Abstract

The relation between ablation threshold fluence upon femtosecond laser pulse irradiation and the average dissociation energy density of silicate based multicomponent glass is studied. A simple model based on multiphoton absorption quantifies the absorbed energy density at the ablation threshold fluence. This energy density is compared to a calculated energy density which is necessary to decompose the glass compound into its atomic constituents. The results confirm that this energy density is a crucial intrinsic material parameter for the description of the femtosecond laser ablation threshold fluence of dielectrics.

© 2014 Optical Society of America

1. Introduction

An outstanding characteristic of femtosecond (fs) laser pulse ablation is its high intensity and the absence of laser interaction with the ablation plume. The result is a minimal heat-affected zone and a precise, efficient energy deposition to the irradiated solid. Material removal (ablation) takes place when the deposited areal energy density (fluence) overcomes a material dependent threshold. At fluences close to this threshold, material can be removed over areas smaller than the diffraction limit [1]. The origin and the dynamics of the ablation have been studied extensively in the last decades, investigating the optical absorption mechanisms [27], the pulse duration dependence of the ablation threshold [813], the surface morphology upon fs-laser irradiation [1416], and the temporal evolution of the material response/removal [1720]. Considerable work is devoted to the permanent structural modification of the material after fs-induced modification [2127]. For ablation of dielectrics, the generation of free carriers in the conduction band (CB) of the solid is of uppermost importance, as it is the origin of the materials response to the ultrashort laser pulse irradiation. Different approaches to model a rate of the generation of free carriers by strong electric field ionization (SFI) are based on the Keldysh theory, which derives a SFI rate W for the excitation of the dielectric involving the parameters of the band gap and the reduced effective mass of the electron-hole pair [28]. For comparatively low laser pulse intensities I, the Keldysh theory converges to a multiphoton absorption law, namely W~Im, which scales with the number of simultaneously absorbed photons m necessary to overcome the band gap energy Eg [29,30]. For higher laser pulse intensities, the strong electric field distorts the electronic band structure of the material to that extent that tunnel ionization becomes a more appropriate (simplified) physical picture describing the carrier generation rate. Quasi free electrons in the conduction band, which are generated from these initial (nonlinear) excitation processes, are subsequently able to absorb further photons in a stepwise (linear) absorption process (free-carrier absorption). Once such electrons gained enough energy Ee > Eg, they can transfer their kinetic energy to another electron in the valence band which then gets excited to the conduction band. This process is referred to as impact ionization.

While for strong absorbing materials and pulse durations in the ns-range (or longer), thermodynamical criteria for the ablation threshold are generally accepted [31], defining a theoretical criterion for the ablation threshold is a very controversial subject in the field of femtosecond laser interaction with dielectrics. Two fundamentally different approaches are found in the literature. The first criterion considers that the ablation commences when the free-electron plasma density Ne in the CB exceeds a critical density Nc. This critical density is often defined as the density at which the density dependent electron plasma frequency ωPl equals the laser frequency ωL. When the laser wavelength is centered around 800 nm, Nc should be 1.74 x1021 cm−3 in the approximation of a free electron gas [8,32].

In recent publications, a second more thermodynamical criterion is suggested, which is based on an intrinsic material property [5,33,34]. In this case, a certain material related energy density needs to be overcome to predict the materials response to the impact of the laser pulse. It is suggested by Chimier et al. [15] and others [5], that this energy density might be the one to heat and decompose the dielectric into its atomic constituents. This is reasonable, since upon femtosecond laser pulse irradiation the total absorbed fraction of the laser pulse energy will initially be stored in the electron gas, which previously formed the binding orbitals of the dielectric. The absorbed energy is transferred from the electron gas to the lattice after the laser pulse has passed the excited volume. If then the absorbed energy density exceeds the average binding energy density the glass will start to decompose. The ablation characteristics are sometimes derived from a model for the crater depth [17,32,33,35]. However, studies that reveal the intrinsic material influence on the fs-laser induced ablation are still scarce [33,36].

This paper shows the materials influence on the femtosecond laser-induced ablation by systematically investigating a series of silicate glasses of varying chemical composition with different kind and content of network modifying ions. Taking benefit of the tailored chemical glass compositions, the hypothesis is tested if the single-pulse ablation threshold can be correlated to the material specific average bond or dissociation energy density of the silicate glasses which has to be provided by the nonlinearly absorbed femtosecond laser pulses.

2. Experimental methods

Glass systems based on silica (SiO2) with different kinds and concentrations of network modifying oxides (Li2O, K2O, Na2O, MgO, CaO) and network forming oxides (B2O3, Al2O3, GeO2) were selected. The glasses (except LNMBS, which was provided by Schott Glas AG, Germany) were prepared by mixing reagent grade raw materials of the oxides and subsequent melting in a platinum crucible for 1 hour. The glass melt was quenched between two steel plates and subsequently annealed at temperatures approx. 10 K above the glass transformation temperature (T_g). Then, the manufactured glass plates were cut into pieces of 20x20x2 mm3 and polished with water free lubricant and stored in a desiccator to avoid a possible modification of the glass surfaces. The polishing process assured an optical quality grade of the glass surfaces.

To distinguish the characteristics of each network modifier preferentially binary and ternary glasses were investigated with respect to their fluence thresholds and laser-induced surface morphologies. Characterization of thermophysical properties can be found elsewhere [21]. The stoichiometric (batch-) compositions of the different binary and ternary silicate glasses and two commercial reference glasses (fused silica and Borofloat glass) used in this study are compiled in Table 1. The compositions of the glasses show significant differences to provide direct examinations of the covalent to ionic bonding ratio (i.e. Fused silica, LiSi75, LiSi66, LiSi60, and others), ion radii (i.e. LiSi66, LiNa11Si66, LiNa22Si66, NaSi66, and others) and ion charge (i.e., LiSi60, LiMg20Si60, and others).

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Table 1. Stoichiometric batch composition of the glass samples

Ultrashort laser pulses were provided by a Titanium:sapphire fs-oscillator and subsequently amplified via chirped-pulse-amplification (Spitfire, Spectra Physics) to pulse energies up to 1 mJ at 1 kHz pulse repetition rate. Single laser pulses with the duration of 120 fs and a center wavelength of 800 nm were selected by electronically gating the synchronization and delay generator unit of the regenerative amplifier. The laser pulse energy was coarsely adjusted to the appropriate regime using a semi-reflective dielectric mirror. Fine control of the laser pulse energy was obtained by a half-wave plate and a Glan–Taylor linear polarizer. The pulse energy was monitored in situ via the peak voltage of a photodiode, which was calibrated against a pyroelectric energy detector (Polytec RJ750). The glass samples were placed on a motorized translation xyz-stage (MICOS PLS 85) in the focal plane of a plano-convex lens with 80 mm focal length. The spot radius (1/e2 decay of maximum intensity) of the Gaussian beam was determined with the method proposed by Liu [37] as w0 = (16.2 ± 0.3) µm. All single-pulse irradiations were performed in air. The irradiation spots were separated by a distance of 100 µm in order to avoid incubation effects and material redeposition (debris). The inspection of the irradiated samples has been performed by brightfield optical microscopy (OM) and by scanning force microscopy (SFM) in contact mode.

3. Results and discussion

3.1 Ablation threshold

The diameters of the ablation spots were measured by OM. The beam waist radius w0 is calculated by a series of ablation crater diameters generated at different laser pulse energies. Assuming a spatially Gaussian shape of the beam profile, the ablation threshold fluence Fth,dia is obtained from the series and their associated square of crater diameters (D2) by a least-squares-fit from the relation D²=2w0²ln(F0/Fth,dia), where F0=2E0/(πw0²) describes the incident peak fluence in front of the sample [37].

Figure 1 exemplifies this evaluation procedure of the single-pulse ablation threshold fluences for commercially available Borofloat glass (Schott AG, Germany, black squares) and for the LiGe50Si25 glass (red triangles).

 

Fig. 1 Plot of the squared ablation diameter D2 vs. the peak fluence F0 for LiGe50Si25 (red triangles) and Borofloat glass (black squares). Note the semi-logarithmic data representation. The solid lines correspond to least-squares-fits with the method proposed in [37]. The arrows indicate the ablation threshold obtained from the fits. The horizontal and vertical bars correspond to the statistical errors.

