1. INTRODUCTION

Dielectric materials are transparent from the IR over the visible into the UV spectral region and are therefore ideally suited for nanophotonic devices in the very same spectral range. Thus, machining methods in the few hundred nanometer range and below are necessary. However, the structuring of nonconductive dielectric materials by conventional processing techniques like electron beam lithography or focused ion beam (FIB) milling [1] suffers from the charging of the material’s surface [2]. The implementation of ultrashort laser pulses as a direct patterning method is an attractive alternative, as this can overcome charging effects and also provide very fast processing times. Based on the high nonlinearity of the laser–material interaction, the enhanced energy confinement, and limited heat diffusion, ultrashort laser pulses have become the instrument of choice for dielectric structuring on a micrometer or even nanometer scale [3] as well as for applications in nanosurgery [4,5].

Primary processes induced by ultrafast laser pulses involve nonlinear electronic excitation on the femtosecond time scale and energy transfer to the lattice on the picosecond time scale, followed by phase transitions like ablation or melting. Thus, temporal laser control can facilitate synchronization between the light and the material response and therefore lead to an efficient coupling of the laser energy [6,7]. When restricting the excitation window to the femtosecond regime in order to confine heat diffusion, the generation of a sufficient energy density within the electronic system is the key parameter to initiate the abovementioned phase transitions. The transient free carrier density plays a fundamental role in determining the optical properties in addition to various propagation and relaxation mechanisms. Depending on intensity, free carriers are initially promoted into the conduction band by strong field excitation, i.e., multiphoton ionization (MPI) or tunnel ionization. These free electrons can further absorb energy by inverse bremsstrahlung and subsequently induce carrier multiplication by collisions. This process is often termed avalanche ionization (AI). A detailed overview of laser excitation in dielectrics can be found in Balling and Schou [8] and references therein. Optical damage thresholds were used as experimental evidence for exceeding a certain critical electron density after the laser interaction, and the regulatory effect of pulse duration has been investigated over the last two decades [9,10]. Studies of transient electron densities range from intensities below [11,12] up to well above the breakdown threshold [13–15], confirming the described scenario. Optical damage thresholds were also used to demonstrate control of MPI and AI [16]. Furthermore, it has been demonstrated that direct structuring of dielectric materials with temporal Airy pulses (TAPs) generates reproducible surface structures reaching the sub-100-nm regime [17], which is an order of magnitude below the diffraction limit. Here, a first experimental indication was given that TAPs can create deeper structures as compared to bandwidth-limited pulses. Other approaches to creating high aspect ratio channels in dielectrics basically utilize spatial beam propagation based on self-focusing effects or Bessel beam generation and will be discussed later.

In this contribution we demonstrate the creation of high aspect ratio channels in fused silica by specifically temporally tailored femtosecond laser pulses in a power regime where self-focusing effects can be neglected. The findings are supported by rate equation simulations.

2. IDENTIFICATION OF THE TECHNOLOGICAL REQUIREMENTS

The physical picture behind our temporal pulse tailoring is quite intuitive: ablation of dielectrics is often attributed to a critical electron density of a pure electron-hole plasma in the range of ${10}^{21}$ $\text{electrons}/{\mathrm{cm}}^3$ rather than a critical energy density $W$ within the electronic system. In the Drude model, the corresponding plasma frequency ${\omega }_{\mathrm{pl}}=\sqrt{e^2{N}_{\mathrm{CB}}/m_e{\epsilon }_0}$ is in the near-IR, and laser light at 785 nm will start to be strongly absorbed, i.e., the penetration depth into the material will strongly decrease with increasing electron density. A special feature regarding the conduction band electron dynamics in fused silica is a fast mechanism leading to a rapid reduction of the electrons into a self-trapped exciton (STE) state, settled on a time scale of 150 fs [11]. The decrease in conduction band electron density goes hand in hand with the decrease in the Drude absorption. However, STEs can serve as an additional source for the creation of free electrons on the time scale of the laser interaction and eventually contribute to the energy transfer to the lattice on time scales of a few hundreds of picoseconds [18,19].

