedded in an epoxy resin, both transparent in the visible and near-IR spectrum, represents a highly scattering and available material with a translucent aspect, which is ideal to test the beam performance to mitigate through-material scattering and to machine. Among the different laser processing possibilities, this study concentrates on the drilling of FR4, as it is one of the essential processes to increase integration in PCBs by creating multilevel interconnects [20]. Traditionally, among the possible drilling methods, mechanical drilling has been employed, as taper-free 150-µm diameter holes can be routinely produced [21,22]. However, the 100-µm drill bits wear out after ~ 800 repetitions and its positioning exhibits a 25 µm lateral tolerance. Alternatively, laser drilling in a multi-shot percussion modality has led to repeatable holes with controlled depth produced without contact and with diameters around 50 µm. For over two decades, nanosecond UV and CO₂ laser sources with Gaussian or top-hat beam profiles have been traditionally employed, since they are opaque to FR4, resulting in repeatable machining of holes with different depths and diameters down to a few tenths of micrometers in a percussion modality [23–25]. More recently, the appearance of commercial ultra-short laser sources has allowed exploiting the reduced thermal effects of femtosecond pulses, finding similar hole sizes but minimal-taper holes with very clean edges [26,27]. Lately, the extremely high repetition rates in the MHz, have already shown some improvements for laser drilling [28], and GHz-bursts are expected to further improve the drilling quality as has been observed in dielectrics [29]. Additionally, alternative studies have considered drilling by plasmas produced by air filamentation, which could provide enhanced results for PCB machining, but these are less stable and robust than beams in linear propagation conditions [30,31]. Nonetheless, none of the studies have focused on exploiting the high aspect ratios and non-diffractive properties of Bessel beams for PCB drilling. It was only recently that Marx et al. employed a 800-nm 110-fs Bessel beam to engrave trenches and drill holes on a copper-covered FR4 substrate, finding a penetration depth of 80 µm and substantial taper due to the narrow core and wider side lobes [32].

In this work, the non-diffractive self-healing properties of customized Bessel beams to compensate scattering and drill through the composite material FR4 are evaluated. First, we calculate, produce and

characterize three Bessel-like beams with different core sizes, lengths, and on-axis distributions by employing static optics. Then, to test the performance of the produced beams for volume modification, several holes through the FR4 substrate are machined by systematically varying the pulse number and pulse energy. With this, we show that the length of the Bessel beam should be optimally adjusted to match the sample thickness. Moreover, since scattering inevitably causes increasing intensity losses with depth, extra-shaping of the on-axis Bessel beam into a smoothly increasing intensity profile is demonstrated as a solution to deliver more energy at larger depths. Finally, in the best-found conditions, a repeatability study is carried out. A higher control of the hole quality and diameter is found for the flipped Bessel beam with respect to the other ones, which supports the use of dedicated beam-shaping and non-diffractive beams for laser processing of scattering media.

## 2. Experimental setup

The experimental setup is schematically represented in Fig. 1. It consists of a laser source (Pharos, Light Conversion) delivering linearly polarized < 200-fs pulses at a wavelength of 1030 nm, maximum pulse energy of 500 µJ, repetition rate of 10 kHz, and output spot size of 1.4 mm (full width at half maximum, FWHM) at a TEM₀₀ mode (M² < 1.3). Straight from the laser source output, the energy is controlled by a halfwave plate (λ/2) and polarizer (pol.). Immediately after, the beam passes through a telescope (F1, F2) to increase the beam size and control the Bessel beam length [33]. The magnification M = -F2/F1 is 1.5 times for the Bessel beams (F1 = -50 mm, F2 = 75 mm), whereas it is three times for the flipped Bessel beam (F1 = -50 mm, F2 = 150 mm). The magnified beam is directed to the axicon. Two axicons with base angles of 1° and 2° are employed (Thorlabs AX251-B and AX252-B) resulting in Bessel beams of around 350 and 130 mm in length, respectively. To decrease the beam dimensions, a 4-f configuration is used. The middle lens (F4 = 200 mm) is positioned in such a way to relay the highest intensity point of the beam to the microscope objective pupil (20x, NA = 0.4, Mitutoyo M Plan APO NIR). This results in a demagnification factor of 20. Finally, the beam is focused on the sample. Additionally, to further shape the Bessel beam on-axis profile, a converging lens (F3 = 300 mm) is placed in front of the axicon, resulting in an axicon-lens doublet. All pulse energy values are measured before the microscope objective, but the given value corresponds to the energy at the focus considering the microscope transmission factor.

