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Abstract
Microgroove processing of glass is important in many fields, however, it is difficult to achieve the processing with a high speed. In this study, we developed a novel method for the high-speed microgroove processing of glass using two types of lasers, namely a femtosecond laser and a near-infrared continuous-wave (CW) laser. A single femtosecond laser pulse was initially focused on the surface of the material, enabling the area to absorb the CW laser, which is otherwise not absorbed by the glass. The CW laser was then scanned along the material surface, expanding the machined hole to form a groove. The resulting grooves, with a width of approximately 10 µm and depths of up to 350 µm, can be machined with a scanning speed of up to 200 mm/s, 25 times faster than conventional methods. This method exhibits the potential to improve the industrial application of fast laser microprocessing of glass.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Microgroove processing of glass is required for various applications, such as the manufacturing of packages of integrated circuits [1,2], microfluidic bio-chips [3–5], and solar cells [6]. Traditionally, mechanical methods have been used to machine glasses. However, owing to the high brittleness and hardness of glass, efficient microprocessing is difficult [7–10]. Laser processing is an alternative method, where continuous-wave (CW) lasers with wavelengths of approximately 1 $\mathrm {\mu }$m are often used in the processing of metal materials. However, they are hardly absorbed by transparent materials with large bandgaps, such as glass, making it difficult to utilize them for this purpose [11,12]. The use of femtosecond lasers, on the other hand, is considered one of the most versatile microprocessing methods for transparent materials, owing to their high spatial and temporal energy concentrations [13–18]. However, processing efficiency is a crucial limitation of this technique, with the typical material removal efficiency for glass less than $5\times 10^5\;\mathrm {\mu }\textrm {m}^3/\textrm {s}$ [19]. Subsequently, a number of studies have focused on increasing the efficiency of femtosecond laser processing methods [20–23]. Shin et al. developed a processing method for glass cutting and groove processing, obtaining a maximum processing speed of $3\times 10^6\;\mathrm {\mu }\textrm {m}^3/\textrm {s}$ [24]. However, owing to the low average power of the femtosecond laser and the difficulty in increasing the repetition rate, it is difficult to further improve the processing efficiency of this technique.
Transient and selective laser (TSL) processing is a recently-developed microdrilling method for glass. In TSL, a single femtosecond laser pulse creates an excited region of high electron density, which allows the region to absorb the CW laser [25,26]. Note that the CW laser (with a wavelength of 1070 nm) is not otherwise absorbed by the glass. After absorption, the CW laser heats the excited region and removes the material with high efficiency. Despite this high-efficiency, selective microdrilling using a single femtosecond laser pulse is currently limited to hole drilling. Although it is possible to machine microgrooves by repeating the TSL drilling, the processing speed is restricted by the repetition rate of the femtosecond laser, and thus, it is difficult to achieve high-speed grooving.
In this study, based on TSL processing, we developed a method for microgroove processing at high speed using a CW laser and a single femtosecond laser pulse. In this method, we proposed to expand the high-temperature region, where the absorption coefficient is transiently high, by scanning the CW laser in the horizontal direction. The scanning enables heating of the non-excited region and the machining of microgrooves with a speed of up to 200 mm/s. For a groove with a width of approximately 10 $\mathrm {\mu }\textrm {m}$, a depth of 130 $\mathrm {\mu }$m, and a length of 20 mm, the processing time employing the proposed method was 0.1 s, less than $4\%$ that of conventional femtosecond laser processing with a pulse energy of 65 $\mathrm {\mu }$J and a repetition rate of 100 kHz [27]. This translates to a processing efficiency increase of 25 times.
2. Method
A conceptual illustration of the proposed method, experimental setup, and the timing of irradiation of the two types of lasers is displayed in Fig. 1. A mode-locked amplified Yb:KGW laser system (Light Conversion; Pharos) and a high-power fiber laser system (SPI Laser; RED POWER) were employed for the initial excitation of electrons and subsequent heating, respectively. The femtosecond laser had a pulse energy, pulse duration, and wavelength of 60 $\mathrm {\mu }$J, 180 fs, and 514 nm, which is the second harmonic of the Yb:KGW laser, respectively. The fiber laser system generated a CW laser beam with a power of up to 200 W and a wavelength of 1070 nm. During the experiment, both beams were co-axially focused on the surface of a non-alkali glass sample using an objective lens (Mitutoyo; M Plan Apo NIR 5x). The diameters of the focused laser beams were 9.7 $\mathrm {\mu }$m (femtosecond laser) and 14.6 $\mathrm {\mu }$m (CW laser). Note that the absorption coefficient of the glass at the wavelength of the CW laser (1070 nm) was very small (0.3 $\textrm {cm}^{-1}$).
