Abstract

In accordance with the increasing demand for high-speed processing, the repetition rate of ultrashort pulse lasers has continued to increase. With the development of these lasers, there is a growing demand for the prediction of shapes processed at high repetition rates. However, the prediction of these shapes is a major challenge, because of the difficulty associated with the estimation of heat accumulation. In this study, we developed a simulation of ultrashort laser drilling in glass including heat accumulation calculation between pulses. In this simulation model, temperature is considered as an additional criterion of material removal, thus, the dependency of the repetition rate can be estimated. Two model parameters of laser absorption at high temperatures are investigated and determined by experiments under high environmental temperatures. Using the simulation model, high shape-prediction accuracy at high repetition rates was achieved and validated by comparison with experiments. This study may contribute to broadening the applications of high-repetition-rate ultrashort pulse lasers.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Glass micromachining is a key part of various processes such as the manufacturing of packages for integrated circuits [1,2] , microfluidic biochips [3,4] and optical waveguides [5–7]. In the micromachining of transparent materials such as glass and sapphire, ultrashort pulse lasers are a widespread processing tool that enable precise processing with minimal damage and heat-affected zones [8,9]. The processing result of ultrashort pulse laser is closely related to the processing conditions [10,11]. Therefore, the prediction of machining results under different processing conditions is needed.

Numerical simulation is the most effective method for shape prediction after ultrashort pulse laser machining and has been studied by a host of researchers [12–17]. Sun et al. succeeded in developing a simulation model for the ultrashort pulse laser drilling of glass utilizing a combination of the beam propagation method (BPM) and rate equation of electron density [18–20]. The BPM is used to calculate the intensity distribution of laser irradiation inside a glass material; the density of electrons can then be calculated from the irradiation intensity using the rate equation of electron density. Electron density is considered as the criterion of material removal in their model, meaning that when the electron density rises over the ablation threshold, the material is considered removed. The model shows high precision in the shape prediction of ultrashort pulse laser drilling. However, using their model, the dependence of the repetition rate cannot be reflected, although the repetition rate has a significant effect on the machining results because of the heat accumulation between laser pulses [21]. Moreover, in recent years, the application of high-repetition-rate pulse laser has become more common due to its high machining efficiency [22–25], therefore, it is necessary to consider heat accumulation between pulses [26]. In their simulation model, the electron density and lattice temperature are not associated, which prevents the heat accumulation from being calculated.

In the present work, we added another material removal criterion, namely, lattice temperature, to the simulation model. This means that other than the electron density, when the temperature rises over the boiling point, the material is also considered removed. To estimate the energy transfer between electrons and phonons, we conducted laser drilling experiments at high environmental temperatures. The experimental results showed that the depth of the drilled holes was dependent on the environmental temperature. These results were then adopted in the simulation model, enabling us to precisely estimate the heat accumulation effect. The improved model was validated by experimental results at a high repetition rate up to 100 kHz.

2. Methods

2.1 Simulation

In the simulation model, the BPM is used to calculate the electric field as the laser beam propagates into the glass. Assuming that the envelope varies slowly in the $z$ direction, a paraxial Helmholtz equation in a cylindrical coordinate system can be derived as follows:

$$2ik_{0}\frac{\partial E}{\partial z}={-}\frac{\partial ^2E}{\partial r^2}-\frac{1}{r}\frac{\partial E}{\partial r}-{k_{0}}^{2}\left( \varepsilon _{\textrm{r}}-1 \right) E \textrm{,}$$
where $k_{0}$ is the wave number of the laser beam, $E$ is the electric field and $r$ is the radial distance. In Eq. (1), the relative complex permittivity $\varepsilon _{\textrm {r}}$ of the material is expressed as
$$\varepsilon _{\textrm {r}}\left( \omega \right) =1-\frac{\rho _{\textrm{B}}e^2}{m\varepsilon _{0}}\frac{\omega ^2-{\omega _{0}}^{2}-i\chi \omega}{{\bigg(} \omega ^2-{\omega _{0}}^{2} {\bigg)} ^2+\chi ^2\omega ^2} \textrm{,}$$
where $\rho _{\textrm{B}}$ is the bound electron density, $\omega$ is the angular frequency of the laser, $m_{\textrm {e}}$ is the effective mass of a quasi-free electron, $e$ is the elementary charge, $\varepsilon _{0}$ is the vacuum dielectric permittivity, $\omega _{0}$ is the frequency of the harmonic oscillators, and $\chi$ is the damping constant [27]. The free electron density $\rho$ is calculated based on the rate equation [18,28,29]:
$$\frac{\partial \rho}{\partial t}=\sigma I^k+\alpha _{\textrm{c}}I\rho -\eta _{\textrm{rec}}\rho ^2-\eta _{\textrm{diff}}\rho \textrm{,}$$
where $t$ is time, $I$ is the intensity, $k$ is the number of photons for multi-photon ionization, $\sigma$ is the coefficient of multi-photon ionization, $\alpha _{\textrm {c}}$ is the coefficient of cascade ionization, $\eta _{\textrm {rec}}$ is the coefficient of recombination, and $\eta _{\textrm {diff}}$ is the coefficient of diffusion; the distribution of free electron density can be obtained with Eq. (3). The material in the region where the free electron density exceeds the plasma density [28], which is expressed as $\rho _{\textrm {crit}}={\omega ^2m_{\textrm {e}}\varepsilon _0}/{e^2}$, is considered to be removed. The energy of the electrons in the unremoved material is then transferred to phonons, causing an increase in lattice temperature, which is expressed as follows [30,31]:
$$\varDelta T=\frac{E_{\textrm{av}}}{3nk_{\textrm{B}}}\int_0^{\infty}{\left( \sigma I^k+\alpha _cI\rho \right) dt}\textrm{,}$$
where $E_{\textrm {av}}$ is the average electron energy, $n$ is the number of atoms in unit volume, and $k_{\textrm {B}}$ is the Boltzmann constant [32]. The two-temperature model (TTM) is a representative calculating model for the heat-transfer calculation between free electrons and phonons [33–35]. However, in this study, we have assumed that the entire energy of free electrons is transferred to phonons, because the heat capacity of electrons is small compared to that of the lattice [36]. After the energy transfer from free electrons to phonons, the heat diffusion process was calculated, because the electron-phonon relaxation time is negligible compared with the time scale of the heat diffusion process [37].