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The ablation threshold value for Borofloat glass of 4.4 J/cm2 obtained by extrapolation to D2 → 0 is in agreement with the ablation threshold fluence value reported in [38].

All glass samples listed in Table 1 have been investigated with the above mentioned method. In order to calculate the fluence entering the sample material, the threshold fluences obtained from the crater diameters are subsequently revised by a factor for the transmission through the air-glass interface Φth,dia=Fth,dia(1R), where R represents the reflectivity of the glass surface at normal incidence. Experimental and numerical simulations show that R is similar to the Fresnel reflectivity for fluence values up to the ablation fluence threshold [39]. The obtained values for Fth,dia, Φth,dia, R and nd of all glass samples are compiled in Table 2.

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Table 2. Incident ablation threshold fluences Fth,dia obtained by the D2-method along with the ablation threshold fluence Φth,dia corrected by the reflection losses (R). All error bars are derived from the fitting procedure. The refractive indexes nd are taken from [40]. The Fresnel reflectivity is calculated neglecting the difference in n of the two wavelengths 589 and 800 nm, which is not significantly affecting the values of R here

3.2 Crater topography

Additionally, a second assessment of the ablation craters has been performed by means of their topography measured by SFM. For the evaluation of an ablation criterion and the modeling of the absorbed fraction of the laser pulse at the ablation threshold fluence, a nonlinear absorption model was used [41]:

dI(z)dz=αmIm(z).

Here, I represents the laser beam intensity within the sample, the coordinate z denotes the position below the glass surface and αm the linear and nonlinear absorption coefficients of the order m. For reasons of simplicity, all absorption mechanisms except the multiphoton absorption of the m-th order are neglected and I is substituted with I=Φ/τ=F(1R)/τ where τ is the pulse duration. Considering the reflected parts of the beam according to Fresnel reflection R, Eq. (1) can then be reduced to:

dF(z)dz=αmτm1(1R)m1Fm(z).
Equation (2) can be solved analytically by separation of the variables [17]. Considering the boundary condition that ablation stops in depth at the (maximum) crater depth dmax where the local fluence falls below the ablation thresholdΦ(dmax)=Φth,dep=Fth,dep(1R), the following expression for the material and fluence dependence of the crater depth is derived:

dmax=τm1(m1)αmdep(1R)m1[1Fth,depm11F0m1].

In the following it is considered that m is of the third order since the band gap energy of the silicate glass samples is around Eg = 4.5 eV. Hence, three photons are needed to bridge the band gap energy. Least-squares-fitting Eq. (3) to the experimental SFM data of the silicate glasses allows to simultaneously obtain both the fluence threshold for the specific glass and the third order nonlinear (3-photon) absorption coefficient α3dep as fit parameters.

As an example, in Fig. 2 the maximum ablation crater depth is plotted versus the peak laser fluence along with a least-squares-fit of Eq. (3) to a series of ablation craters of two glasses (LiGe50Si25 and Borofloat glass). The model of Eq. (3) is in good agreement with the experimental data. The LiGe50Si25 glass shows a relatively low ablation threshold fluence of Fth,dep = 2.4 J/cm2 and shallow crater profiles (depths up to ~150 nm), whereas Borofloat glass has almost a doubled ablation threshold fluence with comparatively large crater depths up to 330 nm. Since the average dissociation energies of the glasses are similar (see Table 6), this supposedly corresponds to the different 3-photon absorption (3-PA) coefficient α3 of the two glasses, i.e., 9.3 × 10−23 and 1.3 × 10−23 cm3/W2, respectively.

 

Fig. 2 Maximum depth of the ablation craters dmax vs. the incident peak fluence F0 for LiGe50Si25 (red circles) and Borofloat glass (black squares). The solid lines correspond to a least-squares-fit using Eq. (3).

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Analogous results are found for all other glasses. The obtained fit parameters (Fth,dia, α3dep) are compiled in Table 3 along with the fluence thresholds Φth,dia corrected by the Fresnel reflection losses R of the air glass interface and with the three photon absorption coefficients obtained from z-scan technique in the fluence regime F ~0.02 × Fth,dia [42]. The values obtained for the ablation threshold fluences from the crater depths Fth,dep agree well with the ones obtained from the ablation diameters (Fth,dia) presented in Table 2.

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Table 3. Ablation threshold fluences Fth,dia and 3-PA coefficients α3dep of the glasses derived from fits of the crater depth vs. the applied laser fluence F0 (Eq. (3)) and ablation threshold fluences Φth,dia with the considered reflection losses of the air-glass interface. Additionally, nonlinear absorption coefficients from z-scan technique are listed [42]. Error values are statistical deviations obtained from the least-squares-fitting procedure

The threshold fluences from the 3-PA model Eq. (3) are in average about 5% lower than those evaluated with the method of Liu [37]. Such a phenomenon is also found in [33], where the ablation threshold energy from the crater depth is obtained from a linear regression of the crater depth vs. the logarithmic incident energy close to the threshold. Interestingly, the 3-PA coefficients α3 derived from the crater depths using Eq. (3) are very similar to the ones found by z-scan technique at a much lower fluence regime F0 ~0.02 × Fth,dia [42]. From that one might conclude, that the impact ionization plays only a minor role for the given conditions. Simulations by Rethfeld [43] describe the multiphoton absorption as the dominant absorption process in this intensity (I = 1013 W) and pulse length (τ = 120fs) regime for a dielectric with a bandgap of 9 eV and a laser photon energy of 2.5 eV.

Moreover, the crater topography can be predicted from the 3-PA model, when substituting a spatial Gaussian fluence profile to the fluence variable in Eq. (3). One then obtains for the radial dependence of the crater depth:

d(r)=τ²2α3(1R)²[1Fth²exp{4r²/w0²}F0²],
where r is distance from the center of the ablation crater.

Figure 3 shows the surface topographies of a selection of six ablation craters obtained from the same SFM measurements previously shown in Fig. 2. Horizontal cross sections through the center of the craters are shown on the right hand side of Fig. 3. For each material, all cross sections have been least-squares-fitted with the same 3-PA coefficient (listed in Table 3) by using Eq. (4).

 

Fig. 3 SFM surface topography of a selection of laser-induced ablation craters on Borofloat (upper row) and LiGe50Si25 (lower row) glasses. The corresponding horizontal cross-sectional profiles (open symbols) along with the plots of Eq. (4) (solid lines) are shown on the right hand side.

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From crater profiles shown in Fig. 3 it is evident that the fits based on Eq. (4) using the parameters of Table 3 are in excellent agreement with the experimentally obtained crater topographies. Hence, the 3-PA model is a sufficient model to estimate the absorbed optical energy densities.

Similar analyses can be obtained for materials with larger optical band gap energies, such as fused silica (Eg = 7.2 eV) and sapphire (Eg = 9.9 eV). Taking the crater depth measurements for both materials from Ref. [17]. allows an additional test of the model (Eq. (3)) for higher orders (m) of multiphoton absorption. The results are listed in Table 4, and show a good agreement with the model (as previously underlined in [17]).

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Table 4. Ablation threshold fluences Fth,depand multiphoton absorption (m-PA) coefficients αmdepof fused silica and sapphire derived from fits of the crater depth vs. the incident laser fluence F0 (taken from Ref [17].) and the ablation threshold fluences Φth,depwith the considered reflection losses of the air-glass interface. Additionally, the band gap energies and the refractive indices are listed

3.3 Material specific ablation criterion: dissociation energy

To relate the ablation threshold fluence to an intrinsic material property it was suggested to associate the absorbed fraction of the pulse to the minimum energy density which needs to be overcome to heat and completely decompose the material into its atomic constituents [8,15]. This energy density can be calculated for each of the silicate glasses and sapphire with a method described by Sun and Huggins [44,45]. These authors state that the dissociation energy from the oxide (bulk glass) into gaseous atoms is a constant characteristic of the element (Me) behaving approximately additive. The dissociation energy of the oxides is taken from [44,45] and converted to SI units as listed in Table 5.

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Table 5. Molar mass and dissociation energy of the glass oxides

To calculate the average dissociation energy εb of the chemical bonds in multicomponent glasses, the dissociation energiesεiMeO of the i-th oxide MeO in bulk glass are weighted with their corresponding molar fraction using:

εb=imol%iεiMeO
The average dissociation energy per volume Edisscalc in [kJcm³] is then calculated by:
Edisscalc=εbρimol%iMi=εbρM
where Mi is the molar mass of the i-th oxide MeO, and ρ and M are the mass density and molar mass of the multicomponent glass.