Fig. 1. (a) The conceptional process of the proposed method. (a1) Transient excitation of electrons, (a2) selective absorption of CW laser into the excited region, (a3) scanning of the CW laser to expand the heated region, and (a4) groove generation. FS: femtosecond; CW: continuous wave. (b) Experimental setup. The setup for coaxial observation is illustrated in dotted frame. IL: illumination laser (640 nm, 50 ns); BF: band-pass filter for the illumination laser; x axis: the direction of laser scanning (opposite to the direction of stage moving). (c) Timing of the laser irradiation.
The sample was fixed to a high-speed motorized XY scanning stage (Thorlabs; MLS203-1). The scanning stage could move at a speed of up to 200 mm/s, allowing the laser beams to be scanned through the sample at the same speed. The movement of the scanning stage, as well as the irradiation of the femtosecond laser pulse and CW laser, were precisely controlled using a delay generator (Stanford Research Systems; DG645). In the experiments, the irradiation of the femtosecond laser pulse was initiated 100 $\mathrm {\mu }$s after the start of irradiation of the CW laser. Because the maximum acceleration of the stage was 2000 mm$^{2}$/s; the acceleration of scanning took only tens of milliseconds. The irradiation of the lasers was slightly delayed, ensuring that the speed of the sample was stable during processing. Various scanning speeds (ranging from to 50-200 mm/s) and powers of the CW laser (80-200 W) were used. The irradiation time of the CW laser was adjusted based on the scanning speed to ensure a fixed scanning distance.
To focus the two lasers on the surface of the glass sample, a white illumination light was co-axially delivered, and the reflected light was observed using a charge-coupled device (CCD) camera (Baumer; TXG02c). We defined the position where the sample surface was clearly observed as the focal position, as the objective lens used in the experiment corrected the chromatic aberration ranging from 480 to 1800 nm. High-speed phenomena during processing (up to 100,000 fps) were observed using a high-speed camera (Shimadzu; Hyper Vision HPV-X2) and an illumination laser (Cavitar; CAVILUX HF) with a wavelength of 640 nm and a pulse duration of 50 ns. The observation was carried out from both horizontal direction and vertical direction (coaxial).
3. Results and discussion
A side view of the grooves machined using the proposed method is shown in Fig. 2. Grooves with a width of approximately 10 $\mathrm {\mu }$m and depths ranging from 80 to 350 $\mathrm {\mu }$m were generated with a scanning speed of up to 200 mm/s. During processing, the femtosecond laser pulse and the CW laser were irradiated on the surface of the sample, drilling a hole. Then, as the CW laser was scanned along the surface, a groove was formed in the scanning direction (arrow in Fig. 2(a)). This demonstrates that the high-temperature area formed during the drilling process was expanded by the scanning of the CW laser. Notably, the processing did not occur without the femtosecond laser pulse irradiation. Although cracks were found at the beginning and end of the machined grooves, almost no cracks occurred in-between.
Fig. 2. Side view of the machined grooves. The power of the CW laser was 80 W for (a) and (b), and 160 W for (c) and (d). The scanning speeds were (a) 50, (b) 100, (c) 100, and (d) 150 mm/s. H: hole; G: groove; C: cracks. Scale bar: 100 $\mathrm {\mu }$m.
When glass is heated, valence electrons are excited and become free electrons, increasing the laser absorption rate [12]. During the TSL drilling process, a high temperature area in the shape of a hole was formed, which in turn heated the surrounding area via heat transfer, thereby increasing the absorption rate. When the CW laser was scanned, absorption occurred in the surrounding area, expanding the processing area in the scanning direction. This resulted in groove generation, and therefore, continuous groove processing of a discretionary length and depth in glass can be achieved using a CW laser, which is otherwise not absorbed.