The damping constant $\chi$ in Eq. (2) is a key factor in the model as it describes the relationship between the dielectric properties and the free electron density. In previous studies, $\chi$ is usually given by:

$$\chi =\chi _{\max}\frac{\rho _{\max}}{\rho _{\max}+\beta \rho _{\textrm{crit}}} \textrm{,}$$
where $\rho _{\textrm {max}}$ is the maximum free-electron density at each position within one pulse duration and $\chi _{\max }$ is the maximum value of the damping constant [18]. The $\rho _{\textrm {max}}$ is calculated from the temporal course of the laser intensity using Eq. (3). $\beta$ is a model parameter determined by the laser processing experiments [38]. In our study, we added another model parameter to this model to increase its flexibility. In this model, $\chi$ is given by
$$\chi =\chi _{\max}\frac{\rho _{\max}^{\alpha}}{\rho _{\max}^{\alpha}+\beta \rho _{crit}^{\alpha}}\textrm{,}$$
where $\alpha$ and $\beta$ are model parameters to be determined. The relative complex permittivity of the material under different free electron densities can be then calculated via Eq. (2) and Eq. (6). From the obtained temperature distribution, the material in the region where the temperature exceeds the boiling point, is considered to be removed by evaporation.

The heat diffusion process between pulses is then calculated via the commercial finite element method (FEM) software ABAQUS (Dassault Systemes). Axial symmetrical model was used for the calculation. The shape of the model was calculated from the BPM simulation. Temperature dependent specific heat capacity and thermal conductivity were used. The temperature field obtained from the free electron density was used as the predefined field. Heat transfer in the form of radiation and thermal conduction at the top and bottom surface of the sample was taken into consideration. Emissivity was set to 0.95 and the heat transfer coefficient was set to 5 W/($\textrm {m}^2$ K). Environmental temperature was set to 25 °C. As for the boundary condition, the side surface perpendicular to the top surface was set as an isothermal wall with 25 °C.

The temperature distribution after the heat diffusion and the drilled shape are then used for the calculation of the next laser pulse and, the effect of the heat accumulation can be taken into account.

2.2 Experiment

The model works correctly only when proper values of the two model parameters $\alpha$ and $\beta$ are determined. We estimated $\alpha$ and $\beta$ by conducting the drilling experiment at high environmental temperatures.

Figure 1 shows the experimental setup. An aluminosilicate glass sample (AGC; AN100) was clamped and heated by a ceramic heater (Sakaguchi; MS–5). The temperature of the ceramic heater was measured by a thermocouple. The ceramic heater and thermocouple were both connected to a temperature controller (Misumi; MTCS), allowing us to stabilize the temperature of the ceramic heater with feedback control. The temperature range of the ceramic heater was up to 500 °C. The sample and ceramic heater were surrounded by an insulator to reduce heat loss. The glass sample partially protruded from the ceramic heater so that the sample was exposed to the laser pulses. A Ti:Sapphire femtosecond laser was used for the drilling experiment. The pulse width of the laser pulses was 228 fs, repetition rate was 1 kHz, wavelength was 514 nm, and pulse energy was 25 $\mu$J. When the temperature of the ceramic heater was stabilized, indicating that the temperature of the glass sample was also stabilized, multiple laser pulses were then focused on the surface of the sample with a spot diameter of 13.6 $\mu$m using an objective lens (Mitsutoyo; M Plan Apo NIR 5$\times$) with a focal length of 40 mm to drill holes. The location where the laser pulses were focused was 1 mm away from the edge of the ceramic heater. After the experiment, drilled holes were observed by an optical microscope.

 

Fig. 1. (a) Illustration of the experimental setup. (b) Actual experimental setup.

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We measured the temperature at the location where laser pulses were focused using a thermography (Nippon Avionics; InfRec R300) so that the temperature of the ceramic heater and that of the processed area were associated. One of the pictures taken by the thermography is shown in Fig. 2(a). The temperature distribution of the area, which is 1 mm away from the ceramic heater (the area surrounded by the rectangle with a white solid line in Fig. 2(a)), is shown in Fig. 2(b), where $T_{\textrm {c}}$ is the temperature of the ceramic heater. Here, we assumed that the temperature between the two orange dotted lines is approximately uniform. Therefore, we calculated the average within this region and considered it to be the temperature of the processed region.

 

Fig. 2. (a) Thermography of the heated sample. (b) Temperature distribution of the measured region

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3. Results and discussion

The model parameters $\alpha$ and $\beta$ significantly influence the performance of the model. The temperature distributions after the first laser pulse was focused, calculated with different values of $\alpha$ and $\beta$, are shown in Fig. 3.

 

Fig. 3. Dependence of simulated temperature distribution after one pulse on values of (a) $\alpha$ and (b) $\beta$. (c) Comparison of temperature distribution with different conditions that allow for similar drilled-hole depths. (Left: depth = 0.626 $\mu \textrm{m}$, right: depth = 0.680 $\mu \textrm{m}$)

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Both the changes of $\alpha$ (Fig. 3(a)) and $\beta$ (Fig. 3(b)) have similar effects on the damping constant $\chi$; as the value of $\alpha$ or $\beta$ increases, $\chi$ decreases, and, therefore, the penetration depth of the laser pulse increases. As the inner area is heated with a larger $\alpha$ or $\beta$, the depth of the hole drilled by one pulse increases, as shown in Table 1. These results validated the increase of the model flexibility. As an example, with different values of $\alpha$ and $\beta$, the results of temperature distribution were different as compared in Fig. 3(c); however, the results of the hole depths can be similar as shown in Table 1. The hole depths were 0.626 $\mu \textrm{m}$ when $\alpha$ = 5.0 and $\beta$ = 0.01, and 0.680 ${\mu } \textrm {m}$ when $\alpha$ = 2.0 and $\beta$ = 1.0.

Tables Icon

Table 1. Simulated depth [$\mu$m] of holes drilled by one laser pulse, with different values of $\alpha$ and $\beta$.

View Table

The results of the drilling experiment are shown in Fig. 4. The depth of the drilled holes increased as the environmental temperature rose. Here, we considered that the final temperature difference of the material was resulted from the difference of initial temperature (environmental temperature). If the initial temperature is higher, there would be more volume of the material reaching the boiling point (criteria of removal) and considered removed, causing the increase of drilling depth. The absorption coefficient of the material at 25 °C and higher temperature (up to 370 °C) are not significantly different [39]. Therefore, it is appropriate to consider that the material absorbed almost the same energy from the laser irradiation at different environmental temperature (up to 370 °C), indicating that the temperature increments of the material should be nearly the same, although the increments could be slightly different due to the different specific heat capacity at different temperature.