This means that the STEs play an important role for all pulses longer than 150 fs. To take advantage of this, an optimized pulse sequence consists of a short and intense pulse followed by a long, low-intensity part. The short pulse is intense enough to excite a significant number of electrons into the conduction band, well below the critical electron density. This allows the laser pulse to penetrate deeply into the material. Shortly after the excitation, the electrons are stored in STEs and are ready for a re-excitation by lower intensities, as those states are located within the bandgap. This is realized by the low-intensity part of the ideal pulse sequence. This re-excitation process might be repeated several times until the energy density for ablation is reached. In order to limit effects due to heat diffusion, the overall pulse sequence should be in the range of a few picoseconds. Temporal pulse shapes that mimic the optimal behavior can be synthesized with the help of spectral phase modulation [20]. In a Taylor expansion of the spectral phase, the third term ${\phi }_3$ leads to third-order dispersion (TOD). Mathematically, the temporal pulse envelope is described by the product of an Airy function and an exponential decay [21]. This is why we refer to these pulses as TAPs. Pulses with positive ${\phi }_3$ start with an intense main pulse followed by a pulse sequence with decreasing intensity [see the upper panel of Fig. 2(d)].

Increasing ${\phi }_3$ enlarges the pulse duration as well as the temporal asymmetry, whereas the instantaneous frequency remains constant. In contrast, modulation with the second-order term ${\phi }_2$ leads to group delay dispersion (GDD), which is characterized by a temporally symmetric intensity profile [see the upper panel of Fig. 2(e)] and a linear sweep of the instantaneous frequency. An increase in ${\phi }_2$ also leads to an elongated pulse duration. A detailed mathematical description can be found in Wollenhaupt et al. [21,22].

In our experiments, we focus linearly polarized femtosecond laser pulses with a central wavelength $\lambda =785\mathrm{nm}$ under ambient conditions with a long distance microscope objective ($\mathrm{NA}=0.5$) above, on, and below a fused silica surface [Figs. 1 and 2(a)] with a bandgap of $E_{\mathrm{gap},\mathrm{VB}}=9\mathrm{eV}$ [23]. Three different pulse shapes are used: bandwidth-limited pulses of 30 fs duration, TAPs with increasing TOD, where the statistical pulse duration [21] increases from 260 fs for ${\phi }_3=1\times {10}^5{\mathrm{fs}}^3$ via 770 fs for ${\phi }_3=3\times {10}^5{\mathrm{fs}}^3$ to 1.5 ps for ${\phi }_3=6\times {10}^5{\mathrm{fs}}^3$, and temporally symmetric pulses with a duration of about 1.4 ps (${\phi }_2=1.5\times {10}^4{\mathrm{fs}}^2$), matching the statistical pulse duration of the longest TAP. For each pulse shape, the fluence is 2.5 times above the corresponding damage threshold ($2.5\times E_{\text{thr}}$). In addition, ablation structures resulting from the longest TAPs are compared to structures of a bandwidth-limited pulse at the same fluence. The results for selected pulse shapes are displayed and compared to simulations in Fig. 2. The upper panels show the relative intensity profile of each pulse with respect to the bandwidth-limited pulse at a fluence of $2.5\times E_{\text{thr}}$ [Fig. 2(b)]. In the simulations the excitation and recombination dynamics in the direction of laser propagation ($z$-axis) are calculated via rate equations, taking the electron density in the conduction, valence, and trapping bands as well as the total electron density into account (for details, see Supplement 1).

3. EXPERIMENTAL SETUP

The experimental setup is sketched in Fig. 1. Laser pulses of 30 fs duration (FWHM) at a central wavelength of 785 nm are provided by an amplified Ti:sapphire laser system (Femtolasers Femtopower Pro). Single pulse selection is achieved via the Pockels cell of the amplifier. Before entering the material processing platform, the pulses are guided through our high-precision home-built pulse shaper [24]. The pulse shaper is used in a “phase-only modulation” mode, and the overall dispersion of optical elements up to the sample surface is coarsely compensated with the help of a commercial acousto-optic pulse shaper (Dazzler) contained in the amplifier and fine adjusted with the home-built pulse shaper prior to applying the required phase functions. Temporal pulse characterization of selected pulse shapes was performed via cross-correlation measurements directly in the interaction region. The linearly polarized and temporally shaped laser pulses are focused on a UV-grade fused silica sample (Spectrosil 2000) using a microscope objective (Zeiss LD Epiplan 50×/0.50 NA) with a 7 mm working distance. The $1/e^2$ intensity spot radius was measured using a knife-edge method, and the obtained value of 1 μm was applied in the simulations. The calculated Rayleigh length for the measured spot radius is 4 μm. The sample is translated by a three-axis piezo table for each pulse exposure. The focal position is changed in steps of $\mathrm{\Delta }z=1\mathrm{\mu m}$ for fixed pulse energy and pulse shape. After laser processing and cleaning, the samples are analyzed by cross-section cutting with FIB followed by scanning electron microscopy imaging.