The relationship between the groove depth and processing conditions is shown in Fig. 3. Figure 3(a) illustrates the proportionality of the groove depth to the power of the CW laser, and its inverse proportionality to the scanning speed. The groove depth was plotted against laser fluence (energy input per unit area) as well to evaluate the relationship, as shown in Fig. 3(b). The laser fluence was calculated using the equation $\textit {P/Dv}$, where P is the power of the CW laser, D is the diameter of the laser spot, and v is the scanning speed. The majority of the data points are situated in a single curve, indicating that the groove depth is largely determined by the fluence of the CW laser. This agrees with the relation existing in the laser processing of metals [28,29]. Owing to the thermal excitation of electrons during this processing method, the laser absorption property of glass possibly becomes similar to that of metals.
Fig. 3. The dependences of groove depth (a) on the power of the CW laser with varying scanning speed and (b) on the fluence of the CW laser with varying power of CW laser.
After processing, the samples were mechanically cut to observe their cross sections, seen in Figs. 4(a) and 4(b). These images show that the surface of the side wall of the groove is smooth. Although there were almost no cracks in the main part of the groove, a heat-affected zone (HAZ) around the groove and minor cracks near the bottom were observed. Because of the thermal process, the inner area is thermally affected and the residual stress potentially resulted in the crack formation. In most cases, molten glass blocked the top of the groove. Although this block is an obstacle if an open groove is required, as the thickness of the molten glass is small, it can be easily removed using post-processing methods such as femtosecond laser processing or wet etching. The dependence of the area of material removal and HAZ on the fluence of the CW laser is displayed in Figs. 4(c) and 4(d), which illustrate that the areas of material removal and HAZ are determined by the fluence of the CW laser. In the past study of TSL drilling, the mechanism of the expansion of processing area was investigated. The excitation of the electrons initiated by the femtosecond laser pulse and high absorption rate of the excited area with high electron density were considered the primary reasons [26]. However, this theory is not adequately persuasive in the situation of groove processing. Near the side wall of the initially processed hole, the density of electrons are not considered high enough because it is relatively distant from the focal point of the femtosecond laser. Therefore it is necessary to investigate the possible mechanism of the expansion of processing area in the horizontal direction.
Fig. 4. The cross-section of a processed sample for (a) laser power 80 W, scanning speed 100 mm/s and (b) laser power 80 W, scanning speed 50 mm/s. B: block; HAZ: heat affected zone; RA: removed area; C: crack. (c) The dependence of removed area in cross section on fluence of CW laser. (d) The dependence of HAZ on fluence of CW laser.
To reveal the mechanism of the expansion, a simulation model of the TSL groove processing is built. In this simulation model, beam propagation method (BPM) is utilized to describe the propagation of femtosecond laser pulse [30–32]. BPM is usually described with
The free electron density is calculated based on the rate equation [31,32].
The temperature increase causes the generation of thermal electrons, resulting in the increase of absorption coefficient of the CW laser [35,36]. The density of thermal electrons $\rho _{\text {therm}}$ was calculated with the equation
The first term in this equation $\alpha _{0}$ refers to the absorption coefficient of CW laser at room temperature and $\eta ^{\prime }_{\text {casc}}$ is the coefficient of cascade ionization of the CW laser [12]. With the absorption coefficient $\alpha (T)$, we can estimate the laser intensity in the material with
In the calculation of the absorption of CW laser, a 3-dimensional Cartesian coordinate system was utilized. The temperature criterion of material removal and the maximum temperature defined in this simulation model are both 3000 $^\text {o}$C because glass can be evaporated at a higher temperature. Besides, in order to investigate the early stage of the expansion, we fixed the irradiation time of the CW laser in the simulation to 0.4 ms. With this model, the heating and heat transfer induced by the absorption of CW laser was calculated.
The simulation result is shown in Fig. 5 and Fig. 6. The red dotted line in Fig. 5 shows the irradiation position of the femtosecond laser pulse. From the result of side view, as the scanning of CW laser, there is a continuously increasing misalignment between the center of yellow area (removed area) and the red dotted line, indicating significant expansion of processed area (shown as yellow area) in the direction of the scanning of CW laser. The speed of the expansion is approximately identical to the scanning speed. The result of top view shows that the area of processing starts to protrude from the hole between 150 $\mathrm {\mu }$s and 200 $\mathrm {\mu }$s after the start of processing, which is consistent with the experimental result. Based on these simulation results, we confirmed the mechanism of groove processing using the proposed method: the absorption coefficient in high temperature region increases, causing the horizontal expansion of absorption area. When the scanning speed is too high, the speed of heat diffusion cannot follow the moving of the laser and let the processing cease.