 

Fig. 4. (a) Shape of holes drilled by 100 pulses at different environmental temperatures. (b) Depth of drilled holes at different environmental temperatures.

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To fit the experimental results of hole diameter and depth shown in Fig. 5(a), two model parameters $\alpha$ = 4.6 and $\beta$ = 0.1 were selected. The results of the simulation under different environmental temperatures are shown in Fig. 5(b) and compared with experimental results in Fig. 5(c). The conditions of laser irradiation used in the simulation were the same as those used in the experiments. The simulation results agree with the experimental results when the environmental temperature was 200 °C or lower. When the environmental temperature was over 300 °C, the simulation could not reproduce the results of the experiment, because the melted material caused the instability of drilled shape. The diameter near the top of the hole was slightly different from the experimental result, presumably because the reflow and resolidification were not taken into consideration in our simulation model.

 

Fig. 5. (a) Shape of holes drilled by 50 pulses at different environmental temperatures. (b) Shape and temperature distribution of holes drilled by 50 pulses at different environmental temperatures. (c) Depth comparison of experiment and simulation after 50 pulses at different environmental temperatures.

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The distribution of laser intensity, distribution of free electron density and temporal course of the temperature distribution after the 100th pulse are shown in Fig. 6. The non-uniform initial temperature distribution (shown in Fig. 6(c) at 0.0 $\mu$s) was resulted from non-uniform distribution of laser intensity inside the sample (shown in Fig. 6(a)) and distribution of free electron density (shown in Fig. 6(b)), which were calculated by the BPM simulation. The others were the results of heat diffusion simulation. Until 0.1 ms after the pulse, the heat was not diffused completely. However, at 1 ms after the pulse, there was little heat left, indicating that if the repetition rate of the laser was lower than 1 kHz, the effect of heat accumulation was small.

 

Fig. 6. (a) Distribution of laser intensity, (b) distribution of free electron density and (c) temporal course of temperature distribution after the 100th pulse.

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It is obvious from Fig. 6(c4) that at 10 $\mu$s the pulse, which should be the timing for next pulse when the repetition rate is 100 kHz, there are some regions where the temperature is over the environmental temperature scope of our experiments. However, the proportion of these regions is approximately 6% of the region where temperature is over 105 °C. Moreover, they are totally located near the top of the hole. Besides, the maximum temperature of these regions is lower than 825 °C. Therefore, although the lack of experimental data at higher environmental temperature may lead to insufficient prediction of the top shape of the crater, it will not impair the overall validity of the simulation model. Especially, it will not affect the prediction accuracy of depth and diameter of the machined holes, which are our top concerns. Within 50 $\mu$s from the 100th pulse, the temperature of whole region falls within the scope of 25–370 °C, so the prediction of machining up to 20 kHz has higher validity.

To validate the shape prediction performance of the simulation model considering the effect of heat accumulation, we compared the simulation and experiment results at varying repetition rates. As shown in Fig. 7, the simulation results adequately reproduced the depth increase of the drilled holes as the repetition rate rose. The simulation model showed favourable shape prediction accuracy up to a repetition rate of 100 kHz.

 

Fig. 7. (a) Shape of holes drilled by 50 pulses at different repetition rates. (b) Shape of holes drilled by 50 pulses at different repetition rates. (c) Depth comparison of experiment and simulation after 50 pulses at different repetition rates.

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4. Conclusion

In this study, we developed a simulation model for ultrashort pulse laser drilling at high repetition rates. We estimated the temperature distribution from the free electron density and adopted two material-removal criteria: free electron density above plasma density and temperature above the boiling point. Two model parameters were used for high flexibility, enabling the model to accurately calculate the heat generated from the laser pulse. The roles of the two parameters were investigated and their values were selected based on experiments at high temperatures. The shape prediction performance of the model at high repetition rates was confirmed by experiments. This study may meet the industrial need of shape prediction in various applications of high-repetition-rate ultrashort pulse lasers.

Funding

Japan Society for the Promotion of Science (19K23477).

Acknowledgements

This study was conducted as part of the Social Cooperation Programs of the University of Tokyo "Creation of High-tech Glass," financially supported by AGC Inc.

Disclosures

The authors declare no conflict of interest.

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8. P. Gečys, J. Dudutis, and G. Račiukaitis, “Nanosecond laser processing of soda-lime glass,” J. Laser Micro/Nanoeng. 10(5), 254 (2015).