 

Fig. 1. Schematic of the experimental setup for generating high aspect ratio nanochannels in fused silica together with a scanning electron micrograph of a created high aspect ratio channel (lower right). The measured spot diameter of 2 μm is indicated by the red arrows on the sample.

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4. MACHINING RESULTS AND HIGH ASPECT RATIO FORMATION

The machining results for bandwidth-limited pulses at 100 nJ $(2.5\times E_{\text{thr}})$ pulse energy are displayed in Fig. 2(b). Shallow ablation structures are created for all focal positions. When the pulse energy is increased to 250 nJ, the hole depth stagnates, as can be seen in Fig. 2(c).

 

Fig. 2. Machining results for (b), (c) bandwidth-limited pulses, (d) TAPs with ${\phi }_3=6\times {10}^5{\mathrm{fs}}^3$, and (e) temporally symmetric pulses with ${\phi }_2=1.5\times {10}^4{\mathrm{fs}}^2$ at three different focus positions with respect to the surface of the fused silica sample as indicated in (a). For each focus position, scanning electron microscope images of cross-sections obtained by FIB milling (left) are compared to simulations (right). Experiments in (b), (d), and (e) were performed at approximately $2.5\times E_{\text{thr}}$ for the corresponding pulse shape. Results for bandwidth-limited pulses approximately 6 times above their threshold and corresponding to the same pulse energy as used for shaped pulses in (d) are displayed in (c) showing shallow structures. The peak intensities of the applied pulses in the pulse pictograms are normalized to the simulated bandwidth-limited pulse shown in (b). The dark shaded areas close to the hole in the scanning electron microscope images are attributed to densified material after material processing. Vertical white lines in the middle column in (d) and (e) are FIB milling artifacts, and horizontal white bars in (d) and (e) indicate the measured hole depth.

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This observation changes when fused silica is processed with shaped laser pulses. When the temporal pulse shape is tailored to the abovementioned asymmetric [Fig. 2(d)] and symmetric [Fig. 2(e)] intensity distributions with pulse lengths of 1.5 and 1.4 ps, respectively, hole structures with a huge aspect ratio (hole depth to channel width) up to 30:1 are observed. The hole depth of each pulse shape and the focusing position are well reproduced in the simulations. We observe that the deeper the laser focus is located inside the bulk material, the longer the ablation structure is.

For asymmetric pulses, the channel width of the ablation structures is in the range of 200–350 nm, and therefore well below the 785 nm wavelength. A decrease in the temporal asymmetry, accompanied by a shorter temporal pulse duration, leads to a decrease in the hole depth and aspect ratio, as presented in Figs. 3(a)–3(c).

 

Fig. 3. Experimental hole depth (blue squares), simulated hole depth (solid blue line), and measured aspect ratio (green diamonds) with respect to focus position (minus/plus: focus below/above surface) for four different pulse shapes. (a)–(c) TAP shapes with decreasing TOD parameter and correspondingly decreasing statistical pulse duration [(a) ${\phi }_3=6\times {10}^5{\mathrm{fs}}^3$; 1.5 ps, (b) ${\phi }_3=3\times {10}^5{\mathrm{fs}}^3$; 770 fs, (c) ${\phi }_3=1\times {10}^5{\mathrm{fs}}^3$; 260 fs], where the pulse duration in (a) corresponds to the data in Fig. 2(d). (d) Temporally symmetric pulse shape with ${\phi }_2=1.5\times {10}^4{\mathrm{fs}}^2$ (1.4 ps pulse duration) corresponding to the data shown in Fig. 2(e). Each set was recorded with a pulse energy $2.5\times E_{\text{thr}}$. All analyzed pulse shapes are identified by cross-correlation measurements and included as insets in (a)–(d). All cross-correlations are normalized in intensity. The time axes in (a)–(c) are shown for a range of 1 ps, whereas it is 4 ps in (d). Error bars stem from an inaccuracy of $\pm 0.5\mathrm{\mu m}$ for the focus position and from postmortem hole depth analysis. The aspect ratio is calculated as the hole depth divided by the full channel width at half depth.