Values of the mass densities ρ were obtained from a measurement based on Archimedes principle and are listed in Table 6.Some glass densities are taken from the Glass Property Information System [40]. Additionally, the available band gap energies Eg are compiled.

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Table 6. Density, molar mass, dissociation energy, and band gap energy of the investigated glasses

The dissociation energies (Edisscalc) of the glasses obtained from Eqs. (5) and (6) are also listed in Table 6. For fused silica, values between 54 and 64 kJ/cm3 are reported in the literature [5,33], which agree with our calculated value of 65 kJ/cm3.

A first assessment of the influence of the materials resistance to femtosecond laser irradiation is obvious when plotting the ablation threshold fluence Φth,dia versus the calculated dissociation energies Edisscalc, as shown in Fig. 4. A fair linear correlation can be seen in that figure which supports the hypothesis of a relation between the threshold fluence and the dissociation energy.

 

Fig. 4 Ablation threshold fluenceΦth,dia vs. the calculated dissociation energy Edisscalc for the investigated silicate glasses (black squares), Fused silica (green triangle) [17] and sapphire (blue rhomb) [17]. Additionally, values for tellurite and bismuthate glasses (red circles) from [33] are presented.

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The absorbed fraction of the laser pulse in terms of energy density can be calculated by Eq. (2) for a given depth of d below the surface. At the ablation threshold fluence, the energy density absorbed at the surface is given by:

Ethm-PA=dΦdepdz|z0=αmτm1[Φth,dep]m
where α3and Φth,dep are obtained from the least-squares-fit of the maximum crater depths to Eq. (3), as listed in Table 3.

To further support the statement that the material intrinsic property of the glass dissociation energy is a suitable parameter to predict the ablation characteristics, the absorbed energy densities Ethm-PA obtained from Eq. (7) can be compared to the calculation of the dissociation energy densities Edisscalc for the glasses on the basis of the Eq. (6). Both of the parameters are plotted against each other in Fig. 5.

 

Fig. 5 Absorbed energy density at the ablation threshold vs. the calculated dissociation energy density for the investigated silicate glasses (black squares), Fused silica (green triangle) and Sapphire (blue rhomb). The solid (red) line represents the identity of both entities.

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The results shown in Fig. 5 revealed that the absorbed energy density is in good agreement with the energy density needed to dissociate the specific material (the equality of both entities is represented by the straight red line in that graph). It is concluded that the femtosecond laser ablation threshold of the different silicate glasses is determined by (1) a material specific energy barrier to decompose the material into its atomic constituents and (2) the energy deposition into the glass modeled with a nonlinear absorption law. This model can be used as a powerful tool to either predict the ablation craters topography or to determine average dissociation energy.

5. Conclusion

In this work a thermodynamically motivated model for the femtosecond laser ablation threshold is developed and tested for silicate glasses of different compositions and sapphire. The model allows to derive a specific energy density which is absorbed at the ablation threshold fluence of the irradiated material. This energy density quantitatively agrees with the value derived on basis of a work from Sun and Huggins [44,45] which provides the compositional dependent energy density to decompose the dielectric material determined primarily by kind and amount of the glass oxides in the composition. It is therefore reasonable that the femtosecond laser ablation fluence threshold of (multicomponent) glasses is determined by two intrinsic properties of the material, i.e., (1) the energy density needed to dissociate the oxidic composition of the glass to its atomic (gaseous) constituents, and (2) the intrinsic property of the material to absorb ultrashort laser pulse radiation in a nonlinear (multiphoton) absorption process.

Acknowledgments

The authors would like to thank R. Johne-Michaelis from IKTS for the mass density measurements. The authors acknowledge the funding of the German Science Foundation DFG (grants no. EB 248/4–2; EI 110/30–2; RO 2074/8–2).

References and links

1. A. P. Joglekar, H. H. Liu, E. Meyhöfer, G. Mourou, and A. J. Hunt, “Optics at critical intensity: Applications to nanomorphing,” Proc. Natl. Acad. Sci. U.S.A. 101(16), 5856–5861 (2004). [CrossRef]   [PubMed]  

2. B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Optical ablation by high-power short-pulse lasers,” J. Opt. Soc. Am. B 13(2), 459–468 (1996). [CrossRef]  

3. E. G. Gamaly, A. V. Rode, B. Luther-Davies, and V. T. Tikhonchuk, “Ablation of solids by femtosecond lasers: Ablation mechanism and ablation thresholds for metals and dielectrics,” Phys. Plasmas 9(3), 949 (2002). [CrossRef]  

4. S. S. Mao, F. Quéré, S. Guizard, X. Mao, R. E. Russo, G. Petite, and P. Martin, “Dynamics of femtosecond laser interactions with dielectrics,” Appl. Phys., A Mater. Sci. Process. 79, 1695–1709 (2004). [CrossRef]  

5. T. Q. Jia, Z. Z. Xu, R. X. Li, D. H. Feng, X. X. Li, C. F. Cheng, H. Y. Sun, N. S. Xu, and H. Z. Wang, “Mechanisms in fs-laser ablation in fused silica,” J. Appl. Phys. 95(9), 5166–5171 (2004). [CrossRef]  

6. C. Mézel, A. Bourgeade, and L. Hallo, “Surface structuring by ultrashort laser pulses: A review of photoionization models,” Phys. Plasmas 17(11), 113504 (2010). [CrossRef]  

7. N. S. Shcheblanov, E. P. Silaeva, and T. E. Itina, “Electronic excitation and relaxation processes in wide band gap dielectric materials in the transition region of the Keldysh parameter,” Appl. Surf. Sci. 258(23), 9417–9420 (2012). [CrossRef]  

8. B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B Condens. Matter 53(4), 1749–1761 (1996). [CrossRef]   [PubMed]  

9. D. Du, X. Liu, G. Korn, J. Squier, and G. Mourou, “Laser‐induced breakdown by impact ionization in SiO2 with pulse widths from 7 ns to 150 fs,” Appl. Phys. Lett. 64(23), 3071–3073 (1994). [CrossRef]  

10. N. Sanner, O. Utéza, B. Chimier, M. Sentis, P. Lassonde, F. Légaré, and J. C. Kieffer, “Toward determinism in surface damaging of dielectrics using few-cycle laser pulses,” Appl. Phys. Lett. 96(7), 071111 (2010). [CrossRef]  

11. M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, C. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond optical breakdown in dielectrics,” Phys. Rev. Lett. 80(18), 4076–4079 (1998). [CrossRef]  

12. P. Rudolph, J. Bonse, J. Krüger, and W. Kautek, “Femtosecond-and nanosecond-pulse laser ablation of bariumalumoborosilicate glass,” Appl. Phys., A Mater. Sci. Process. 69(7), S763–S766 (1999). [CrossRef]  

13. M. Mero, J. Liu, W. Rudolph, D. Ristau, and K. Starke, “Scaling laws of femtosecond laser pulse induced breakdown in oxide films,” Phys. Rev. B 71(11), 115109 (2005). [CrossRef]  

14. B. H. Christensen and P. Balling, “Modeling ultrashort-pulse laser ablation of dielectric materials,” Phys. Rev. B 79(15), 155424 (2009). [CrossRef]  

15. B. Chimier, O. Utéza, N. Sanner, M. Sentis, T. Itina, P. Lassonde, F. Legare, F. Vidal, and J. C. Kieffer, “Damage and ablation thresholds of fused-silica in femtosecond regime,” Phys. Rev. B 84(9), 094104 (2011). [CrossRef]  

16. A. Ben-Yakar, R. L. Byer, A. Harkin, J. Ashmore, H. A. Stone, M. Shen, and E. Mazur, “Morphology of femtosecond-laser-ablated borosilicate glass surfaces,” Appl. Phys. Lett. 83(15), 3030–3032 (2003). [CrossRef]  

17. D. Puerto, J. Siegel, W. Gawelda, M. Galvan-Sosa, L. Ehrentraut, J. Bonse, and J. Solis, “Dynamics of plasma formation, relaxation, and topography modification induced by femtosecond laser pulses in crystalline and amorphous dielectrics,” J. Opt. Soc. Am. B 27(5), 1065–1076 (2010). [CrossRef]  