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References

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  • Publication
  1. V. Sukumaran, Q. Chen, F. Liu, N. Kumbhat, T. Bandyopadhyay, H. Chan, S. Min, C. Nopper, V. Sundaram, and R. Tummala, “Through-package-via formation and metallization of glass interposers,” Proc. - Electron. Components Technol. Conf. pp. 557–563 (2010).
  2. F. Flamini, L. Magrini, A. S. Rab, N. Spagnolo, V. D’Ambrosio, P. Mataloni, F. Sciarrino, T. Zandrini, A. Crespi, R. Ramponi, and R. Osellame, “Thermally reconfigurable quantum photonic circuits at telecom wavelength by femtosecond laser micromachining,” Light: Sci. Appl. 4(11), e354 (2015).
    [Crossref]
  3. F. He, H. Xu, Y. Cheng, J. Ni, H. Xiong, Z. Xu, K. Sugioka, and K. Midorikawa, “Fabrication of microfluidic channels with a circular cross section using spatiotemporally focused femtosecond laser pulses,” Opt. Lett. 35(7), 1106 (2010).
    [Crossref]
  4. Y. Liao, J. Song, E. Li, Y. Luo, Y. Shen, D. Chen, Y. Cheng, Z. Xu, K. Sugioka, and K. Midorikawa, “Rapid prototyping of three-dimensional microfluidic mixers in glass by femtosecond laser direct writing,” Lab Chip 12(4), 746–749 (2012).
    [Crossref]
  5. T. T. Fernandez, S. M. Eaton, G. Della Valle, R. M. Vazquez, M. Irannejad, G. Jose, A. Jha, G. Cerullo, R. Osellame, and P. Laporta, “Femtosecond laser written optical waveguide amplifier in phospho-tellurite glass,” Opt. Express 18(19), 20289 (2010).
    [Crossref]
  6. T. Calmano, J. Siebenmorgen, O. Hellmig, K. Petermann, and G. Huber, “Nd:YAG waveguide laser with 1.3 W output power, fabricated by direct femtosecond laser writing,” Appl. Phys. B: Lasers Opt. 100(1), 131–135 (2010).
    [Crossref]
  7. L. B. Fletcher, J. J. Witcher, N. Troy, S. T. Reis, R. K. Brow, and D. M. Krol, “Direct femtosecond laser waveguide writing inside zinc phosphate glass,” Opt. Express 19(9), 7929 (2011).
    [Crossref]
  8. P. Gečys, J. Dudutis, and G. Račiukaitis, “Nanosecond laser processing of soda-lime glass,” J. Laser Micro/Nanoeng. 10(5), 254 (2015).
  9. J. Dudutis, R. Stonys, G. Račiukaitis, and P. Gečys, “Glass dicing with elliptical bessel beam,” Opt. Laser Technol. 111, 331–337 (2019).
    [Crossref]
  10. 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. Autom. Technol. 10(6), 863–873 (2016).
    [Crossref]
  11. M. Sun, U. Eppelt, C. Hartmann, W. Schulz, J. Zhu, and Z. Lin, “Towards crack-free ablation cutting of thin glass sheets with picosecond pulsed lasers,” Pac. Rim Laser Damage 2017: Opt. Mater. for High-Power Lasers 10339, 103390O (2017).
    [Crossref]
  12. K.-H. Leitz, H. Koch, A. Otto, and M. Schmidt, “Numerical simulation of process dynamics during laser beam drilling with short pulses,” Appl. Phys. A 106(4), 885–891 (2012).
    [Crossref]
  13. A. Otto and M. Schmidt, “Towards a universal numerical simulation model for laser material processing,” Phys. Procedia 5, 35–46 (2010).
    [Crossref]
  14. Y. Zhang, Z. Shen, and X. Ni, “Modeling and simulation on long pulse laser drilling processing,” Int. J. Heat Mass Transfer 73, 429–437 (2014).
    [Crossref]
  15. X.-X. Liang, Z. Zhang, and A. Vogel, “Multi-rate-equation modeling of the energy spectrum of laser-induced conduction band electrons in water,” Opt. Express 27(4), 4672–4693 (2019).
    [Crossref]
  16. X. Liang, N. Linz, J. Noack, and A. Vogel, “Modelling of optical breakdown in dielectrics including thermal effects relevant for nanosecond pulses and sequences of ultra-short laser pulses,” in CLEO/Europe-EQEC 2009-European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference, (IEEE, 2009), p. 1.
  17. A. Vogel, N. Linz, S. Freidank, and X. Liang, “Controlled nonlinear energy deposition in transparent materials: experiments and theory,” in AIP Conference Proceedings, vol. 1278 (American Institute of Physics, 2010), pp. 51–55.
  18. 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 (2013).
    [Crossref]
  19. U. Eppelt, S. Russ, C. Hartmann, M. Sun, C. Siebert, and W. Schulz, “Diagnostic and simulation of ps-laser glass cutting,” ICALEO 2012 - 31st International Congress on Applications of Lasers and Electro-Optics pp. 835–844 (2012).
  20. 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,” Proc. SPIE 8530, 853007 (2012).
    [Crossref]
  21. M. Sun, U. Eppelt, C. Hartmann, W. Schulz, J. Zhu, and Z. Lin, “Damage morphology and mechanism in ablation cutting of thin glass sheets with picosecond pulsed lasers,” Opt. Laser Technol. 80, 227–236 (2016).
    [Crossref]
  22. R. Streubel, S. Barcikowski, and B. Gökce, “Continuous multigram nanoparticle synthesis by high-power, high-repetition-rate ultrafast laser ablation in liquids,” Opt. Lett. 41(7), 1486 (2016).
    [Crossref]
  23. T. Witting, C. H. Lu, F. J. Furch, A. H. Kung, and M. J. Vrakking, “Near single-cycle laser pulses at high average power and high repetition rate from an all-solid-state setup,” 2018 Conf. Lasers and Electro-Optics, CLEO 2018 - Proc. 26, SW3N.6 (2018).
    [Crossref]
  24. S. Hädrich, T. Eidam, A. Hoffmann, S. Wunderlich, F. Jansen, D. Steil, S. Mathias, and J. Limpert, “High photon flux and high repetition rate fiber-laser driven HHG,” Opt. InfoBase Conf. Pap.Part F82-CLEO_Europe 2017, 172002 (2017).
  25. E. Markauskas and P. Gečys, “Thin water film assisted glass ablation with a picosecond laser,” Procedia CIRP 74, 328–332 (2018).
    [Crossref]
  26. G. Raciukaitis, M. Brikas, P. Gecys, and M. Gedvilas, “Accumulation effects in laser ablation of metals with high-repetition-rate lasers,” in High-Power Laser Ablation VII, vol. 7005 (International Society for Optics and Photonics, 2008), p. 70052L.
  27. L. Jiang and H. L. Tsai, “Prediction of crater shape in femtosecond laser ablation of dielectrics,” J. Phys. D: Appl. Phys. 37(10), 1492–1496 (2004).
    [Crossref]
  28. A. Vogel, J. Noack, G. Hüttman, and G. Paltauf, “Mechanisms of femtosecond laser nanosurgery of cells and tissues,” Appl. Phys. B: Lasers Opt. 81(8), 1015–1047 (2005).
    [Crossref]
  29. P. K. Kennedy, “A First-Order Model for Computation of Laser-Induced Breakdown Thresholds in Ocular and Aqueous Media: Part I—Theory,” IEEE J. Quantum Electron. 31(12), 2241–2249 (1995).
    [Crossref]
  30. 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 (2013).
    [Crossref]
  31. 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]
  32. N. W. Ashcroft and N. D. Mermin, “Solid state physics,” ch 22, (1976).
  33. A. Ruf, D. Breitling, P. Berger, F. Dausinger, and H. Huegel, “Modeling and investigation of melt ejection dynamics for laser drilling with short pulses,” Third Int. Symp. on Laser Precis. Microfabr. 4830, 73 (2003).
    [Crossref]
  34. H. E. Elsayed-Ali, “Comment on Thermal response of metals to ultrashort-pulse laser excitation,” Phys. Rev. Lett. 64(15), 1846 (1990).
    [Crossref]
  35. B. N. Chichkov, C. Momma, S. Nolte, F. von Alvensleben, and A. Tünnermann, “Femtosecond, picosecond and nanosecond laser ablation of solids,” Appl. Phys. A 63(2), 109–115 (1996).
    [Crossref]
  36. T. Q. Qiu and C. L. Tien, “Heat transfer mechanisms during short-pulse laser heating of metals,” J. Heat Transfer 115(4), 835–841 (1993).
    [Crossref]
  37. R. R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photonics 2(4), 219–225 (2008).
    [Crossref]
  38. J. V. De Aldana, C. Méndez, L. Roso, and P. Moreno, “Propagation of ablation channels with multiple femtosecond laser pulses in dielectrics: numerical simulations and experiments,” J. Phys. D: Appl. Phys. 38(16), 2764–2768 (2005).
    [Crossref]
  39. B. Wedding, “Measurements of high-temperature absorption coefficients of glasses,” J. Am. Ceram. Soc. 58(3-4), 102–105 (1975).
    [Crossref]