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For symmetric pulses, the same depth is reached; however, larger diameters and irregularities are observed. The mechanisms responsible for the irregularities have not been identified so far. These pulses seem to be less robust with respect to high aspect ratio machining.

Figure 3 summarizes the hole depths in the experiment and the simulation and the aspect ratio achieved with respect to the focus position for increasing the temporal asymmetry and the symmetric pulse profile. In addition, cross-correlations of temporal pulse shapes, measured directly in the interaction region, are displayed.

5. DISCUSSION

Bandwidth-limited pulses have a significantly higher peak intensity than elongated temporally shaped pulses for the same pulse energy. Even when setting the same relative pulse energies with respect to $E_{\text{thr}}$, the bandwidth-limited pulse still has a peak intensity approximately 3 times higher than that of a TAP with ${\phi }_3=6\times {10}^5{\mathrm{fs}}^3$ [Figs. 2(b) and 2(d)]. At these high laser intensities, air close to the target will be excited, since the ionization potential of air $E_{\text{gap},\text{air}}=14.6\mathrm{eV}$ is only $1.6\times E_{\mathrm{gap},\mathrm{CB}}$ of fused silica. This leads to a significant absorption [25] of the laser pulse before it reaches the surface of the sample, limiting the energy input into the material. In our simulations, we included absorption in air for bandwidth-limited pulses based on results from Liu et al. [26]. In addition, bandwidth-limited laser pulses of 30 fs create a very high conduction band electron density within the first few hundreds of nanometers that will lead to a rapid and strong absorption and reflection of the laser pulse, suppressing energy deposition beyond this distance. As the maximum temporal intensity of the pulse has passed, the conduction band electron density $N_{\mathrm{CB}}(t)$ strongly decreases due to the fast trapping mechanism of 150 fs [11] into exciton states ($E_{\text{gap},\mathrm{TB}}=5.2\mathrm{eV}$ [23]), as illustrated in Fig. 4(b). Free carrier absorption in air and inside the sample due to a high conduction band electron density is one mechanism leading to stagnation of the hole depth. Stagnation from absorption due to strong field excitation [27] is not considered in our simulations.

In comparison to bandwidth-limited laser pulses, temporally shaped pulses—either symmetrically or asymmetrically—interact with the material in a different fashion. Their low peak intensities avoid absorption in air as well as strong absorption close to the surface. Thus, these pulses are able to provide more energy for the excitation in the depth of the material, which might be sufficient for material ablation. The temporal structure of the asymmetric pulse is furthermore responsible for the characteristic interplay of trapping and re-excitation of electrons ending in an oscillating behavior of $N_{\mathrm{CB}}(t)$ [Fig. 4(c)], showing that there is still an observable energy deposition after 2.5 ps. The maximum $N_{\mathrm{CB}}(t)$ is much lower than for bandwidth-limited pulses, even though the same deposited energy of $W=1.4\frac{\mathrm{kJ}}{{\mathrm{cm}}^3}$ is accomplished at the end of the pulse [Fig. 4(a)]. As listed in Table S1 of Supplement 1, it is noteworthy within this context that 52% (36% for the symmetric and less than 1% for the bandwidth-limited pulse) of the energy required for ablation is discharged into the material by the re-excitation of STEs via MPI and mainly AI. As a consequence, the energy deposition takes place in a confined region, because the re-excited STEs are localized close to a single ${\mathrm{SiO}}_2$ complex [11].

Regarding the subwavelength dimensions of the hole structures, we note that not all critically excited material can be ejected during the ablation process. This is supported by the rims formed close to the craters. The rims are not significantly larger for temporally shaped laser pulses than for holes generated by bandwidth-limited pulses, as shown in Fig. 2. As the excited material is nearly completely enclosed by the unexcited material, high pressure inside the material can lead to the formation of super dense material phases arising during the excitation and ablation process and ending in densified material close to the channel crater. This was recently observed in the case of void formations in fused silica [28] and silicon [29]. In addition, it was recently found that laser excitation in water by TAP pulses is distributed over a strongly reduced area and greater depth compared to ultrashort bandwidth-limited laser pulses [30].