The processed sample, mounted at the focal plane on XYZ motorized stages, is a commercial 200-µm thick FR4 substrate without any copper film (RS Pro Epoxy Glass FR-4, 203–5180). As can be observed from the cross-section image and schematic illustration in Fig. 1, it consists of a mesh of 6–9 µm thick glass fibers embedded in transparent epoxy resin, with approximate refractive indices of 1.50 and 1.58, respectively [34]. This refractive index difference alongside some embedded air bubbles defects resulting from its fabrication lead to its translucent appearance (top-right image). The fiber bundles direction, with a pitch of 420 and 455 µm along the x-y axes, are visible at bare eye. Unlike common green PCB substrates, this FR4 sheet is transparent to visible light, with a measured total transmittance of 84 % at 1030 nm. Nonetheless, it exhibits strong scattering with only 20 % direct transmission (measured with an integrating sphere in a Shimadzu UV-2600 spectrophotometer).

For imaging of the sample surface and positioning of the sample with respect to the laser beam plane, an in-situ reflection microscope is used. It is composed of the same focusing microscope objective, a tube lens (TL, 200 mm), a CCD camera, and a halogen lamp for illumination. A beam splitter (BS) and dichroic mirror (DM) are inserted in the beam path to guide the light to the camera.

The Bessel beams produced after the microscope objective are characterized by another custom microscopy system (50x, NA = 0.42, Mitutoyo M Plan Apo NIR microscope objective and 200 mm tube lens) coupled to a CMOS camera (Thorlabs CS165MU), not represented on Fig. 1. The reconstruction is performed by scanning the microscope
<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Schematic representation of the employed experimental setup consisting of the near-IR femtosecond source, halfwave plate (λ/2), polarizer (Pol.), telescope (F1, F2), dielectric mirrors (M1, M2), axicon and lens (F3, optional) doublet, imaging lens (F4), microscope objective, and sample (FR4). A custom imaging system is employed to visualize the sample surface. It comprises a CCD camera, tube lens (TL), beam splitter (BS), dichroic mirror (DM), and halogen lamp. The two inset images show the heterogeneous scattering structure of FR4 with fiberglass embedded in epoxy resin (bottom right scheme).</figcaption></figure>

system mounted on a motorized translation stage along the optical axis with step sizes of 10 µm.

The samples are analyzed by optical (VHX-7000, Keyence) and
confocal (VK-X3050, Keyence) microscopy. Scanning electron micro-
scopy (SEM, JEOL JSM-6390) and energy-dispersive X-ray spectroscopy
(EDX) are also performed.

3. Results

3.1. *Generation of customized non-diffractive beams*

With the idea to reduce the scattering propagation effects of het-
erogeneous transparent materials and test their machining performance,
several non-diffractive Bessel-like beams with different characteristics
are generated. First, two ‘regular’ Bessel beams are produced by using 1°
and 2° axicons (F3 lens in Fig. 1 is not present). The resulting beams

<figure><img src="image_4.png" /><figcaption>**Fig. 2.** a) Normalized measured intensity maps of the generated regular and flipped Bessel beams: on-axis map (right) and transverse map at the highest intensity of the z axis (left). The $\bar{k}$ wavevector indicates the beam propagation direction. b) Corresponding simulated intensity maps employing the Fresnel propagation transfer function. c) Measured x/y axis profiles and on-axis profiles of the imaged beams in (a). d) Corresponding x/y and on-axis profiles of the simulated beams in (b). The sample thickness is sketched, highlighting the importance of adapting the beam length (the relative position is not representative).</figcaption></figure>
measured after the microscope objective are shown in Fig. 2a (first and second line), where the transverse (x-y plane) and longitudinal on-axis (x-z plane) intensity maps are represented. One observes a very symmetrical Bessel beam in the x-y plane, with a high intensity core surrounded by characteristic concentric rings in both cases. The axial distributions are elongated and slowly decreasing in the wavevector direction ($\vec{k}$), featuring an aspect ratio of 300. The corresponding FWHM of the central peak (at the z coordinate of maximum intensity), the length of the beam at FWHM, and the aspect ratio are shown in Table 1. Some on-axis intensity modulations are visible, most probably due to the imperfect tip of the used axicon [33,35].