18. D. von der Linde and H. Schüler, “Breakdown threshold and plasma formation in femtosecond laser–solid interaction,” J. Opt. Soc. Am. B 13(1), 216–222 (1996). [CrossRef]  

19. J. Siegel, D. Puerto, W. Gawelda, G. Bachelier, J. Solis, L. Ehrentraut, and J. Bonse, “Plasma formation and structural modification below the visible ablation threshold in fused silica upon femtosecond laser irradiation,” Appl. Phys. Lett. 91(8), 082902 (2007). [CrossRef]  

20. G. M. Petrov and J. Davis, “Interaction of intense ultra-short laser pulses with dielectrics,” J. Phys. B- At. Mol. Opt. 41(2), 025601 (2008). [CrossRef]  

21. T. Seuthe, M. Grehn, A. Mermillod-Blondin, H. J. Eichler, J. Bonse, and M. Eberstein, “Structural modifications of binary lithium silicate glasses upon femtosecond laser pulse irradiation probed by micro-Raman spectroscopy,” Opt. Mater. Express 3(6), 755–764 (2013). [CrossRef]  

22. J. W. Chan, T. R. Huser, S. H. Risbud, and D. M. Krol, “Modification of the fused silica glass network associated with waveguide fabrication using femtosecond laser pulses,” Appl. Phys., A Mater. Sci. Process. 76(3), 367–372 (2003). [CrossRef]  

23. D. J. Little, M. Ams, S. Gross, P. Dekker, C. T. Miese, A. Fuerbach, and M. J. Withford, “Structural changes in BK7 glass upon exposure to femtosecond laser pulses,” J. Raman Spectrosc. 42(4), 715–718 (2011). [CrossRef]  

24. D. Ehrt, T. Kittel, M. Will, S. Nolte, and A. Tünnermann, “Femtosecond-laser-writing in various glasses,” J. Non-Cryst. Solids 345-346, 332–337 (2004). [CrossRef]  

25. M. Grehn, F. Reinhardt, J. Bonse, M. Eberstein, and T. Seuthe, “Response to “Comment on 'Femtosecond laser-induced ablation of potassium-magnesium silicate glasses: An analysis of structural changes by near edge x-ray absorption spectroscopy,”' [Appl. Phys. Lett. 102, 196101 (2012)],” Appl. Phys. Lett. 102(19), 196102 (2013). [CrossRef]  

26. T. Seuthe, M. Höfner, F. Reinhardt, W. J. Tsai, J. Bonse, M. Eberstein, H. J. Eichler, and M. Grehn, “Femtosecond laser-induced modification of potassium-magnesium silicate glasses: an analysis of structural changes by near edge x-ray absorption spectroscopy,” Appl. Phys. Lett. 100(22), 224101 (2012). [CrossRef]  

27. M. Grehn, T. Seuthe, F. Reinhardt, M. Höfner, N. Griga, M. Eberstein, and J. Bonse, “Debris of potassium-magnesium silicate glass generated by femtosecond laser-induced ablation in air: an analysis by near edge X-ray absorption spectroscopy, micro Raman and energy dispersive X-ray spectroscopy,” Appl. Surf. Sci. (2013), doi:. [CrossRef]  

28. L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307–1314 (1965).

29. P. Balling and J. Schou, “Femtosecond-laser ablation dynamics of dielectrics: basics and applications for thin films,” Rep. Prog. Phys. 76(3), 036502 (2013). [CrossRef]   [PubMed]  

30. V. E. Gruzdev and J. K. Chen, “Laser-induced ionization and intrinsic breakdown of wide band-gap solids,” Appl. Phys., A Mater. Sci. Process. 90(2), 255–261 (2007). [CrossRef]  

31. D. Bäuerle, Laser Processing and Chemistry, 4th ed. (Springer-Verlag, 2011)

32. L. Jiang and H. L. Tsai, “Energy transport and material removal in wide bandgap materials by a femtosecond laser pulse,” Int. J. Heat Mass Tran. 48(3-4), 487–499 (2005). [CrossRef]  

33. M. Watanabe, Y. Kuroiwa, and S. Ito, “Study of femtosecond laser ablation of multicomponent glass,” Reports Res. Lab. Asahi Glass 55, 27–31 (2005).

34. N. Varkentina, N. Sanner, M. Lebugle, M. Sentis, and O. Utéza, “Absorption of a single 500 fs laser pulse at the surface of fused silica: Energy balance and ablation efficiency,” J. Appl. Phys. 114(17), 173105 (2013). [CrossRef]  

35. S. Guizard, A. Semerok, J. Gaudin, M. Hashida, P. Martin, and F. Quéré, “Femtosecond laser ablation of transparent dielectrics: measurement and modelisation of crater profiles,” Appl. Surf. Sci. 186(1-4), 364–368 (2002). [CrossRef]  

36. M. Lancry, B. Poumellec, A. Chahid-Erraji, M. Beresna, and P. G. Kazansky, “Dependence of the femtosecond laser refractive index change thresholds on the chemical composition of doped-silica glasses,” Opt. Mater. Express 1(4), 711–723 (2011). [CrossRef]  

37. J. M. Liu, “Simple technique for measurements of pulsed Gaussian-beam spot sizes,” Opt. Lett. 7(5), 196–198 (1982). [CrossRef]   [PubMed]  

38. A. Ben-Yakar and R. L. Byer, “Femtosecond laser ablation properties of borosilicate glass,” J. Appl. Phys. 96(9), 5316–5323 (2004). [CrossRef]  

39. A. Q. Wu, I. H. Chowdhury, and X. Xu, “Femtosecond laser absorption in fused silica: Numerical and experimental investigation,” Phys. Rev. B 72(8), 085128 (2005). [CrossRef]  

40. A. I. Priven, “General method for calculating the properties of oxide glasses and glass forming melts from their composition and temperature,” Glass Technol. 45, 244–254 (2004).

41. S. Preuss, M. Späth, Y. Zhang, and M. Stuke, “Time resolved dynamics of subpicosecond laser ablation,” Appl. Phys. Lett. 62(23), 3049 (1993). [CrossRef]  

42. M. Grehn, T. Seuthe, W.-J. Tsai, M. Höfner, A. W. Achtstein, A. Mermillod-Blondin, M. Eberstein, H. J. Eichler, and J. Bonse, “Nonlinear absorption and refraction of binary and ternary alkaline and alkaline earth silicate glasses,” Opt. Mater. Express 3(12), 2132–2140 (2013). [CrossRef]  

43. B. Rethfeld, “Free-electron generation in laser-irradiated dielectrics,” Phys. Rev. B 73(3), 035101 (2006). [CrossRef]  

44. K. H. Sun, “Fundamental condition of glass formation,” J. Am. Ceram. Soc. 30(9), 277–281 (1947). [CrossRef]  

45. K. H. Sun and M. L. Huggins, “Energy Additivity in Oxygen-containing Crystals and Glasses,” J. Phys. Colloid Chem. 51(2), 438–443 (1947). [CrossRef]   [PubMed]  