2019 (2)

J. Dudutis, R. Stonys, G. Račiukaitis, and P. Gečys, “Glass dicing with elliptical bessel beam,” Opt. Laser Technol. 111, 331–337 (2019).
[Crossref]

X.-X. Liang, Z. Zhang, and A. Vogel, “Multi-rate-equation modeling of the energy spectrum of laser-induced conduction band electrons in water,” Opt. Express 27(4), 4672–4693 (2019).
[Crossref]

2018 (3)

T. Witting, C. H. Lu, F. J. Furch, A. H. Kung, and M. J. Vrakking, “Near single-cycle laser pulses at high average power and high repetition rate from an all-solid-state setup,” 2018 Conf. Lasers and Electro-Optics, CLEO 2018 - Proc. 26, SW3N.6 (2018).
[Crossref]

E. Markauskas and P. Gečys, “Thin water film assisted glass ablation with a picosecond laser,” Procedia CIRP 74, 328–332 (2018).
[Crossref]

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]

2017 (1)

M. Sun, U. Eppelt, C. Hartmann, W. Schulz, J. Zhu, and Z. Lin, “Towards crack-free ablation cutting of thin glass sheets with picosecond pulsed lasers,” Pac. Rim Laser Damage 2017: Opt. Mater. for High-Power Lasers 10339, 103390O (2017).
[Crossref]

2016 (3)

M. Sun, U. Eppelt, C. Hartmann, W. Schulz, J. Zhu, and Z. Lin, “Damage morphology and mechanism in ablation cutting of thin glass sheets with picosecond pulsed lasers,” Opt. Laser Technol. 80, 227–236 (2016).
[Crossref]

R. Streubel, S. Barcikowski, and B. Gökce, “Continuous multigram nanoparticle synthesis by high-power, high-repetition-rate ultrafast laser ablation in liquids,” Opt. Lett. 41(7), 1486 (2016).
[Crossref]

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. Autom. Technol. 10(6), 863–873 (2016).
[Crossref]

2015 (2)

P. Gečys, J. Dudutis, and G. Račiukaitis, “Nanosecond laser processing of soda-lime glass,” J. Laser Micro/Nanoeng. 10(5), 254 (2015).

F. Flamini, L. Magrini, A. S. Rab, N. Spagnolo, V. D’Ambrosio, P. Mataloni, F. Sciarrino, T. Zandrini, A. Crespi, R. Ramponi, and R. Osellame, “Thermally reconfigurable quantum photonic circuits at telecom wavelength by femtosecond laser micromachining,” Light: Sci. Appl. 4(11), e354 (2015).
[Crossref]

2014 (1)

Y. Zhang, Z. Shen, and X. Ni, “Modeling and simulation on long pulse laser drilling processing,” Int. J. Heat Mass Transfer 73, 429–437 (2014).
[Crossref]

2013 (2)

2012 (3)

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,” Proc. SPIE 8530, 853007 (2012).
[Crossref]

K.-H. Leitz, H. Koch, A. Otto, and M. Schmidt, “Numerical simulation of process dynamics during laser beam drilling with short pulses,” Appl. Phys. A 106(4), 885–891 (2012).
[Crossref]

Y. Liao, J. Song, E. Li, Y. Luo, Y. Shen, D. Chen, Y. Cheng, Z. Xu, K. Sugioka, and K. Midorikawa, “Rapid prototyping of three-dimensional microfluidic mixers in glass by femtosecond laser direct writing,” Lab Chip 12(4), 746–749 (2012).
[Crossref]

2011 (1)

2010 (4)

T. T. Fernandez, S. M. Eaton, G. Della Valle, R. M. Vazquez, M. Irannejad, G. Jose, A. Jha, G. Cerullo, R. Osellame, and P. Laporta, “Femtosecond laser written optical waveguide amplifier in phospho-tellurite glass,” Opt. Express 18(19), 20289 (2010).
[Crossref]

T. Calmano, J. Siebenmorgen, O. Hellmig, K. Petermann, and G. Huber, “Nd:YAG waveguide laser with 1.3 W output power, fabricated by direct femtosecond laser writing,” Appl. Phys. B: Lasers Opt. 100(1), 131–135 (2010).
[Crossref]

F. He, H. Xu, Y. Cheng, J. Ni, H. Xiong, Z. Xu, K. Sugioka, and K. Midorikawa, “Fabrication of microfluidic channels with a circular cross section using spatiotemporally focused femtosecond laser pulses,” Opt. Lett. 35(7), 1106 (2010).
[Crossref]

A. Otto and M. Schmidt, “Towards a universal numerical simulation model for laser material processing,” Phys. Procedia 5, 35–46 (2010).
[Crossref]

2008 (1)

R. R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photonics 2(4), 219–225 (2008).
[Crossref]

2005 (2)

J. V. De Aldana, C. Méndez, L. Roso, and P. Moreno, “Propagation of ablation channels with multiple femtosecond laser pulses in dielectrics: numerical simulations and experiments,” J. Phys. D: Appl. Phys. 38(16), 2764–2768 (2005).
[Crossref]

A. Vogel, J. Noack, G. Hüttman, and G. Paltauf, “Mechanisms of femtosecond laser nanosurgery of cells and tissues,” Appl. Phys. B: Lasers Opt. 81(8), 1015–1047 (2005).
[Crossref]

2004 (1)

L. Jiang and H. L. Tsai, “Prediction of crater shape in femtosecond laser ablation of dielectrics,” J. Phys. D: Appl. Phys. 37(10), 1492–1496 (2004).
[Crossref]

2003 (1)

A. Ruf, D. Breitling, P. Berger, F. Dausinger, and H. Huegel, “Modeling and investigation of melt ejection dynamics for laser drilling with short pulses,” Third Int. Symp. on Laser Precis. Microfabr. 4830, 73 (2003).
[Crossref]

1996 (1)

B. N. Chichkov, C. Momma, S. Nolte, F. von Alvensleben, and A. Tünnermann, “Femtosecond, picosecond and nanosecond laser ablation of solids,” Appl. Phys. A 63(2), 109–115 (1996).
[Crossref]

1995 (1)

P. K. Kennedy, “A First-Order Model for Computation of Laser-Induced Breakdown Thresholds in Ocular and Aqueous Media: Part I—Theory,” IEEE J. Quantum Electron. 31(12), 2241–2249 (1995).
[Crossref]

1993 (1)

T. Q. Qiu and C. L. Tien, “Heat transfer mechanisms during short-pulse laser heating of metals,” J. Heat Transfer 115(4), 835–841 (1993).
[Crossref]

1990 (1)

H. E. Elsayed-Ali, “Comment on Thermal response of metals to ultrashort-pulse laser excitation,” Phys. Rev. Lett. 64(15), 1846 (1990).
[Crossref]

1975 (1)

B. Wedding, “Measurements of high-temperature absorption coefficients of glasses,” J. Am. Ceram. Soc. 58(3-4), 102–105 (1975).
[Crossref]

Ashcroft, N. W.