In view of using such beams to machine through-holes inside scattering media like FR4, the on-axis profile exhibiting a slow decrease after the intensity peak (Fig. 2c, blue and red curves) may not appear ideal. Indeed, one might expect that despite the self-healing properties of Bessel beams, the inner material structure induces cumulative scattering intensity losses reducing the beam intensity well below the material modification threshold at a shallow depth. In view of mitigating this, a growing on-axis profile would be preferable to allow a higher-intensity core at a deeper depth, expecting to compensate for the scattering losses and allow more ballistic photons to reach deeper. A simple way leading to this inverted on-axial profile is adding a spherical phase to the conical one by placing a converging lens in front of the axicon [36,37]. This is represented by the axicon-lens (F3) doublet in Fig. 1. By this simple method the axial profile can be tuned, obtaining a growing-intensity axial profile. This modified Bessel beam is often named ‘pseudo-’ or ‘quasi-Bessel’ beam in the literature [36]. However, to stress out the inversion of the axial profile, we will name this type of custom beam ‘flipped Bessel’ hereafter.

Adding a lens to the axicon obviously results in smaller beams. So, to design regular Bessel beams and flipped ones with similar characteristics in terms of core size and length (to allow comparative assessment of their machining performance), numerical simulations are performed using a *homemade* code developed in MATLAB® and based on Fresnel propagation [38]. Considering the input beam parameters, Figs. 2b and 2d show the simulated intensity maps and respective profiles. The general trends of experimental and simulated results for axicons of 1° and 2° correspond well (see also Table 1), especially regarding the central core, but slightly longer, which difference can be attributed to a residual divergence resulting from the magnifying telescope (F1 and F2 in Fig. 1) and a minor imbalance of the 4-f system (F4) if the Fourier transform is not applied precisely at the center of the beam. Based on these simulations, combinations of adapted input beam size and axicon-lens doublet are chosen to obtain beams with the same core size and length, but with opposite on-axis profiles. Adjusting the focal length of the added lens offers the ability to control not only the core diameter, but also the profile of the flipped Bessel beam, including its length, the growing intensity profile of the leading edge, and the steepness of the trailing edge. Adjusting the input beam size enables independent control of the length of the Bessel beam.

Fig. 2b (bottom line) shows the optimized simulated conditions for the flipped Bessel beam, where the use of a 1° axicon combined with a

<caption>**Table 1**</caption>

Relevant design parameters of the regular and flipped Bessel beams represented in Fig. 2. Both the measured and simulated beam diameter (x) and length (z) at FWHM, and the aspect ratio (calculated as z/x) are displayed.

<table><thead><tr><th></th><th></th><th>Bessel, Long</th><th>Bessel, Short</th><th>Flipped Bessel</th></tr></thead><tbody><tr><td rowspan="4">Measurement</td><td>x<sub>FWHM</sub> [µm]</td><td>1°</td><td>2°</td><td>1°+300 mm</td></tr><tr><td>z<sub>FWHM</sub> [µm]</td><td>2.4</td><td>1.2</td><td>1.2</td></tr><tr><td>ratio (z/x)</td><td>720</td><td>360</td><td>200</td></tr><tr><td></td><td>300</td><td>300</td><td>170</td></tr><tr><td rowspan="4">Simulation</td><td>x<sub>FWHM</sub> [µm]</td><td>2.3</td><td>1.2</td><td>1.2</td></tr><tr><td>z<sub>FWHM</sub> [µm]</td><td>450</td><td>225</td><td>230</td></tr><tr><td>ratio (z/x)</td><td>195</td><td>190</td><td>190</td></tr></tbody></table>

300 mm lens enables to generate the same core size and length as obtained using solely a 2° axicon, but with a flipped on-axis intensity distribution (see also Table 1). Meanwhile, as illustrated in Fig. 2d, the regular Bessel beam exhibits a steep leading-edge followed by a slowly decreasing trailing edge, whereas it is the opposite for the flipped Bessel beam. In addition, the length of the short Bessel and the corresponding flipped version is around 230 µm (Table 1), which is roughly the width of the sample (note that when penetrating inside the sample, the beams will experience a longitudinal stretching by a factor equal to the refractive index). This is an interesting point to facilitate the experimental implementation for material processing. Indeed, by optimizing the placing of the sample along the z-profile (see illustration in Figs. 2c, d), the expected beam profile inside the sample is either increasing or decreasing, exactly as wanted. Moreover, on the same range, the long Bessel beam (blue profile on Fig. 2d) keeps almost a constant intensity level along the propagation axis. In this regard, even if by a 1°+750 mm doublet we were able to simulate the flipped version of the long Bessel beam, the effective on-axis profile respect to the sample thickness is almost the same. Therefore, the benefit of using a slowly increasing Bessel beam to deliver a more intense spot deep inside must be investigated with a beam whose length is adapted to the sample thickness, otherwise the sample just sees a rather uniform axial profile. In view of this, we focus our attention on comparing three types of beams, the long (as a reference), the short and the short-flipped versions, with lengths adapted to the sample thickness. This allows to examine the influence of the on-axis profile on the formation of the beam inside the scattering sample, and the subsequent drilling capabilities.