References

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  1. A. P. Joglekar, H. H. Liu, E. Meyhöfer, G. Mourou, and A. J. Hunt, “Optics at critical intensity: Applications to nanomorphing,” Proc. Natl. Acad. Sci. U.S.A. 101(16), 5856–5861 (2004).
    [Crossref] [PubMed]
  2. B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Optical ablation by high-power short-pulse lasers,” J. Opt. Soc. Am. B 13(2), 459–468 (1996).
    [Crossref]
  3. E. G. Gamaly, A. V. Rode, B. Luther-Davies, and V. T. Tikhonchuk, “Ablation of solids by femtosecond lasers: Ablation mechanism and ablation thresholds for metals and dielectrics,” Phys. Plasmas 9(3), 949 (2002).
    [Crossref]
  4. S. S. Mao, F. Quéré, S. Guizard, X. Mao, R. E. Russo, G. Petite, and P. Martin, “Dynamics of femtosecond laser interactions with dielectrics,” Appl. Phys., A Mater. Sci. Process. 79, 1695–1709 (2004).
    [Crossref]
  5. T. Q. Jia, Z. Z. Xu, R. X. Li, D. H. Feng, X. X. Li, C. F. Cheng, H. Y. Sun, N. S. Xu, and H. Z. Wang, “Mechanisms in fs-laser ablation in fused silica,” J. Appl. Phys. 95(9), 5166–5171 (2004).
    [Crossref]
  6. C. Mézel, A. Bourgeade, and L. Hallo, “Surface structuring by ultrashort laser pulses: A review of photoionization models,” Phys. Plasmas 17(11), 113504 (2010).
    [Crossref]
  7. N. S. Shcheblanov, E. P. Silaeva, and T. E. Itina, “Electronic excitation and relaxation processes in wide band gap dielectric materials in the transition region of the Keldysh parameter,” Appl. Surf. Sci. 258(23), 9417–9420 (2012).
    [Crossref]
  8. B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B Condens. Matter 53(4), 1749–1761 (1996).
    [Crossref] [PubMed]
  9. D. Du, X. Liu, G. Korn, J. Squier, and G. Mourou, “Laser‐induced breakdown by impact ionization in SiO2 with pulse widths from 7 ns to 150 fs,” Appl. Phys. Lett. 64(23), 3071–3073 (1994).
    [Crossref]
  10. N. Sanner, O. Utéza, B. Chimier, M. Sentis, P. Lassonde, F. Légaré, and J. C. Kieffer, “Toward determinism in surface damaging of dielectrics using few-cycle laser pulses,” Appl. Phys. Lett. 96(7), 071111 (2010).
    [Crossref]
  11. M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, C. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond optical breakdown in dielectrics,” Phys. Rev. Lett. 80(18), 4076–4079 (1998).
    [Crossref]
  12. P. Rudolph, J. Bonse, J. Krüger, and W. Kautek, “Femtosecond-and nanosecond-pulse laser ablation of bariumalumoborosilicate glass,” Appl. Phys., A Mater. Sci. Process. 69(7), S763–S766 (1999).
    [Crossref]
  13. M. Mero, J. Liu, W. Rudolph, D. Ristau, and K. Starke, “Scaling laws of femtosecond laser pulse induced breakdown in oxide films,” Phys. Rev. B 71(11), 115109 (2005).
    [Crossref]
  14. B. H. Christensen and P. Balling, “Modeling ultrashort-pulse laser ablation of dielectric materials,” Phys. Rev. B 79(15), 155424 (2009).
    [Crossref]
  15. B. Chimier, O. Utéza, N. Sanner, M. Sentis, T. Itina, P. Lassonde, F. Legare, F. Vidal, and J. C. Kieffer, “Damage and ablation thresholds of fused-silica in femtosecond regime,” Phys. Rev. B 84(9), 094104 (2011).
    [Crossref]
  16. A. Ben-Yakar, R. L. Byer, A. Harkin, J. Ashmore, H. A. Stone, M. Shen, and E. Mazur, “Morphology of femtosecond-laser-ablated borosilicate glass surfaces,” Appl. Phys. Lett. 83(15), 3030–3032 (2003).
    [Crossref]
  17. D. Puerto, J. Siegel, W. Gawelda, M. Galvan-Sosa, L. Ehrentraut, J. Bonse, and J. Solis, “Dynamics of plasma formation, relaxation, and topography modification induced by femtosecond laser pulses in crystalline and amorphous dielectrics,” J. Opt. Soc. Am. B 27(5), 1065–1076 (2010).
    [Crossref]
  18. D. von der Linde and H. Schüler, “Breakdown threshold and plasma formation in femtosecond laser–solid interaction,” J. Opt. Soc. Am. B 13(1), 216–222 (1996).
    [Crossref]
  19. J. Siegel, D. Puerto, W. Gawelda, G. Bachelier, J. Solis, L. Ehrentraut, and J. Bonse, “Plasma formation and structural modification below the visible ablation threshold in fused silica upon femtosecond laser irradiation,” Appl. Phys. Lett. 91(8), 082902 (2007).
    [Crossref]
  20. G. M. Petrov and J. Davis, “Interaction of intense ultra-short laser pulses with dielectrics,” J. Phys. B- At. Mol. Opt. 41(2), 025601 (2008).
    [Crossref]
  21. T. Seuthe, M. Grehn, A. Mermillod-Blondin, H. J. Eichler, J. Bonse, and M. Eberstein, “Structural modifications of binary lithium silicate glasses upon femtosecond laser pulse irradiation probed by micro-Raman spectroscopy,” Opt. Mater. Express 3(6), 755–764 (2013).
    [Crossref]
  22. J. W. Chan, T. R. Huser, S. H. Risbud, and D. M. Krol, “Modification of the fused silica glass network associated with waveguide fabrication using femtosecond laser pulses,” Appl. Phys., A Mater. Sci. Process. 76(3), 367–372 (2003).
    [Crossref]
  23. D. J. Little, M. Ams, S. Gross, P. Dekker, C. T. Miese, A. Fuerbach, and M. J. Withford, “Structural changes in BK7 glass upon exposure to femtosecond laser pulses,” J. Raman Spectrosc. 42(4), 715–718 (2011).
    [Crossref]
  24. D. Ehrt, T. Kittel, M. Will, S. Nolte, and A. Tünnermann, “Femtosecond-laser-writing in various glasses,” J. Non-Cryst. Solids 345-346, 332–337 (2004).
    [Crossref]
  25. M. Grehn, F. Reinhardt, J. Bonse, M. Eberstein, and T. Seuthe, “Response to “Comment on 'Femtosecond laser-induced ablation of potassium-magnesium silicate glasses: An analysis of structural changes by near edge x-ray absorption spectroscopy,”' [Appl. Phys. Lett. 102, 196101 (2012)],” Appl. Phys. Lett. 102(19), 196102 (2013).
    [Crossref]
  26. T. Seuthe, M. Höfner, F. Reinhardt, W. J. Tsai, J. Bonse, M. Eberstein, H. J. Eichler, and M. Grehn, “Femtosecond laser-induced modification of potassium-magnesium silicate glasses: an analysis of structural changes by near edge x-ray absorption spectroscopy,” Appl. Phys. Lett. 100(22), 224101 (2012).
    [Crossref]
  27. M. Grehn, T. Seuthe, F. Reinhardt, M. Höfner, N. Griga, M. Eberstein, and J. Bonse, “Debris of potassium-magnesium silicate glass generated by femtosecond laser-induced ablation in air: an analysis by near edge X-ray absorption spectroscopy, micro Raman and energy dispersive X-ray spectroscopy,” Appl. Surf. Sci. (2013), doi:.
    [Crossref]
  28. L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307–1314 (1965).
  29. P. Balling and J. Schou, “Femtosecond-laser ablation dynamics of dielectrics: basics and applications for thin films,” Rep. Prog. Phys. 76(3), 036502 (2013).
    [Crossref] [PubMed]
  30. V. E. Gruzdev and J. K. Chen, “Laser-induced ionization and intrinsic breakdown of wide band-gap solids,” Appl. Phys., A Mater. Sci. Process. 90(2), 255–261 (2007).
    [Crossref]
  31. D. Bäuerle, Laser Processing and Chemistry, 4th ed. (Springer-Verlag, 2011)
  32. L. Jiang and H. L. Tsai, “Energy transport and material removal in wide bandgap materials by a femtosecond laser pulse,” Int. J. Heat Mass Tran. 48(3-4), 487–499 (2005).
    [Crossref]
  33. M. Watanabe, Y. Kuroiwa, and S. Ito, “Study of femtosecond laser ablation of multicomponent glass,” Reports Res. Lab. Asahi Glass 55, 27–31 (2005).
  34. N. Varkentina, N. Sanner, M. Lebugle, M. Sentis, and O. Utéza, “Absorption of a single 500 fs laser pulse at the surface of fused silica: Energy balance and ablation efficiency,” J. Appl. Phys. 114(17), 173105 (2013).
    [Crossref]
  35. S. Guizard, A. Semerok, J. Gaudin, M. Hashida, P. Martin, and F. Quéré, “Femtosecond laser ablation of transparent dielectrics: measurement and modelisation of crater profiles,” Appl. Surf. Sci. 186(1-4), 364–368 (2002).
    [Crossref]
  36. M. Lancry, B. Poumellec, A. Chahid-Erraji, M. Beresna, and P. G. Kazansky, “Dependence of the femtosecond laser refractive index change thresholds on the chemical composition of doped-silica glasses,” Opt. Mater. Express 1(4), 711–723 (2011).
    [Crossref]
  37. J. M. Liu, “Simple technique for measurements of pulsed Gaussian-beam spot sizes,” Opt. Lett. 7(5), 196–198 (1982).
    [Crossref] [PubMed]
  38. A. Ben-Yakar and R. L. Byer, “Femtosecond laser ablation properties of borosilicate glass,” J. Appl. Phys. 96(9), 5316–5323 (2004).
    [Crossref]
  39. A. Q. Wu, I. H. Chowdhury, and X. Xu, “Femtosecond laser absorption in fused silica: Numerical and experimental investigation,” Phys. Rev. B 72(8), 085128 (2005).
    [Crossref]
  40. A. I. Priven, “General method for calculating the properties of oxide glasses and glass forming melts from their composition and temperature,” Glass Technol. 45, 244–254 (2004).
  41. S. Preuss, M. Späth, Y. Zhang, and M. Stuke, “Time resolved dynamics of subpicosecond laser ablation,” Appl. Phys. Lett. 62(23), 3049 (1993).
    [Crossref]
  42. M. Grehn, T. Seuthe, W.-J. Tsai, M. Höfner, A. W. Achtstein, A. Mermillod-Blondin, M. Eberstein, H. J. Eichler, and J. Bonse, “Nonlinear absorption and refraction of binary and ternary alkaline and alkaline earth silicate glasses,” Opt. Mater. Express 3(12), 2132–2140 (2013).
    [Crossref]
  43. B. Rethfeld, “Free-electron generation in laser-irradiated dielectrics,” Phys. Rev. B 73(3), 035101 (2006).
    [Crossref]
  44. K. H. Sun, “Fundamental condition of glass formation,” J. Am. Ceram. Soc. 30(9), 277–281 (1947).
    [Crossref]
  45. K. H. Sun and M. L. Huggins, “Energy Additivity in Oxygen-containing Crystals and Glasses,” J. Phys. Colloid Chem. 51(2), 438–443 (1947).
    [Crossref] [PubMed]