For temporally symmetrically shaped pulses, the ablation threshold is approximately 1.8 times higher compared to the that of asymmetrically shaped ones (178 versus 100 nJ; see Table S1 of Supplement 1) due to the even lower peak intensity. In this case, almost the first half of the pulse is not intense enough to excite a significant number of initial seed electrons for AI, as indicated by the shaded area in Fig. 4(d). In addition, Fig. 4(a) shows the accumulated energy density over time, which starts to increase after time zero, showing that the second half of the pulse mainly provides the energy for ablation. For higher pulse energies, the onset of absorption will be shifted toward earlier parts of the pulse, but a significant fraction of the pulse will still be unused for excitation. In the end, the absorbed part of the temporally symmetric pulse is a temporally asymmetric shape. As mentioned above, this is reflected in the very similar temporal dependences of the accumulated energy density for both shaped pulses, as shown in Fig. 4(a).

 

Fig. 4. (a) Cumulative simulated time-dependent total energy density $W$ transferred to the fused silica sample for bandwidth-limited pulses (dotted line), TAPs with a TOD of ${\phi }_3=6\times {10}^5{\mathrm{fs}}^3$ (solid line), and temporally symmetric pulses with ${\phi }_2=1.5\times {10}^4{\mathrm{fs}}^2$ (dashed line), each at their corresponding ablation threshold $E_{\text{thr}}$. For all pulse shapes the same accumulated energy density of $W_{\mathrm{cr}}=1.4\frac{\mathrm{kJ}}{{\mathrm{cm}}^3}$ has been transferred at the end of the laser pulse. (b)–(d) Simulated time-dependent conduction band electron density (black line) in the first layer (1 nm) below the surface in the center of the laser pulse for (b) bandwidth-limited pulses, (c) TAPs with ${\phi }_3=6\times {10}^5{\mathrm{fs}}^3$, and (d) GDD-shaped laser pulses with ${\phi }_2=1.5\times {10}^4{\mathrm{fs}}^2$, each at their corresponding ablation threshold. The intensities of the temporal pulse shapes (red shaded, right $y$-axis) are normalized to the bandwidth-limited pulse in (b). Note the different plot range for (b) for conduction band electron density and the temporal close-up of the pulse shape. The black shaded area in (d) shows the part of the intensity that does not contribute to the ablation energy density.

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Regarding the slightly larger channel width, we assume that the continuous heating of the conduction band electrons results in a high average kinetic energy, causing a distribution of electrons over a larger volume. The consequence is supposed to be an extended affected zone of deposited energy and therefore an increased channel width, resulting in a smaller aspect ratio for temporally symmetrically shaped pulses.

This is supported by Fig. 4(d). On one hand, the maximum $N_{\mathrm{CB}}(t)$ is clearly larger than for TAPs, and no oscillations within $N_{\mathrm{CB}}(t)$ can be observed. On the other hand, the maximum $N_{\mathrm{CB}}(t)$ is noticeably smaller than for bandwidth-limited pulses, due to the smaller peak intensity and the electron trapping. As mentioned above, the re-excitation of STEs contributes noticeably to $W$ with about 36% (Table S1 of Supplement 1), which is attributed to the elongation of the pulse in time.

In the end, all this also manifests in a high penetration depth [Fig. 3(d)] for temporally symmetric shaped pulses, albeit with much lower efficiency and smaller aspect ratios.

A direct comparison of the experiment and simulation in Fig. 2 shows that on one hand the hole depths are in very good agreement, while on the other hand the channel width could be less well reproduced. This is related to the obvious limitations of the simulation, which includes neither the energy transfer to the lattice nor subsequent phase transitions, as discussed above.

To estimate the limits of the presented temporal pulse shaping technique, we simulated the maximum depth in the simulations for focusing at the surface. We increased the power for the TAP with ${\phi }_3=6\times {10}^5{\mathrm{fs}}^3$ to $33.3\times E_{\text{thr}}$ (Table S3 of Supplement 1), reaching the critical power for self-focusing. The simulated ablation depth of 15.5 μm is more than 4 times larger than the Rayleigh range. In terms of the temporal asymmetry and pulse duration, we increased the TOD parameter to ${\phi }_3=2\times {10}^6{\mathrm{fs}}^3$, with a corresponding pulse duration of 5.1 ps. The simulated hole depth for $2.5\times E_{\text{thr}}$ is around 4.7 μm, which is only slightly deeper than for ${\phi }_3=6\times {10}^5{\mathrm{fs}}^3$. However, the higher the temporal asymmetry and pulse duration, the more energy it takes until the critical power for self-focusing is reached compared to a low TOD parameter and shorter pulse durations. Furthermore, the simulations show that the channel diameter is nearly constant over the Rayleigh length. Thus, focusing below the surface can double the range, as seen in Fig. 2(d).