N. W. Ashcroft and N. D. Mermin, “Solid state physics,” ch 22, (1976).

Bandyopadhyay, T.

V. Sukumaran, Q. Chen, F. Liu, N. Kumbhat, T. Bandyopadhyay, H. Chan, S. Min, C. Nopper, V. Sundaram, and R. Tummala, “Through-package-via formation and metallization of glass interposers,” Proc. - Electron. Components Technol. Conf. pp. 557–563 (2010).

Barcikowski, S.

Berger, P.

A. Ruf, D. Breitling, P. Berger, F. Dausinger, and H. Huegel, “Modeling and investigation of melt ejection dynamics for laser drilling with short pulses,” Third Int. Symp. on Laser Precis. Microfabr. 4830, 73 (2003).
[Crossref]

Breitling, D.

A. Ruf, D. Breitling, P. Berger, F. Dausinger, and H. Huegel, “Modeling and investigation of melt ejection dynamics for laser drilling with short pulses,” Third Int. Symp. on Laser Precis. Microfabr. 4830, 73 (2003).
[Crossref]

Brikas, M.

G. Raciukaitis, M. Brikas, P. Gecys, and M. Gedvilas, “Accumulation effects in laser ablation of metals with high-repetition-rate lasers,” in High-Power Laser Ablation VII, vol. 7005 (International Society for Optics and Photonics, 2008), p. 70052L.

Brow, R. K.

Calmano, T.

T. Calmano, J. Siebenmorgen, O. Hellmig, K. Petermann, and G. Huber, “Nd:YAG waveguide laser with 1.3 W output power, fabricated by direct femtosecond laser writing,” Appl. Phys. B: Lasers Opt. 100(1), 131–135 (2010).
[Crossref]

Cerullo, G.

Chan, H.

V. Sukumaran, Q. Chen, F. Liu, N. Kumbhat, T. Bandyopadhyay, H. Chan, S. Min, C. Nopper, V. Sundaram, and R. Tummala, “Through-package-via formation and metallization of glass interposers,” Proc. - Electron. Components Technol. Conf. pp. 557–563 (2010).

Chen, D.

Y. Liao, J. Song, E. Li, Y. Luo, Y. Shen, D. Chen, Y. Cheng, Z. Xu, K. Sugioka, and K. Midorikawa, “Rapid prototyping of three-dimensional microfluidic mixers in glass by femtosecond laser direct writing,” Lab Chip 12(4), 746–749 (2012).
[Crossref]

Chen, Q.

V. Sukumaran, Q. Chen, F. Liu, N. Kumbhat, T. Bandyopadhyay, H. Chan, S. Min, C. Nopper, V. Sundaram, and R. Tummala, “Through-package-via formation and metallization of glass interposers,” Proc. - Electron. Components Technol. Conf. pp. 557–563 (2010).

Cheng, Y.

Y. Liao, J. Song, E. Li, Y. Luo, Y. Shen, D. Chen, Y. Cheng, Z. Xu, K. Sugioka, and K. Midorikawa, “Rapid prototyping of three-dimensional microfluidic mixers in glass by femtosecond laser direct writing,” Lab Chip 12(4), 746–749 (2012).
[Crossref]

F. He, H. Xu, Y. Cheng, J. Ni, H. Xiong, Z. Xu, K. Sugioka, and K. Midorikawa, “Fabrication of microfluidic channels with a circular cross section using spatiotemporally focused femtosecond laser pulses,” Opt. Lett. 35(7), 1106 (2010).
[Crossref]

Chichkov, B. N.

B. N. Chichkov, C. Momma, S. Nolte, F. von Alvensleben, and A. Tünnermann, “Femtosecond, picosecond and nanosecond laser ablation of solids,” Appl. Phys. A 63(2), 109–115 (1996).
[Crossref]

Crespi, A.

F. Flamini, L. Magrini, A. S. Rab, N. Spagnolo, V. D’Ambrosio, P. Mataloni, F. Sciarrino, T. Zandrini, A. Crespi, R. Ramponi, and R. Osellame, “Thermally reconfigurable quantum photonic circuits at telecom wavelength by femtosecond laser micromachining,” Light: Sci. Appl. 4(11), e354 (2015).
[Crossref]

D’Ambrosio, V.

F. Flamini, L. Magrini, A. S. Rab, N. Spagnolo, V. D’Ambrosio, P. Mataloni, F. Sciarrino, T. Zandrini, A. Crespi, R. Ramponi, and R. Osellame, “Thermally reconfigurable quantum photonic circuits at telecom wavelength by femtosecond laser micromachining,” Light: Sci. Appl. 4(11), e354 (2015).
[Crossref]

Dausinger, F.

A. Ruf, D. Breitling, P. Berger, F. Dausinger, and H. Huegel, “Modeling and investigation of melt ejection dynamics for laser drilling with short pulses,” Third Int. Symp. on Laser Precis. Microfabr. 4830, 73 (2003).
[Crossref]

De Aldana, J. V.

J. V. De Aldana, C. Méndez, L. Roso, and P. Moreno, “Propagation of ablation channels with multiple femtosecond laser pulses in dielectrics: numerical simulations and experiments,” J. Phys. D: Appl. Phys. 38(16), 2764–2768 (2005).
[Crossref]

Della Valle, G.

Dudutis, J.

J. Dudutis, R. Stonys, G. Račiukaitis, and P. Gečys, “Glass dicing with elliptical bessel beam,” Opt. Laser Technol. 111, 331–337 (2019).
[Crossref]

P. Gečys, J. Dudutis, and G. Račiukaitis, “Nanosecond laser processing of soda-lime glass,” J. Laser Micro/Nanoeng. 10(5), 254 (2015).