Following simulations that helped to define the optimized conditions, the designed flipped Bessel beam is generated. Figs. 2a and 2c show the measured intensity maps of the flipped Bessel beam featuring, as expected, an inverted on-axis profile. Both core size and length closely match the simulations (Table 1) and are similar to the short Bessel beam. All-in-all, by using simple optical elements (axicon and lens) and simulations, it is shown here a straightforward solution to customize the Bessel beam on-axis profile and central core as a powerful tool to design interesting configurations for exploring various laser processing options.

## 3.2. Laser drilling performance

After generating the different non-diffractive beams, their performance to drill a translucent commercial 200-µm thick fiberglass epoxy resin FR4 sample is investigated. First, the material response to ablation is considered by determining the fluence surface damage threshold ($F_{th}$). Based on Liu's method, which assumes a threshold damage response and a Gaussian beam distribution, single-shot irradiations at different energies are carried out [39]. In this case, one must remove the axicon-lens doublet and F4 lens from the experimental scheme in Fig. 1 to generate a Gaussian beam by directly focusing onto the sample surface with the 20x microscope objective. The results are plotted in Fig. 3, showing the radius $R$ of the surface damage increasing with the pulse energy $E$. By confocal microscopy (insets in the figure), we unveil an increasing material-removal rate with pulse energy (~3 µm/mJ in depth), as craters become deeper. By assuming a Gaussian beam distribution, the damage radius is expected to write: $R^2 = \omega_0^2/2\ln(E/E_{th})$, where $\omega_0$ is the beam waist, and $E$ the pulse energy, related to the peak fluence by $F = 2E/\pi\omega_0^2$. A good fit is obtained for values below 40 µJ (47.5 J/cm²), with $\omega_0 = 7.3$ µm and $F_{th} = 1.2$ J/cm² (blue curve in Fig. 3). Above this energy, one observes a linear trend with a slope of ~84 µm/mJ (red curve in Fig. 3). The peak intensity corresponding to the tipping point of 40 µJ is $2\times10^{14}$ W/cm², which is around the air breakdown threshold [40]. Therefore, such high intensity most probably leads to the appearance of a prefocal plasma due to air breakdown that results in a higher material removal rate. Nonetheless, it must be noted that this plasma typically distorts the beam profile, resulting in an enlarged spot that might compromise the resolution [30,41].
<figure><img src="image_5.png" /><figcaption>**Fig. 3.** Radius of single-pulse damage spots versus the pulse energy produced by a Gaussian beam. At low energies we observe a logarithmic trend (fitted blue curve, $\omega_0 = 7.3$ µm and $F_{th} = 1.2$ J/cm²), whereas it exhibits a linear trend at high energies (fitted red curve, 84 µm/mJ slope) due to beam distortion under nonlinear propagation regime in air. The fluence (top axis) is computed with the obtained beam waist. The insets correspond to optical reflection and confocal microscopy images (pulse energies are indicated on the arrows).</figcaption></figure>

Now, using the various Bessel beams generated above, matrices with different conditions are produced (Fig. 4) by systematically varying the pulse energy (50–100 µJ) and pulse number (100–1000 pulses) at a constant repetition rate of 10 kHz. The energy range is considered in view of the capacity to perform through-holes. The beam position with

respect to the sample surface, an important parameter considering the asymmetric on-axis profile of the beams and sample thickness, is determined by performing holes at different depths (a “z-scan” with steps of 100 or 50 µm for the long and short beams, respectively) at 100 µJ and 1000 pulses (not shown here). In all cases, through-holes in a range larger than 250 µm along the axial direction are found, which points out one of the advantages of Bessel beams over Gaussian focusing. In fact, Gaussian beams with similar beam waists (~2 µm) would lead to a confocal parameter of only ~ 12 µm, much smaller than the sample thickness, that makes therefore impossible to drill through the whole sample without scanning the beam longitudinally. For systematic analysis and comparison, drilling is performed in all cases at the middle point between the drilling limits determined in the z-scan in a static manner.