2013 (5)

T. Seuthe, M. Grehn, A. Mermillod-Blondin, H. J. Eichler, J. Bonse, and M. Eberstein, “Structural modifications of binary lithium silicate glasses upon femtosecond laser pulse irradiation probed by micro-Raman spectroscopy,” Opt. Mater. Express 3(6), 755–764 (2013).
[Crossref]

M. Grehn, F. Reinhardt, J. Bonse, M. Eberstein, and T. Seuthe, “Response to “Comment on 'Femtosecond laser-induced ablation of potassium-magnesium silicate glasses: An analysis of structural changes by near edge x-ray absorption spectroscopy,”' [Appl. Phys. Lett. 102, 196101 (2012)],” Appl. Phys. Lett. 102(19), 196102 (2013).
[Crossref]

P. Balling and J. Schou, “Femtosecond-laser ablation dynamics of dielectrics: basics and applications for thin films,” Rep. Prog. Phys. 76(3), 036502 (2013).
[Crossref] [PubMed]

N. Varkentina, N. Sanner, M. Lebugle, M. Sentis, and O. Utéza, “Absorption of a single 500 fs laser pulse at the surface of fused silica: Energy balance and ablation efficiency,” J. Appl. Phys. 114(17), 173105 (2013).
[Crossref]

M. Grehn, T. Seuthe, W.-J. Tsai, M. Höfner, A. W. Achtstein, A. Mermillod-Blondin, M. Eberstein, H. J. Eichler, and J. Bonse, “Nonlinear absorption and refraction of binary and ternary alkaline and alkaline earth silicate glasses,” Opt. Mater. Express 3(12), 2132–2140 (2013).
[Crossref]

2012 (2)

T. Seuthe, M. Höfner, F. Reinhardt, W. J. Tsai, J. Bonse, M. Eberstein, H. J. Eichler, and M. Grehn, “Femtosecond laser-induced modification of potassium-magnesium silicate glasses: an analysis of structural changes by near edge x-ray absorption spectroscopy,” Appl. Phys. Lett. 100(22), 224101 (2012).
[Crossref]

N. S. Shcheblanov, E. P. Silaeva, and T. E. Itina, “Electronic excitation and relaxation processes in wide band gap dielectric materials in the transition region of the Keldysh parameter,” Appl. Surf. Sci. 258(23), 9417–9420 (2012).
[Crossref]

2011 (3)

B. Chimier, O. Utéza, N. Sanner, M. Sentis, T. Itina, P. Lassonde, F. Legare, F. Vidal, and J. C. Kieffer, “Damage and ablation thresholds of fused-silica in femtosecond regime,” Phys. Rev. B 84(9), 094104 (2011).
[Crossref]

D. J. Little, M. Ams, S. Gross, P. Dekker, C. T. Miese, A. Fuerbach, and M. J. Withford, “Structural changes in BK7 glass upon exposure to femtosecond laser pulses,” J. Raman Spectrosc. 42(4), 715–718 (2011).
[Crossref]

M. Lancry, B. Poumellec, A. Chahid-Erraji, M. Beresna, and P. G. Kazansky, “Dependence of the femtosecond laser refractive index change thresholds on the chemical composition of doped-silica glasses,” Opt. Mater. Express 1(4), 711–723 (2011).
[Crossref]

2010 (3)

D. Puerto, J. Siegel, W. Gawelda, M. Galvan-Sosa, L. Ehrentraut, J. Bonse, and J. Solis, “Dynamics of plasma formation, relaxation, and topography modification induced by femtosecond laser pulses in crystalline and amorphous dielectrics,” J. Opt. Soc. Am. B 27(5), 1065–1076 (2010).
[Crossref]

N. Sanner, O. Utéza, B. Chimier, M. Sentis, P. Lassonde, F. Légaré, and J. C. Kieffer, “Toward determinism in surface damaging of dielectrics using few-cycle laser pulses,” Appl. Phys. Lett. 96(7), 071111 (2010).
[Crossref]

C. Mézel, A. Bourgeade, and L. Hallo, “Surface structuring by ultrashort laser pulses: A review of photoionization models,” Phys. Plasmas 17(11), 113504 (2010).
[Crossref]

2009 (1)

B. H. Christensen and P. Balling, “Modeling ultrashort-pulse laser ablation of dielectric materials,” Phys. Rev. B 79(15), 155424 (2009).
[Crossref]

2008 (1)

G. M. Petrov and J. Davis, “Interaction of intense ultra-short laser pulses with dielectrics,” J. Phys. B- At. Mol. Opt. 41(2), 025601 (2008).
[Crossref]

2007 (2)

J. Siegel, D. Puerto, W. Gawelda, G. Bachelier, J. Solis, L. Ehrentraut, and J. Bonse, “Plasma formation and structural modification below the visible ablation threshold in fused silica upon femtosecond laser irradiation,” Appl. Phys. Lett. 91(8), 082902 (2007).
[Crossref]

V. E. Gruzdev and J. K. Chen, “Laser-induced ionization and intrinsic breakdown of wide band-gap solids,” Appl. Phys., A Mater. Sci. Process. 90(2), 255–261 (2007).
[Crossref]

2006 (1)

B. Rethfeld, “Free-electron generation in laser-irradiated dielectrics,” Phys. Rev. B 73(3), 035101 (2006).
[Crossref]

2005 (4)

A. Q. Wu, I. H. Chowdhury, and X. Xu, “Femtosecond laser absorption in fused silica: Numerical and experimental investigation,” Phys. Rev. B 72(8), 085128 (2005).
[Crossref]

L. Jiang and H. L. Tsai, “Energy transport and material removal in wide bandgap materials by a femtosecond laser pulse,” Int. J. Heat Mass Tran. 48(3-4), 487–499 (2005).
[Crossref]

M. Watanabe, Y. Kuroiwa, and S. Ito, “Study of femtosecond laser ablation of multicomponent glass,” Reports Res. Lab. Asahi Glass 55, 27–31 (2005).