Eaton, S. M.

Eidam, T.

S. Hädrich, T. Eidam, A. Hoffmann, S. Wunderlich, F. Jansen, D. Steil, S. Mathias, and J. Limpert, “High photon flux and high repetition rate fiber-laser driven HHG,” Opt. InfoBase Conf. Pap.Part F82-CLEO_Europe 2017, 172002 (2017).

Elsayed-Ali, H. E.

H. E. Elsayed-Ali, “Comment on Thermal response of metals to ultrashort-pulse laser excitation,” Phys. Rev. Lett. 64(15), 1846 (1990).
[Crossref]

Eppelt, U.

M. Sun, U. Eppelt, C. Hartmann, W. Schulz, J. Zhu, and Z. Lin, “Towards crack-free ablation cutting of thin glass sheets with picosecond pulsed lasers,” Pac. Rim Laser Damage 2017: Opt. Mater. for High-Power Lasers 10339, 103390O (2017).
[Crossref]

M. Sun, U. Eppelt, C. Hartmann, W. Schulz, J. Zhu, and Z. Lin, “Damage morphology and mechanism in ablation cutting of thin glass sheets with picosecond pulsed lasers,” Opt. Laser Technol. 80, 227–236 (2016).
[Crossref]

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 (2013).
[Crossref]

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 (2013).
[Crossref]

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,” Proc. SPIE 8530, 853007 (2012).
[Crossref]

U. Eppelt, S. Russ, C. Hartmann, M. Sun, C. Siebert, and W. Schulz, “Diagnostic and simulation of ps-laser glass cutting,” ICALEO 2012 - 31st International Congress on Applications of Lasers and Electro-Optics pp. 835–844 (2012).

Fernandez, T. T.

Flamini, F.

F. Flamini, L. Magrini, A. S. Rab, N. Spagnolo, V. D’Ambrosio, P. Mataloni, F. Sciarrino, T. Zandrini, A. Crespi, R. Ramponi, and R. Osellame, “Thermally reconfigurable quantum photonic circuits at telecom wavelength by femtosecond laser micromachining,” Light: Sci. Appl. 4(11), e354 (2015).
[Crossref]

Fletcher, L. B.

Freidank, S.

A. Vogel, N. Linz, S. Freidank, and X. Liang, “Controlled nonlinear energy deposition in transparent materials: experiments and theory,” in AIP Conference Proceedings, vol. 1278 (American Institute of Physics, 2010), pp. 51–55.

Fukasawa, Y.

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]

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. Autom. Technol. 10(6), 863–873 (2016).
[Crossref]

Furch, F. J.

T. Witting, C. H. Lu, F. J. Furch, A. H. Kung, and M. J. Vrakking, “Near single-cycle laser pulses at high average power and high repetition rate from an all-solid-state setup,” 2018 Conf. Lasers and Electro-Optics, CLEO 2018 - Proc. 26, SW3N.6 (2018).
[Crossref]

Gattass, R. R.

R. R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photonics 2(4), 219–225 (2008).
[Crossref]

Gecys, P.

J. Dudutis, R. Stonys, G. Račiukaitis, and P. Gečys, “Glass dicing with elliptical bessel beam,” Opt. Laser Technol. 111, 331–337 (2019).
[Crossref]

E. Markauskas and P. Gečys, “Thin water film assisted glass ablation with a picosecond laser,” Procedia CIRP 74, 328–332 (2018).
[Crossref]

P. Gečys, J. Dudutis, and G. Račiukaitis, “Nanosecond laser processing of soda-lime glass,” J. Laser Micro/Nanoeng. 10(5), 254 (2015).

G. Raciukaitis, M. Brikas, P. Gecys, and M. Gedvilas, “Accumulation effects in laser ablation of metals with high-repetition-rate lasers,” in High-Power Laser Ablation VII, vol. 7005 (International Society for Optics and Photonics, 2008), p. 70052L.

Gedvilas, M.

G. Raciukaitis, M. Brikas, P. Gecys, and M. Gedvilas, “Accumulation effects in laser ablation of metals with high-repetition-rate lasers,” in High-Power Laser Ablation VII, vol. 7005 (International Society for Optics and Photonics, 2008), p. 70052L.

Gökce, B.

Hädrich, S.

S. Hädrich, T. Eidam, A. Hoffmann, S. Wunderlich, F. Jansen, D. Steil, S. Mathias, and J. Limpert, “High photon flux and high repetition rate fiber-laser driven HHG,” Opt. InfoBase Conf. Pap.Part F82-CLEO_Europe 2017, 172002 (2017).

Hartmann, C.

M. Sun, U. Eppelt, C. Hartmann, W. Schulz, J. Zhu, and Z. Lin, “Towards crack-free ablation cutting of thin glass sheets with picosecond pulsed lasers,” Pac. Rim Laser Damage 2017: Opt. Mater. for High-Power Lasers 10339, 103390O (2017).
[Crossref]

M. Sun, U. Eppelt, C. Hartmann, W. Schulz, J. Zhu, and Z. Lin, “Damage morphology and mechanism in ablation cutting of thin glass sheets with picosecond pulsed lasers,” Opt. Laser Technol. 80, 227–236 (2016).
[Crossref]

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 (2013).
[Crossref]

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,” Proc. SPIE 8530, 853007 (2012).
[Crossref]

U. Eppelt, S. Russ, C. Hartmann, M. Sun, C. Siebert, and W. Schulz, “Diagnostic and simulation of ps-laser glass cutting,” ICALEO 2012 - 31st International Congress on Applications of Lasers and Electro-Optics pp. 835–844 (2012).

He, F.

Hellmig, O.

T. Calmano, J. Siebenmorgen, O. Hellmig, K. Petermann, and G. Huber, “Nd:YAG waveguide laser with 1.3 W output power, fabricated by direct femtosecond laser writing,” Appl. Phys. B: Lasers Opt. 100(1), 131–135 (2010).
[Crossref]

Hoffmann, A.

S. Hädrich, T. Eidam, A. Hoffmann, S. Wunderlich, F. Jansen, D. Steil, S. Mathias, and J. Limpert, “High photon flux and high repetition rate fiber-laser driven HHG,” Opt. InfoBase Conf. Pap.Part F82-CLEO_Europe 2017, 172002 (2017).

Huber, G.

T. Calmano, J. Siebenmorgen, O. Hellmig, K. Petermann, and G. Huber, “Nd:YAG waveguide laser with 1.3 W output power, fabricated by direct femtosecond laser writing,” Appl. Phys. B: Lasers Opt. 100(1), 131–135 (2010).
[Crossref]

Huegel, H.