For all tested beams, it is observed that the front ablation spot size increases with the number of pulses and the delivered energy (Fig. 4). From a general glance, the flipped Bessel shows through-holes at the lowest pulse number and energy, whereas the short Bessel exhibits the largest collateral effects. To have a clearer view, we analyze each case in more detail by measuring the diameters of the front surface ablation and the rear surface hole. Since the holes are not perfectly symmetrical and in order to facilitate comparison, the average hole diameter (d) is computed by measuring the hole area (A) and assuming it has a circular contour: $d = 2\sqrt{A/\pi}$. For the long (1°) and short (2°) Bessel beams (Figs. 4a,b), front surface ablation diameters from 110 to 220 µm, and 200 to 300 µm are respectively obtained. Measured results are plotted in Figs. 5a,b. The difference in diameter can be related to a twice smaller core size (Table 1) for the short Bessel, which despite being tighter, leads to peak fluences four times higher at the same energy value. Therefore, the produced modifications are wider, and a significant heat affected zone (HAZ) in the form of brownish stains appears around the spots at the highest energies and accumulated shots. In fact, despite the low thermal budget of femtosecond laser machining, multiple shots are not free from accumulation effects that might lead to carbonization of the

<figure><img src="image_6.png" /><figcaption>**Fig. 4.** Front surface reflection microscopy images of holes combined with rear illumination. The three designed beams of Fig. 3 are employed: a) Bessel (long, 1°), b) Bessel (short, 2°), and c) flipped Bessel (1°+300 mm). In each matrix the energy increases from left to right (indicated on top) and the pulse number from top to bottom (indicated on the left). The holes identified by red squares are produced at $E = 75$ µJ with 600 and 1000 pulses. Through-holes (bright areas in the middle of the spots) are found for all beams at high pulse number and energy. A higher drilling performance is observed for the flipped Bessel beam, showing through-holes at the lowest pulse number and energy, larger overall holes, and a reduced HAZ.</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>**Fig. 5.** Three-dimensional surface plots of the front surface ablation and inner hole diameters of the through-holes in Fig. 4 carried out with different beams: a) Bessel (long, 1°), b) Bessel (short, 2°), and c) flipped Bessel (1°+300 mm). Values are only displayed when there is a through-hole. The hole diameters increase with the pulse number and energy. d-f) Corresponding 3D surface plots of the taper ratio between the front and inner diameters. The smallest taper is observed for the flipped Bessel (1°+300 mm), with a ratio of around 0.5.</figcaption></figure>

epoxy resin [25,42–44] and redeposit of the ejected debris (see below). For the flipped Bessel beam (Fig. 4c), the front surface ablation diameters range from 110 to 250 µm (Fig. 5c), and a smaller HAZ compared to the short Bessel beam is observed. Comparing these three cases, it can already be noticed that surrounding effects and front surface ablation spots are significantly reduced while using a flipped Bessel compared to a regular Bessel beam. This is even clearer when comparing the different magnified images of holes performed at similar conditions in Fig. 4.

Through drilling is quantified by illuminating the matrices from the rear surface (see insets in Fig. 4). By this, through-holes are considered as those where white light is observed in the middle, which corresponds to the minimum aperture of the hole. As before, the average inner diameter is measured by accounting for the area and plotted in Fig. 5a-c. For the long and short regular Bessel beams average inner diameters as large as 60 and 75 µm are respectively found. The steeper and shorter Bessel allows to machine larger holes, but at the same time it also requires larger pulse numbers and energy, which leads to an extended HAZ. Nonetheless, when the on-axis beam profile is flipped, not only do we observe a reduced HAZ but also a larger range of drilled inner diameters from ~ 10 µm up to 95 µm (Fig. 5c). It is very interesting to notice that holes are obtained at lower pulse number and energy than those obtained with regular Bessel beams, widening the processing window but also the possibility to employ more cost-effective laser sources. This indicates higher drilling efficiency, simply obtained by inverting the on-axis profile as a way to compensate for inner scattering. Nonetheless, flipping the on-axis profile is not the only reason for more efficient drilling but also adapting the beam length to the sample thickness so that the material sees a gradual intensity increase (see scheme in Figs. 2c,d). Lastly, it must be noted that holes performed with the flipped Bessel beam exhibit similar sizes to those obtained by mechanical and laser drilling [20,21,24,25,43], with the ability to precisely control the size.