Fig. 5. Simulation result shown as the side view across the focus position of the lasers and perpendicular to the optical axis of laser and the scanning direction after (a) 10 $\mathrm {\mu }$s (b) 50 $\mathrm {\mu }$s (c) 100 $\mathrm {\mu }$s (d) 150 $\mathrm {\mu }$s (e) 200 $\mathrm {\mu }$s (f) 250 $\mathrm {\mu }$s (g) 300 $\mathrm {\mu }$s (h) 350 $\mathrm {\mu }$s (i) 400 $\mathrm {\mu }$s. Color indicates the temperature distribution. $t$ = 0 $\mathrm {\mu }$s is defined as the time immediately before irradiation of the femtosecond laser pulse. Pulse energy of the femtosecond laser pulse: 65 $\mathrm {\mu }$J. Power of CW laser: 80 W; scanning speed: 50 mm/s. Red dotted line shows the irradiation position of the femtosecond laser pulse.
Fig. 6. Simulation result shown as the top view at the material surface after (a) 50 $\mathrm {\mu }$s (b) 100 $\mathrm {\mu }$s (c) 150 $\mathrm {\mu }$s (d) 200 $\mathrm {\mu }$s (e) 250 $\mathrm {\mu }$s (f) 300 $\mathrm {\mu }$s (g) 350 $\mathrm {\mu }$s (h) 400 $\mathrm {\mu }$s. The simulation conditions are the same as Fig. 5.
The history of the surface temperature distribution along $y$ axis across the focus position of laser is shown in Fig. 7. The front line of high temperature (from 1500 to 3000 $^\text {o}$C) is sharp and moves in a constant speed (same as the scanning speed) after 200 $\mathrm {\mu }$s. Compared with the focus position of CW laser (10 $\mathrm {\mu }$m at 200 $\mathrm {\mu }$s, 15 $\mathrm {\mu }$m at 300 $\mathrm {\mu }$s, etc.), the front line of high temperature always moves behind the focus position of CW laser.
Fig. 7. History of the surface temperature distribution along the direction of laser scanning ($x$ axis), across the focus position of lasers. $t$ = 0 $\mathrm {\mu }$s is defined as the time immediately before irradiation of the femtosecond laser pulse. Pulse energy of the femtosecond laser pulse: 65 $\mathrm {\mu }$J. Power of CW laser: 80 W; scanning speed: 50 mm/s.
Note that the heat capacity and thermal conductivity used in the simulation model are constant because the model of temperature-dependent absorption coefficient that we cited is a model based on constant heat capacity and thermal conductivity [37]. The use of the constant heat capacity may result in the overestimation of material removal and HAZ, and the use of constant thermal conductivity may also influence the simulation result. However, the qualitative conclusions of the simulation are still trustworthy.
The high-speed monitoring result of the processing from the side is displayed in Fig. 8. After 100 $\mathrm {\mu }$s (Fig. 8(b)), the hole was formed, and molten glass was observed approximately 5 $\mathrm {\mu }$m to the left of the center of the hole. The high internal pressure caused by evaporation is likely to have pushed the molten glass to the surface of the sample. After 200 $\mathrm {\mu }$s (Fig. 8(c)), the hole expanded in the scanning direction and the groove started to form. Note that expansion only occurred at the upper part (47 $\mathrm {\mu }$m from the surface in this case) of the hole. At this moment, the irradiation position of the CW laser was 40 $\mathrm {\mu }$m to the right of the center of the hole, while the molten glass was only observed at approximately 10 $\mathrm {\mu }$m to the left of the center of the hole. After 300 $\mathrm {\mu }$s (Fig. 8(d)), following the expansion of the machined groove, the length of the molten glass also expanded 35 $\mathrm {\mu }$m in the same direction. Finally, at 500 $\mathrm {\mu }$s (Fig. 8(f)), the length of the molten glass expanded to 61 $\mathrm {\mu }$m as the length of the groove expanded to 84 $\mathrm {\mu }$m. Additionally, the thickness of the molten glass then decreased because of the rapid decrease of the internal pressure as the vaporized glass in the groove cooled down, causing the molten glass to be partially suctioned into the machined groove. However, a portion of the molten glass remained at the surface of the sample, solidified, and blocked the groove.