A. Ruf, D. Breitling, P. Berger, F. Dausinger, and H. Huegel, “Modeling and investigation of melt ejection dynamics for laser drilling with short pulses,” Third Int. Symp. on Laser Precis. Microfabr. 4830, 73 (2003).
[Crossref]

Hüttman, G.

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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 (2013).
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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,” Proc. SPIE 8530, 853007 (2012).
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T. Calmano, J. Siebenmorgen, O. Hellmig, K. Petermann, and G. Huber, “Nd:YAG waveguide laser with 1.3 W output power, fabricated by direct femtosecond laser writing,” Appl. Phys. B: Lasers Opt. 100(1), 131–135 (2010).
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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 (2013).
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Song, J.

Y. Liao, J. Song, E. Li, Y. Luo, Y. Shen, D. Chen, Y. Cheng, Z. Xu, K. Sugioka, and K. Midorikawa, “Rapid prototyping of three-dimensional microfluidic mixers in glass by femtosecond laser direct writing,” Lab Chip 12(4), 746–749 (2012).
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Sugioka, K.

Y. Liao, J. Song, E. Li, Y. Luo, Y. Shen, D. Chen, Y. Cheng, Z. Xu, K. Sugioka, and K. Midorikawa, “Rapid prototyping of three-dimensional microfluidic mixers in glass by femtosecond laser direct writing,” Lab Chip 12(4), 746–749 (2012).
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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]

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. Autom. Technol. 10(6), 863–873 (2016).
[Crossref]

Sukumaran, V.

V. Sukumaran, Q. Chen, F. Liu, N. Kumbhat, T. Bandyopadhyay, H. Chan, S. Min, C. Nopper, V. Sundaram, and R. Tummala, “Through-package-via formation and metallization of glass interposers,” Proc. - Electron. Components Technol. Conf. pp. 557–563 (2010).

Sun, M.

M. Sun, U. Eppelt, C. Hartmann, W. Schulz, J. Zhu, and Z. Lin, “Towards crack-free ablation cutting of thin glass sheets with picosecond pulsed lasers,” Pac. Rim Laser Damage 2017: Opt. Mater. for High-Power Lasers 10339, 103390O (2017).
[Crossref]

M. Sun, U. Eppelt, C. Hartmann, W. Schulz, J. Zhu, and Z. Lin, “Damage morphology and mechanism in ablation cutting of thin glass sheets with picosecond pulsed lasers,” Opt. Laser Technol. 80, 227–236 (2016).
[Crossref]

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 (2013).
[Crossref]

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 (2013).
[Crossref]

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,” Proc. SPIE 8530, 853007 (2012).
[Crossref]

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Y. Zhang, Z. Shen, and X. Ni, “Modeling and simulation on long pulse laser drilling processing,” Int. J. Heat Mass Transfer 73, 429–437 (2014).
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U. Eppelt, S. Russ, C. Hartmann, M. Sun, C. Siebert, and W. Schulz, “Diagnostic and simulation of ps-laser glass cutting,” ICALEO 2012 - 31st International Congress on Applications of Lasers and Electro-Optics pp. 835–844 (2012).

S. Hädrich, T. Eidam, A. Hoffmann, S. Wunderlich, F. Jansen, D. Steil, S. Mathias, and J. Limpert, “High photon flux and high repetition rate fiber-laser driven HHG,” Opt. InfoBase Conf. Pap.Part F82-CLEO_Europe 2017, 172002 (2017).

X. Liang, N. Linz, J. Noack, and A. Vogel, “Modelling of optical breakdown in dielectrics including thermal effects relevant for nanosecond pulses and sequences of ultra-short laser pulses,” in CLEO/Europe-EQEC 2009-European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference, (IEEE, 2009), p. 1.

A. Vogel, N. Linz, S. Freidank, and X. Liang, “Controlled nonlinear energy deposition in transparent materials: experiments and theory,” in AIP Conference Proceedings, vol. 1278 (American Institute of Physics, 2010), pp. 51–55.

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Figures (7)

Fig. 1.
Fig. 1. (a) Illustration of the experimental setup. (b) Actual experimental setup.

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Fig. 2.
Fig. 2. (a) Thermography of the heated sample. (b) Temperature distribution of the measured region

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Fig. 3.
Fig. 3. Dependence of simulated temperature distribution after one pulse on values of (a) $\alpha$ and (b) $\beta$. (c) Comparison of temperature distribution with different conditions that allow for similar drilled-hole depths. (Left: depth = 0.626 $\mu \textrm{m}$, right: depth = 0.680 $\mu \textrm{m}$)

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Fig. 4.
Fig. 4. (a) Shape of holes drilled by 100 pulses at different environmental temperatures. (b) Depth of drilled holes at different environmental temperatures.

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Fig. 5.
Fig. 5. (a) Shape of holes drilled by 50 pulses at different environmental temperatures. (b) Shape and temperature distribution of holes drilled by 50 pulses at different environmental temperatures. (c) Depth comparison of experiment and simulation after 50 pulses at different environmental temperatures.

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Fig. 6.
Fig. 6. (a) Distribution of laser intensity, (b) distribution of free electron density and (c) temporal course of temperature distribution after the 100th pulse.

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Fig. 7.
Fig. 7. (a) Shape of holes drilled by 50 pulses at different repetition rates. (b) Shape of holes drilled by 50 pulses at different repetition rates. (c) Depth comparison of experiment and simulation after 50 pulses at different repetition rates.

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Tables (1)

Tables Icon

Table 1. Simulated depth [ μ m] of holes drilled by one laser pulse, with different values of α and β .

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Equations (6)

Equations on this page are rendered with MathJax. Learn more.

2 i k 0 ∂ E ∂ z = − ∂ 2 E ∂ r 2 − 1 r ∂ E ∂ r − k 0 2 ( ε r − 1 ) E ,
ε r ( ω ) = 1 − ρ B e 2 m ε 0 ω 2 − ω 0 2 − i χ ω ( ω 2 − ω 0 2 ) 2 + χ 2 ω 2 ,
∂ ρ ∂ t = σ I k + α c I ρ − η rec ρ 2 − η diff ρ ,
Δ T = E av 3 n k B ∫ 0 ∞ ( σ I k + α c I ρ ) d t ,
χ = χ max ρ max ρ max + β ρ crit ,
χ = χ max ρ max α ρ max α + β ρ c r i t α ,

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