M. Mero, J. Liu, W. Rudolph, D. Ristau, and K. Starke, “Scaling laws of femtosecond laser pulse induced breakdown in oxide films,” Phys. Rev. B 71(11), 115109 (2005).
[Crossref]

2004 (6)

A. P. Joglekar, H. H. Liu, E. Meyhöfer, G. Mourou, and A. J. Hunt, “Optics at critical intensity: Applications to nanomorphing,” Proc. Natl. Acad. Sci. U.S.A. 101(16), 5856–5861 (2004).
[Crossref] [PubMed]

S. S. Mao, F. Quéré, S. Guizard, X. Mao, R. E. Russo, G. Petite, and P. Martin, “Dynamics of femtosecond laser interactions with dielectrics,” Appl. Phys., A Mater. Sci. Process. 79, 1695–1709 (2004).
[Crossref]

T. Q. Jia, Z. Z. Xu, R. X. Li, D. H. Feng, X. X. Li, C. F. Cheng, H. Y. Sun, N. S. Xu, and H. Z. Wang, “Mechanisms in fs-laser ablation in fused silica,” J. Appl. Phys. 95(9), 5166–5171 (2004).
[Crossref]

D. Ehrt, T. Kittel, M. Will, S. Nolte, and A. Tünnermann, “Femtosecond-laser-writing in various glasses,” J. Non-Cryst. Solids 345-346, 332–337 (2004).
[Crossref]

A. I. Priven, “General method for calculating the properties of oxide glasses and glass forming melts from their composition and temperature,” Glass Technol. 45, 244–254 (2004).

A. Ben-Yakar and R. L. Byer, “Femtosecond laser ablation properties of borosilicate glass,” J. Appl. Phys. 96(9), 5316–5323 (2004).
[Crossref]

2003 (2)

J. W. Chan, T. R. Huser, S. H. Risbud, and D. M. Krol, “Modification of the fused silica glass network associated with waveguide fabrication using femtosecond laser pulses,” Appl. Phys., A Mater. Sci. Process. 76(3), 367–372 (2003).
[Crossref]

A. Ben-Yakar, R. L. Byer, A. Harkin, J. Ashmore, H. A. Stone, M. Shen, and E. Mazur, “Morphology of femtosecond-laser-ablated borosilicate glass surfaces,” Appl. Phys. Lett. 83(15), 3030–3032 (2003).
[Crossref]

2002 (2)

E. G. Gamaly, A. V. Rode, B. Luther-Davies, and V. T. Tikhonchuk, “Ablation of solids by femtosecond lasers: Ablation mechanism and ablation thresholds for metals and dielectrics,” Phys. Plasmas 9(3), 949 (2002).
[Crossref]

S. Guizard, A. Semerok, J. Gaudin, M. Hashida, P. Martin, and F. Quéré, “Femtosecond laser ablation of transparent dielectrics: measurement and modelisation of crater profiles,” Appl. Surf. Sci. 186(1-4), 364–368 (2002).
[Crossref]

1999 (1)

P. Rudolph, J. Bonse, J. Krüger, and W. Kautek, “Femtosecond-and nanosecond-pulse laser ablation of bariumalumoborosilicate glass,” Appl. Phys., A Mater. Sci. Process. 69(7), S763–S766 (1999).
[Crossref]

1998 (1)

M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, C. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond optical breakdown in dielectrics,” Phys. Rev. Lett. 80(18), 4076–4079 (1998).
[Crossref]

1996 (3)

1994 (1)

D. Du, X. Liu, G. Korn, J. Squier, and G. Mourou, “Laser‐induced breakdown by impact ionization in SiO2 with pulse widths from 7 ns to 150 fs,” Appl. Phys. Lett. 64(23), 3071–3073 (1994).
[Crossref]

1993 (1)

S. Preuss, M. Späth, Y. Zhang, and M. Stuke, “Time resolved dynamics of subpicosecond laser ablation,” Appl. Phys. Lett. 62(23), 3049 (1993).
[Crossref]

1982 (1)

1965 (1)

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307–1314 (1965).

1947 (2)

K. H. Sun, “Fundamental condition of glass formation,” J. Am. Ceram. Soc. 30(9), 277–281 (1947).
[Crossref]

K. H. Sun and M. L. Huggins, “Energy Additivity in Oxygen-containing Crystals and Glasses,” J. Phys. Colloid Chem. 51(2), 438–443 (1947).
[Crossref] [PubMed]

Achtstein, A. W.

Ams, M.

D. J. Little, M. Ams, S. Gross, P. Dekker, C. T. Miese, A. Fuerbach, and M. J. Withford, “Structural changes in BK7 glass upon exposure to femtosecond laser pulses,” J. Raman Spectrosc. 42(4), 715–718 (2011).
[Crossref]

Ashmore, J.

A. Ben-Yakar, R. L. Byer, A. Harkin, J. Ashmore, H. A. Stone, M. Shen, and E. Mazur, “Morphology of femtosecond-laser-ablated borosilicate glass surfaces,” Appl. Phys. Lett. 83(15), 3030–3032 (2003).
[Crossref]

Bachelier, G.

J. Siegel, D. Puerto, W. Gawelda, G. Bachelier, J. Solis, L. Ehrentraut, and J. Bonse, “Plasma formation and structural modification below the visible ablation threshold in fused silica upon femtosecond laser irradiation,” Appl. Phys. Lett. 91(8), 082902 (2007).
[Crossref]

Balling, P.

P. Balling and J. Schou, “Femtosecond-laser ablation dynamics of dielectrics: basics and applications for thin films,” Rep. Prog. Phys. 76(3), 036502 (2013).
[Crossref] [PubMed]

B. H. Christensen and P. Balling, “Modeling ultrashort-pulse laser ablation of dielectric materials,” Phys. Rev. B 79(15), 155424 (2009).
[Crossref]

Ben-Yakar, A.

A. Ben-Yakar and R. L. Byer, “Femtosecond laser ablation properties of borosilicate glass,” J. Appl. Phys. 96(9), 5316–5323 (2004).
[Crossref]

A. Ben-Yakar, R. L. Byer, A. Harkin, J. Ashmore, H. A. Stone, M. Shen, and E. Mazur, “Morphology of femtosecond-laser-ablated borosilicate glass surfaces,” Appl. Phys. Lett. 83(15), 3030–3032 (2003).
[Crossref]

Beresna, M.

Bonse, J.

M. Grehn, T. Seuthe, W.-J. Tsai, M. Höfner, A. W. Achtstein, A. Mermillod-Blondin, M. Eberstein, H. J. Eichler, and J. Bonse, “Nonlinear absorption and refraction of binary and ternary alkaline and alkaline earth silicate glasses,” Opt. Mater. Express 3(12), 2132–2140 (2013).
[Crossref]

T. Seuthe, M. Grehn, A. Mermillod-Blondin, H. J. Eichler, J. Bonse, and M. Eberstein, “Structural modifications of binary lithium silicate glasses upon femtosecond laser pulse irradiation probed by micro-Raman spectroscopy,” Opt. Mater. Express 3(6), 755–764 (2013).
[Crossref]

M. Grehn, F. Reinhardt, J. Bonse, M. Eberstein, and T. Seuthe, “Response to “Comment on 'Femtosecond laser-induced ablation of potassium-magnesium silicate glasses: An analysis of structural changes by near edge x-ray absorption spectroscopy,”' [Appl. Phys. Lett. 102, 196101 (2012)],” Appl. Phys. Lett. 102(19), 196102 (2013).
[Crossref]

T. Seuthe, M. Höfner, F. Reinhardt, W. J. Tsai, J. Bonse, M. Eberstein, H. J. Eichler, and M. Grehn, “Femtosecond laser-induced modification of potassium-magnesium silicate glasses: an analysis of structural changes by near edge x-ray absorption spectroscopy,” Appl. Phys. Lett. 100(22), 224101 (2012).
[Crossref]

D. Puerto, J. Siegel, W. Gawelda, M. Galvan-Sosa, L. Ehrentraut, J. Bonse, and J. Solis, “Dynamics of plasma formation, relaxation, and topography modification induced by femtosecond laser pulses in crystalline and amorphous dielectrics,” J. Opt. Soc. Am. B 27(5), 1065–1076 (2010).
[Crossref]

J. Siegel, D. Puerto, W. Gawelda, G. Bachelier, J. Solis, L. Ehrentraut, and J. Bonse, “Plasma formation and structural modification below the visible ablation threshold in fused silica upon femtosecond laser irradiation,” Appl. Phys. Lett. 91(8), 082902 (2007).
[Crossref]

P. Rudolph, J. Bonse, J. Krüger, and W. Kautek, “Femtosecond-and nanosecond-pulse laser ablation of bariumalumoborosilicate glass,” Appl. Phys., A Mater. Sci. Process. 69(7), S763–S766 (1999).
[Crossref]

M. Grehn, T. Seuthe, F. Reinhardt, M. Höfner, N. Griga, M. Eberstein, and J. Bonse, “Debris of potassium-magnesium silicate glass generated by femtosecond laser-induced ablation in air: an analysis by near edge X-ray absorption spectroscopy, micro Raman and energy dispersive X-ray spectroscopy,” Appl. Surf. Sci. (2013), doi:.
[Crossref]

Bourgeade, A.