Fig. 8. High-speed monitoring images from the side over the course of the processing. Power of CW laser: 80 W; scanning speed: 200 mm/s. M: molten glass. $t$ = 0 $\mathrm {\mu }$s is defined as the time immediately before irradiation of the femtosecond laser pulse.
The high-speed monitoring result from above is shown in Fig. 9. After 200 $\mathrm {\mu }$s (Fig. 9(c)), molten glass started to appear at the surface of the sample. From then, the molten region expanded both in lateral and longitudinal direction (Figs. 9(c)–9(j)). The steady width of the molten glass during the processing is approximately 55 $\mathrm {\mu }$s (Fig. 9(k)). From 400 $\mathrm {\mu }$s after the start of processing, a bright area started to appear in the middle of the molten glass and expanded in the longitudinal direction as the processing proceeded. The bright area may show the width of the processed groove, because the width of the bright area, approximately 10 $\mathrm {\mu }$m, is almost the same as the width of the processed groove which is confirmed by the observation of the cross section after the processing. This value is also consistent with the results of simulation, which is approximately 8-9 $\mathrm {\mu }$m. Based on the analysis of the processing results and the high-speed monitoring, it is possible to estimate mechanism of material removal and block formation (as shown in Fig. 10). When the excited area is irradiated by the CW laser, the surrounding area is also heated via heat transfer, causing the absorption rate of this area to increase. Therefore, as the CW laser scans through the material, the processing area expands in the scanning direction (Figs. 10(a1) and 10(b1)). During this process, the evaporation of the material causes the internal pressure to increase, pushing the molten material toward the side wall and the bottom. The recoil force then presses a portion of the molten glass to the surface of the sample (Figs. 10(a2) and 10(b2)), which remains at the surface and resolidifies, forming a block. The cooling process of the molten material also results in an HAZ around the processing area (Figs. 10(a3) and 10(b3)).
Fig. 9. High-speed monitoring images from above over the course of the processing. Power of CW laser: 40 W; scanning speed: 50 mm/s. M: molten glass. $t$ = 0 $\mathrm {\mu }$s is defined as the time immediately before irradiation of the femtosecond laser pulse. B: the bright area; FS: femtosecond.
Fig. 10. A schematic of the mechanism of material removal and block formation. (a) Side view and top view. (b) Cross-section view.
4. Conclusion
In this study, an original groove machining method for glass, based on the TSL machining method, was developed. The method involved scanning a CW laser following the irradiation of a single femtosecond laser pulse. With this method, microgrooves with depths ranging from 50 to over 300 $\mathrm {\mu }$m and a width of approximately 10 $\mathrm {\mu }$m can be processed at a scanning speed of up to 200 mm/s, which is 25 times faster than conventional femtosecond laser processing. Additionally, the machining mechanism was investigated in detail. This method has the potential to provide faster manufacturing for many industrial applications
Funding
Japan Society for the Promotion of Science (21H01224).
Acknowledgments
We thank Dr. Keiichi Nakagawa of the University of Tokyo for his cooperation in observing the high-speed phenomena, and Mr. Yasuhiro Kuwana of AGC Inc. for his constructive discussion.
Disclosures
A.S., AGC Inc. (E); I.N., AGC Inc. (E); N.S., AGC Inc. (F).