Note that similar observations have been reported using pulse durations of about 0.5 ps [31]. However, as discussed above, a large fraction of the pulse energy does not contribute to the ablation process for temporally symmetric laser pulses.

Other approaches [32–36] in which the resulting dimensions of the structures are comparable to ours apply powers well above the critical power with similar numerical apertures, and thus nonlinear propagation effects become appreciable, like self-focusing and filamentation [37]. In these investigations the laser pulses are either focused into the bulk with multipulse irradiation [32] or onto the surface with single laser pulses [33]. In the latter case, spherical aberrations are also used to elongate the focal region in the propagation direction. However, for similar hole depths and aspect ratios, pulse energies approximately 1 order of magnitude higher are required. A second method for high aspect channel generation is the utilization of spatial pulse shaping techniques, leading to nondivergent Bessel beams, which may exceed the critical power for self-focusing. Long and thin conical profiles with a very high aspect ratio of a secondary crater in borosilicate glass were observed due to spontaneous reshaping of the incoming Gaussian pulse into a Gaussian–Bessel pulse [34], and nanochannel arrays with Bessel beams, focused onto the backside of the material generated via a virtual axicon, were presented as well [35]. It was also demonstrated that temporal stretching of the laser pulse can be beneficial for energy deposition into the material with Bessel beams [36].

Indeed, we show that temporally asymmetric pulse shaping can be utilized for the generation of nanochannels as a temporal analog to spatial pulse shaping like Bessel beams. However, the important point is that for TAP, much less pulse energy is required and all resulting high aspect structures are generated with single laser pulses well below the threshold for self-focusing.

In general, we expect that temporally shaped pulses will also create deeper structures in dielectric materials without a fast trapping mechanisms, as this simple “seed and heat” picture is valid in those materials as well [17,30,31,38].

Just as in the case of fused silica, the earlier part of an elongated pulse will create an electron density well below the damage threshold, leading to moderate absorption. Since the remaining part of the pulse will increase the conduction band electron density step by step, the parts with low intensity at the end of the pulse are affected most from the absorption. In any case, we expect that TAPs will be the most efficient choice for the generation of nanochannels, because nearly the entire pulse contributes to the excitation and nearly no energy is wasted compared to long temporally symmetric laser pulses. The latter aspect could be important in laser machining with competing absorption processes.

Within this context we note that in sapphire, a dielectric material with no distinctive trapping bands, TAPs are able to generate structures with a higher aspect ratio than bandwidth-limited pulses, as was recently demonstrated by Hernandez-Rueda et al. [38]. In that study, the resulting ablation structures were evaluated by atomic force microscopy (AFM). However, in the case of a high aspect ratio and narrow ablation structures with dimensions close to the AFM tip, the resolution of that technique is limited and might not be able to indicate the real depth. To verify this prediction, postmortem analysis providing full spatial information is a fitting approach.

6. SUMMARY AND CONCLUSION

We demonstrated the efficient generation of uniform high aspect ratio ablation structures in fused silica utilizing single-shot TAPs in a regime where the chosen intensity was well below the threshold for self-focusing and thus filamentation. Neither spatial beam shaping methods nor nondivergent beam propagation techniques were applied.

TAPs consist of a short and intense pulse where the peak intensity is well below the intensity needed to create a critical electron density and therefore penetrate deep into the material. The energy density needed for ablation is reached with the trailing part of the laser pulse, making use of AI and a continuous re-excitation of STEs. Heat diffusion is limited by restricting the overall pulse duration to a few picoseconds. Under moderate focusing conditions ($\mathrm{NA}=0.5$), this results in high aspect ratio ablation structures ($\sim 30:1$) with channel widths in the range of a few hundred nanometers. Similar ablation structures with lower aspect ratios were obtained for temporally comparable but symmetrically shaped pulses; however, approximately twice as much pulse energy was required. Furthermore, we controlled the structure depth by tuning the asymmetry, i.e., the pulse duration, of the temporally shaped laser pulses: the more pronounced the asymmetry and the longer the pulse duration, the deeper the structures.

An adapted simplified rate equation model (see Supplement 1) has been developed as supporting evidence. Numerical simulations and experimental results show good agreement with respect to hole depth.

We argued that similar mechanisms could be exploited in other dielectric materials as well. Hence, our results enable a fast processing technique for tailored design in several optical and photonic applications as well as for implementations in nanosurgery.