A method to compare the drilling performance among the different beams is to compute the ratio between the front surface ablated spot and the inner hole diameters, which account for technical parameters as the modified area and the effective hole for an electrical via. This ratio, plotted in Fig. 5d-f, accounts for the taper of the holes, and indicates their shape with respect to an ideal cylindrical hole (ratio = 1). In average, ratios lie between 0.1 and 0.3, indicating a conical structure. An overall higher ratio is observed for the flipped beam, peaking at 0.5 for holes performed at 75 µJ and more than 500 pulses. On the contrary, this ratio is smaller for both regular Bessel beams, with a maximum value of 0.3 at the highest energies and pulse numbers. In view of these results, the maximum taper ratio of 0.5 is higher than that obtained by Marx et al. (0.3, accounting for 15 µm and 50 µm front and rear diameters) [32], which adds up to the ability to drill through a 200 µm substrate (up to 130 µm in their work), highlighting the importance of customized beams for optimized machining. Additionally, to further assess the holes quality, we evaluated their roundness (or circularity) defined as $Rnd = 4\pi A/P^2$, where A and P are the holes area and perimeter, respectively. Values of 0.72 ± 0.13, 0.67 ± 0.13, and 0.68 ± 0.07 for the long, short, and flipped beams were obtained. In average, the obtained roundness of 0.7 is smaller than the ideal circular case (Rnd = 1), but close to a square hole (Rnd ~ 0.8). Besides, the flipped beam holes show a deviation of 10 %, smaller than that of regular beams (20 %), indicating a higher reproducibility.

By employing SEM, the HAZ was analyzed. In Fig. 6a-b optical and SEM images of a hole performed with the flipped Bessel beam at 75 µJ and 1000 pulses are displayed. Remarkably, even if the area around the hole seems to be affected (brownish appearance), on the SEM image only the irradiated area appears to be modified and its surroundings are free from micro-cracks or deformations. It features a large diameter corresponding to the ablation of the epoxy unveiling the fibers, and a second smaller diameter corresponding to the through-hole, which difference in ablation efficiency might be related to the different ablation thresholds
of the composite structure. No substantial debris is observed in all the examined holes. However, in some cases unablated epoxy fragments in the form of unpeeled material can be present as it is visible in the SEM image. By means of EDX we measured the species concentration on the sample. In Fig. 6c the concentration map of the hole and surrounding area are shown. Additionally, four zones of interest (rectangles in Fig. 7a-b) were analyzed in more detail, see Table 2. First, carbon (C) and oxygen (O) are present all over the sample, corresponding to the epoxy resin. Second, silicon (Si) and calcium (Ca) are present where glass fibers are visible (region 2). Also, the concentration of O in the hole is higher. This observation confirms that epoxy is the superficial material, and that glass fibers are embedded inside with a composition including SiO₂ and Ca. Finally, if we compare the C-to-O ratio between the pristine surface (region 1) and the darkened surface around the hole (region 3 and 4), we observe a ratio of 4:1 (C:O) in all cases. This indicates that carbonization is minimal and that the material structure around the outer ablated area appears not to be compromised. However, structural damage might be present around the inner through-hole, where the beam intensity was higher.

## 4. Discussion

It must be noted that the produced modifications are substantially larger (>100 µm) than the beam spot size (~1–2 µm). By considering the measured transverse x-y profiles of the beams (Fig. 2a, left column), and integrating the intensity in the core and each one of the rings, one can determine the corresponding energy and peak fluence. Focusing on the short Bessel beam at its highest energy of 100 µJ, we obtain a core peak fluence of 330 J/cm² (Ecore ~ 4.2 µJ) and the following five consecutive rings have peak fluences of 55, 30, 20, 15, and 12 J/cm², respectively. Similarly, for the flipped Bessel the core peak fluence is 145 J/cm² (Ecore ~ 1.6 µJ) and the following five consecutive rings have peak fluences of 21, 10, 6, 4, and 3 J/cm². With this, we observe that even the rings have peak fluences above the surface modification fluence threshold (1.2 J/cm², from section 3.2). This suggests that at high energies, ablation is achieved by both the central core and the concentric rings. In this regard, at 100 µJ for example, the fifth ring of the flipped beam has a diameter of ~ 17 µm, with a peak fluence of 1.5 J/cm² (above the ablation threshold) at 50 µJ pulse energy and leads to drilling a through-hole with a 20-µm inner diameter. These similar diameters support the hypothesis of drilling by both the core and rings in a percussion