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. M. Deubel, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3(7), 444–447 (2004). [CrossRef]
2. L. Ji, Y. Hu, J. Li, W. Wang, and Y. Jiang, “High-precision micro-through-hole array in quartz glass machined by infrared picosecond laser,” Appl. Phys. A 121(3), 1163–1169 (2015). [CrossRef]
3. Y. Li, K. Itoh, W. Watanabe, K. Yamada, D. Kuroda, J. Nishii, and Y. Jiang, “Three-dimensional hole drilling of silica glass from the rear surface with femtosecond laser pulses,” Opt. Lett. 26(23), 1912–1914 (2001). [CrossRef]
4. K. Sugioka, J. Xu, D. Wu, Y. Hanada, Z. Wang, Y. Cheng, and K. Midorikawa, “Femtosecond laser 3d micromachining: a powerful tool for the fabrication of microfluidic, optofluidic, and electrofluidic devices based on glass,” Lab Chip 14(18), 3447–3458 (2014). [CrossRef]
5. K. Sugioka and Y. Cheng, “Fabrication of 3d microfluidic structures inside glass by femtosecond laser micromachining,” Appl. Phys. A 114(1), 215–221 (2014). [CrossRef]
6. B. Wang, Y. Hua, Y. Ye, R. Chen, and Z. Li, “Transparent superhydrophobic solar glass prepared by fabricating groove-shaped arrays on the surface,” Appl. Surf. Sci. 426, 957–964 (2017). [CrossRef]
7. M. G. Schinker, “Subsurface damage mechanisms at high-speed ductile machining of optical glasses,” Precis. Eng. 13(3), 208–218 (1991). [CrossRef]
8. T. Moriwaki, E. Shamoto, and K. Inoue, “Ultraprecision ductile cutting of glass by applying ultrasonic vibration,” CIRP Ann. 41(1), 141–144 (1992). [CrossRef]
9. T. Ono and T. Matsumura, “Influence of tool inclination on brittle fracture in glass cutting with ball end mills,” J. Mater. Process. Technol. 202(1-3), 61–69 (2008). [CrossRef]
10. Y. Ito, T. Kizaki, R. Shinomoto, M. Ueki, N. Sugita, and M. Mitsuishi, “High-efficiency and precision cutting of glass by selective laser-assisted milling,” Precis. Eng. 47, 498–507 (2017). [CrossRef]
11. A. K. Dubey and V. Yadava, “Laser beam machining—a review,” Int. J. Mach. Tools Manuf. 48(6), 609–628 (2008). [CrossRef]
12. R. Yoshizaki, Y. Ito, N. Miyamoto, A. Shibata, I. Nagasawa, K. Nagato, and N. Sugita, “Abrupt initiation of material removal by focusing continuous-wave fiber laser on glass,” Appl. Phys. A 126(9), 715 (2020). [CrossRef]
13. G. Della Valle, R. Osellame, and P. Laporta, “Micromachining of photonic devices by femtosecond laser pulses,” J. Opt. A: Pure Appl. Opt. 11(1), 013001 (2009). [CrossRef]
14. S. Nikumb, Q. Chen, C. Li, H. Reshef, H. Zheng, H. Qiu, and D. Low, “Precision glass machining, drilling and profile cutting by short pulse lasers,” Thin Solid Films 477(1-2), 216–221 (2005). [CrossRef]
15. L. A. Hof and J. Abou Ziki, “Micro-hole drilling on glass substrates—a review,” Micromachines 8(2), 53 (2017). [CrossRef]
16. H. Jo, Y. Ito, J. Hattori, K. Nagato, and N. Sugita, “High-speed observation of damage generation during ultrashort pulse laser drilling of sapphire,” Opt. Commun. 495, 127122 (2021). [CrossRef]
17. Y. Hanada, K. Sugioka, I. Miyamoto, and K. Midorikawa, “Double-pulse irradiation by laser-induced plasma-assisted ablation (lipaa) and mechanisms study,” Appl. Surf. Sci. 248(1-4), 276–280 (2005). [CrossRef]
18. I. Miyamoto, K. Cvecek, Y. Okamoto, and M. Schmidt, “Internal modification of glass by ultrashort laser pulse and its application to microwelding,” Appl. Phys. A 114(1), 187–208 (2014). [CrossRef]
19. A. Ben-Yakar and R. L. Byer, “Femtosecond laser ablation properties of borosilicate glass,” J. Appl. Phys. 96(9), 5316–5323 (2004). [CrossRef]
20. A. Žemaitis, M. Gaidys, P. Gečys, M. Barkauskas, and M. Gedvilas, “Femtosecond laser ablation by bibursts in the mhz and ghz pulse repetition rates,” Opt. Express 29(5), 7641–7653 (2021). [CrossRef]