<figure><img src="image_8.png" /><figcaption>**Fig. 6.** A) Front surface optical microscope image of a hole fabricated with the flipped Bessel beam, 75 µJ, and 1000 pulses. The white spot in the middle is the light transmitted through rear illumination. Small rectangles correspond to the regions for concentration EDX analysis in Table 2. Region 1 was further than the indicated location. b) SEM image of the same hole. c) Corresponding EDX maps of the same hole, where the main found elements were carbon, oxygen, silicon, and calcium.</figcaption></figure>

<caption>**Table 2**</caption>

Concentration analysis by EDX of the four relevant regions (1-pristine substrate, 2-glass fibers and, 3,4-darkened substrate) shown in Fig. 6a-b and the main element concentration: carbon, oxygen, silicon, and calcium.

<table><thead><tr><th rowspan="2">Region</th><th colspan="4">Concentration [%]</th></tr><tr><th>C</th><th>O</th><th>Si</th><th>Ca</th></tr></thead><tbody><tr><td>1</td><td>81.0</td><td>19.0</td><td>0.0</td><td>0.0</td></tr><tr><td>2</td><td>25.8</td><td>33.4</td><td>25.8</td><td>15.0</td></tr><tr><td>3</td><td>70.5</td><td>15.6</td><td>7.0</td><td>6.9</td></tr><tr><td>4</td><td>78.6</td><td>15.8</td><td>3.7</td><td>1.9</td></tr></tbody></table>

modality, i.e. progressive removal of matter pulse after pulse. In fact, to support this vision, we can consider the ablation rate retrieved from Fig. 2: ~3 µm/mJ. By accumulating 1000 shots at 75 µJ, a total of 75 mJ are delivered, which approximately corresponds to an ablated thickness of 225 µm. At a fixed energy, although the peak fluence of the regular Bessel beam is higher than that of the flipped beam, through-drilling is more performant for the latter, indicating a deeper propagation within the material despite scattering, that is enhanced by customizing both its size and axial profile. This is also in line with the lower drilling energies of the flipped beam, supporting a combined drilling modality by beam propagation and percussion, which is not the case for the regular Bessel beam.

As in the initial study with the Gaussian beam (Fig. 3), we must note that peak fluences above 40 J/cm² translate to peak intensities of 2x10¹⁴ W/cm², which is around the air breakdown threshold. Even if in the case of Gaussian beams this might lead to beam distortion [41], the conical interference formation and propagation of Bessel beams, compared to forward wavefront propagation, might be less prone to distortion [30]. This illustrates the challenge of delivering enough energy deep inside such scattering samples, and the natural advantage of Bessel beams for this task.

In a quest to determine the ability to drill only with the central core, we tried machining holes at lower energies and higher pulse number, but without success. Therefore, despite the non-diffractive behavior of the Bessel-like beams, the 6-µm thick glass fibers (larger than the beams spot size in Table 1) and material defects lead to substantial scattering of the beam and impede the continuous formation of the core by distortion of the conical wavefront requiring a combined effort of both core and rings to drill. In view of this, employing a larger core size to mitigate scattering was investigated, but the hole quality deteriorated, obtaining a larger HAZ and requiring more pulses and energy to drill (not shown here). At the same time, despite this combined percussion drilling modality, we can still observe the self-healing effect as some inner holes do not show a perfect circular contour (see inset images in Fig. 4). Therefore, with slightly smaller heterogenous structures –smaller fiber diameters and embedded air bubbles in this case–, or larger laser wavelengths in the mid-IR, we could expect a better drilling performance of these flipped Bessel beams since there would be less scattering. However, this would require developing high-power femtosecond mid-IR lasers sources or relying on high-power optical parametric amplifier-based systems, which are nowadays rarely accessible and lead to pulse energies in the µJ range, which might unlikely lead to modification showing that more efforts need to be made to compensate for scattering through the material.

In view of the similar core size and length of the short Bessel and the flipped Bessel, but opposite on-axis profile, a repeatability study to highlight the differences at same irradiation conditions is performed. The images of the 5x5 hole matrices drilled with 1000 pulses at 75 µJ are shown in Fig. 7. Holes performed with the flipped beam (Fig. 7b) exhibit a 100 % drilling probability. However, with the short Bessel beam (Fig. 7a) only a 30 % drilling probability is reached. Taking a closer look at the core peak fluence, ~250 and ~110 J/cm² (at 75 µJ pulse energy) for the regular and flipped beams, respectively, we observe a superior drilling performance for the flipped beam. Moreover, the flipped Bessel,
<figure><img src="image_9.png" /><figcaption>**Fig. 7.** Transmission images of 5x5 hole matrices performed with the **a)** short Bessel (2°) and **b)** flipped Bessel (1°+300 mm) beams at 75 µJ and 1000 pulses. **c-d)** SEM images of the holes. **e-f)** SEM images of the surface with a 60° tilt. Reliable drilling with higher taper ratios and reduced HAZ is achieved with the flipped Bessel beam.</figcaption></figure>

having a smaller peak fluence, shows smaller HAZ (orange appearance of Fig. 7), limiting the extent of affected material. From these images we can also evaluate the lateral positioning tolerance (computed considering the deviation of the output hole center respect to the beam positioning), finding a value of 10 µm, which is smaller than that required by mechanical drilling (25 µm) [20,21]. Lastly, the roundness of the holes performed with the flipped Bessel beam (Fig. 6b) is 0.7 ± 0.1, showing its reproducibility.

Finally, to further evaluate the quality and reproducibility of the holes, in Fig. 7c-f SEM images are displayed. Several observations can be extracted from these images. First, like in Fig. 6b, two different ablation regions are apparent: an outer ablated zone concerning the removal of the epoxy superficial layer, and the inner hole. From the previous calculation, the lower peak fluence of the concentric rings only achieves the ablation of the 20-µm thick epoxy layer, whereas the higher fluence of the inner core allows penetrating the glass fibers, indicating different ablation thresholds for the different materials of the FR4 composite. Secondly, As detected from the optical images, a through hole is not always obtained for the short regular Bessel beam —as some fibers and redeposited material are visible—, whereas a high repeatability and through holes are obtained for the flipped Bessel beam. At the same time, from the tilted images (Figs. 7e,f), no substantial redeposit and debris around the holes are observed for the flipped Bessel beam,

whereas molten epoxy is clearly visible for the regular Bessel beam. Thus, despite an apparent substrate color change for the flipped Bessel beam that is associated with the HAZ, it is only on the surface of the regular beam that structural changes are detected. Finally, if we consider the black hole in Fig. 7d, which could be considered as the hole aperture, we find an average entrance diameter of ~ 75 µm. Considering the output diameter from Fig. 5c of ~ 70 µm, this leads to a taper ratio of approximately 1. Thus, the effective holes are almost cylindrical (excluding the 20-µm thick epoxy layer), meaning that the flipped beam is capable of compensating scattering by delivering higher fluences at deeper energies. Nonetheless, in real applications the whole top ablated area has to be considered since it defines the lateral distance between consecutive holes vias. All in all, these results put into evidence the need of customized Bessel beams to optimize energy delivery deeper into the material as a way to mitigate scattering and achieve modification.

## 5. Conclusions

In this work, the non-diffractive properties of different Bessel-like beams were investigated to mitigate inner scattering in the drilling of through-holes of a 200-µm translucent substrate of fiberglass epoxy resin. Employing numerical simulations and the adequate combination of axicons and lenses, Bessel beams with different lengths, core sizes, and axial profiles were generated. In particular, a lens was inserted in front of the axicon leading to a gradually increasing on-axis profile and resulting in a so-called flipped Bessel beam to promote energy deposit with depth. Initially, by systematically varying the pulse number and energy, through-holes were obtained for all designed beams. Superior performance was observed for the flipped Bessel beam, whose length was similar to the sample thickness. Compared to the other beams, it exhibited a lower drilling threshold, less taper, and a reduced heat-affected zone, with diameters ranging from 10 to 95 µm (comparable to those achieved by other techniques). A repeatability study showed that, with a lower peak fluence than the regular beam, the flipped beam can drill at lower pulse number and energy, with the advantage of a smaller heat-affected zone and minimal structural damage. These results underline the need for dedicated beam shaping to adapt the beam to the material's properties and geometry. In this case, the flipped Bessel beam allows mitigating internal scattering and increasing the machining performance. This approach allows not only to adapt the on-axis profile but also optimizing the beam's length and core, expanding the possibilities for in-volume laser processing of novel scattering materials and a broader range of potential applications.

## CRediT authorship contribution statement

P. Sopeña: Writing – review & editing, Writing – original draft, Methodology, Investigation, Conceptualization. N. Sanner: Writing – review & editing, Methodology, Conceptualization.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgements

This work was conducted using LaMP and ASUR facilities at LP3.

## Data availability

Data will be made available on request.
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