21. A. Žemaitis, P. Gečys, M. Barkauskas, G. Račiukaitis, and M. Gedvilas, “Highly-efficient laser ablation of copper by bursts of ultrashort tuneable (fs-ps) pulses,” Sci. Rep. 9(1), 12280 (2019). [CrossRef]
22. E. Bulushev, V. Bessmeltsev, A. Dostovalov, N. Goloshevsky, and A. Wolf, “High-speed and crack-free direct-writing of microchannels on glass by an ir femtosecond laser,” Opt. Lasers Eng. 79, 39–47 (2016). [CrossRef]
23. K. Mishchik, R. Beuton, O. D. Caulier, S. Skupin, B. Chimier, G. Duchateau, B. Chassagne, R. Kling, C. Hönninger, E. Mottay, and J. Lopez, “Improved laser glass cutting by spatio-temporal control of energy deposition using bursts of femtosecond pulses,” Opt. Express 25(26), 33271–33282 (2017). [CrossRef]
24. H. Shin and D. Kim, “Cutting thin glass by femtosecond laser ablation,” Opt. Lasers Technol. 102, 1–11 (2018). [CrossRef]
25. Y. Ito, R. Yoshizaki, N. Miyamoto, and N. Sugita, “Ultrafast and precision drilling of glass by selective absorption of fiber-laser pulse into femtosecond-laser-induced filament,” Appl. Phys. Lett. 113(6), 061101 (2018). [CrossRef]
26. R. Yoshizaki, Y. Ito, S. Yoshitake, C. Wei, A. Shibata, I. Nagasawa, K. Nagato, and N. Sugita, “Mechanism of material removal through transient and selective laser absorption into excited electrons in fused silica,” J. Appl. Phys. 130(5), 053102 (2021). [CrossRef]
27. R. Shinomoto, Y. Ito, T. Kizaki, K. Tatsukoshi, Y. Fukasawa, K. Nagato, N. Sugita, and M. Mitsuishi, “Experimental analysis of glass drilling with ultrashort pulse lasers,” Int. J. Automation Technol. 10(6), 863–873 (2016). [CrossRef]
28. K. Zhao, Z. Jia, W. Liu, J. Ma, and L. Wang, “Material removal with constant depth in cnc laser milling based on adaptive control of laser fluence,” Int. J. Adv. Manuf. Technol. 77(5-8), 797–806 (2015). [CrossRef]
29. M. K. Mohammed, U. Umer, O. Abdulhameed, and H. Alkhalefah, “Effects of laser fluence and pulse overlap on machining of microchannels in alumina ceramics using an nd: Yag laser,” Appl. Sci. 9(19), 3962 (2019). [CrossRef]
30. M. Sun, U. Eppelt, S. Russ, C. Hartmann, C. Siebert, J. Zhu, and W. Schulz, “Laser ablation mechanism of transparent dielectrics with picosecond laser pulses,” in Laser-Induced Damage in Optical Materials: 2012, vol. 8530 (International Society for Optics and Photonics, 2012), p. 853007.
31. M. Sun, U. Eppelt, S. Russ, C. Hartmann, C. Siebert, J. Zhu, and W. Schulz, “Numerical analysis of laser ablation and damage in glass with multiple picosecond laser pulses,” Opt. Express 21(7), 7858–7867 (2013). [CrossRef]
32. U. Eppelt, S. Russ, C. Hartmann, M. Sun, C. Siebert, and W. Schulz, “Diagnostic and simulation of ps-laser glass cutting,” in International Congress on Applications of Lasers & Electro-Optics, vol. 2012 (Laser Institute of America, 2012), pp. 835–844.
33. C. Wei, Y. Ito, R. Shinomoto, K. Nagato, and N. Sugita, “Simulation of ultrashort pulse laser drilling of glass considering heat accumulation,” Opt. Express 28(10), 15240–15249 (2020). [CrossRef]
34. Y. Ito, R. Shinomoto, K. Nagato, A. Otsu, K. Tatsukoshi, Y. Fukasawa, T. Kizaki, N. Sugita, and M. Mitsuishi, “Mechanisms of damage formation in glass in the process of femtosecond laser drilling,” Appl. Phys. A 124(2), 181 (2018). [CrossRef]
35. M. Sun, U. Eppelt, W. Schulz, and J. Zhu, “Role of thermal ionization in internal modification of bulk borosilicate glass with picosecond laser pulses at high repetition rates,” Opt. Mater. Express 3(10), 1716–1726 (2013). [CrossRef]
36. I. Miyamoto, K. Cvecek, and M. Schmidt, “Evaluation of nonlinear absorptivity in internal modification of bulk glass by ultrashort laser pulses,” Opt. Express 19(11), 10714–10727 (2011). [CrossRef]
37. A. Vogel and B. A. Rockwell, “Roles of tunneling, multiphoton ionization, and cascade ionization for femtosecond optical breakdown in aqueous media,” Tech. rep., Lubeck Medical Univ (Germany) Medical Laser Center (2009).