C. Mézel, A. Bourgeade, and L. Hallo, “Surface structuring by ultrashort laser pulses: A review of photoionization models,” Phys. Plasmas 17(11), 113504 (2010).
[Crossref]

Byer, R. L.

A. Ben-Yakar and R. L. Byer, “Femtosecond laser ablation properties of borosilicate glass,” J. Appl. Phys. 96(9), 5316–5323 (2004).
[Crossref]

A. Ben-Yakar, R. L. Byer, A. Harkin, J. Ashmore, H. A. Stone, M. Shen, and E. Mazur, “Morphology of femtosecond-laser-ablated borosilicate glass surfaces,” Appl. Phys. Lett. 83(15), 3030–3032 (2003).
[Crossref]

Chahid-Erraji, A.

Chan, J. W.

J. W. Chan, T. R. Huser, S. H. Risbud, and D. M. Krol, “Modification of the fused silica glass network associated with waveguide fabrication using femtosecond laser pulses,” Appl. Phys., A Mater. Sci. Process. 76(3), 367–372 (2003).
[Crossref]

Chen, J. K.

V. E. Gruzdev and J. K. Chen, “Laser-induced ionization and intrinsic breakdown of wide band-gap solids,” Appl. Phys., A Mater. Sci. Process. 90(2), 255–261 (2007).
[Crossref]

Cheng, C. F.

T. Q. Jia, Z. Z. Xu, R. X. Li, D. H. Feng, X. X. Li, C. F. Cheng, H. Y. Sun, N. S. Xu, and H. Z. Wang, “Mechanisms in fs-laser ablation in fused silica,” J. Appl. Phys. 95(9), 5166–5171 (2004).
[Crossref]

Cheng, Z.

M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, C. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond optical breakdown in dielectrics,” Phys. Rev. Lett. 80(18), 4076–4079 (1998).
[Crossref]

Chimier, B.

B. Chimier, O. Utéza, N. Sanner, M. Sentis, T. Itina, P. Lassonde, F. Legare, F. Vidal, and J. C. Kieffer, “Damage and ablation thresholds of fused-silica in femtosecond regime,” Phys. Rev. B 84(9), 094104 (2011).
[Crossref]

N. Sanner, O. Utéza, B. Chimier, M. Sentis, P. Lassonde, F. Légaré, and J. C. Kieffer, “Toward determinism in surface damaging of dielectrics using few-cycle laser pulses,” Appl. Phys. Lett. 96(7), 071111 (2010).
[Crossref]

Chowdhury, I. H.

A. Q. Wu, I. H. Chowdhury, and X. Xu, “Femtosecond laser absorption in fused silica: Numerical and experimental investigation,” Phys. Rev. B 72(8), 085128 (2005).
[Crossref]

Christensen, B. H.

B. H. Christensen and P. Balling, “Modeling ultrashort-pulse laser ablation of dielectric materials,” Phys. Rev. B 79(15), 155424 (2009).
[Crossref]

Davis, J.

G. M. Petrov and J. Davis, “Interaction of intense ultra-short laser pulses with dielectrics,” J. Phys. B- At. Mol. Opt. 41(2), 025601 (2008).
[Crossref]

Dekker, P.

D. J. Little, M. Ams, S. Gross, P. Dekker, C. T. Miese, A. Fuerbach, and M. J. Withford, “Structural changes in BK7 glass upon exposure to femtosecond laser pulses,” J. Raman Spectrosc. 42(4), 715–718 (2011).
[Crossref]

Du, D.

D. Du, X. Liu, G. Korn, J. Squier, and G. Mourou, “Laser‐induced breakdown by impact ionization in SiO2 with pulse widths from 7 ns to 150 fs,” Appl. Phys. Lett. 64(23), 3071–3073 (1994).
[Crossref]

Eberstein, M.

M. Grehn, F. Reinhardt, J. Bonse, M. Eberstein, and T. Seuthe, “Response to “Comment on 'Femtosecond laser-induced ablation of potassium-magnesium silicate glasses: An analysis of structural changes by near edge x-ray absorption spectroscopy,”' [Appl. Phys. Lett. 102, 196101 (2012)],” Appl. Phys. Lett. 102(19), 196102 (2013).
[Crossref]

T. Seuthe, M. Grehn, A. Mermillod-Blondin, H. J. Eichler, J. Bonse, and M. Eberstein, “Structural modifications of binary lithium silicate glasses upon femtosecond laser pulse irradiation probed by micro-Raman spectroscopy,” Opt. Mater. Express 3(6), 755–764 (2013).
[Crossref]

M. Grehn, T. Seuthe, W.-J. Tsai, M. Höfner, A. W. Achtstein, A. Mermillod-Blondin, M. Eberstein, H. J. Eichler, and J. Bonse, “Nonlinear absorption and refraction of binary and ternary alkaline and alkaline earth silicate glasses,” Opt. Mater. Express 3(12), 2132–2140 (2013).
[Crossref]

T. Seuthe, M. Höfner, F. Reinhardt, W. J. Tsai, J. Bonse, M. Eberstein, H. J. Eichler, and M. Grehn, “Femtosecond laser-induced modification of potassium-magnesium silicate glasses: an analysis of structural changes by near edge x-ray absorption spectroscopy,” Appl. Phys. Lett. 100(22), 224101 (2012).
[Crossref]

M. Grehn, T. Seuthe, F. Reinhardt, M. Höfner, N. Griga, M. Eberstein, and J. Bonse, “Debris of potassium-magnesium silicate glass generated by femtosecond laser-induced ablation in air: an analysis by near edge X-ray absorption spectroscopy, micro Raman and energy dispersive X-ray spectroscopy,” Appl. Surf. Sci. (2013), doi:.
[Crossref]

Ehrentraut, L.

D. Puerto, J. Siegel, W. Gawelda, M. Galvan-Sosa, L. Ehrentraut, J. Bonse, and J. Solis, “Dynamics of plasma formation, relaxation, and topography modification induced by femtosecond laser pulses in crystalline and amorphous dielectrics,” J. Opt. Soc. Am. B 27(5), 1065–1076 (2010).
[Crossref]

J. Siegel, D. Puerto, W. Gawelda, G. Bachelier, J. Solis, L. Ehrentraut, and J. Bonse, “Plasma formation and structural modification below the visible ablation threshold in fused silica upon femtosecond laser irradiation,” Appl. Phys. Lett. 91(8), 082902 (2007).
[Crossref]

Ehrt, D.

D. Ehrt, T. Kittel, M. Will, S. Nolte, and A. Tünnermann, “Femtosecond-laser-writing in various glasses,” J. Non-Cryst. Solids 345-346, 332–337 (2004).
[Crossref]

Eichler, H. J.

Feit, M. D.

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B Condens. Matter 53(4), 1749–1761 (1996).
[Crossref] [PubMed]

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Optical ablation by high-power short-pulse lasers,” J. Opt. Soc. Am. B 13(2), 459–468 (1996).
[Crossref]

Feng, D. H.

T. Q. Jia, Z. Z. Xu, R. X. Li, D. H. Feng, X. X. Li, C. F. Cheng, H. Y. Sun, N. S. Xu, and H. Z. Wang, “Mechanisms in fs-laser ablation in fused silica,” J. Appl. Phys. 95(9), 5166–5171 (2004).
[Crossref]

Fuerbach, A.

D. J. Little, M. Ams, S. Gross, P. Dekker, C. T. Miese, A. Fuerbach, and M. J. Withford, “Structural changes in BK7 glass upon exposure to femtosecond laser pulses,” J. Raman Spectrosc. 42(4), 715–718 (2011).
[Crossref]

Galvan-Sosa, M.

Gamaly, E. G.

E. G. Gamaly, A. V. Rode, B. Luther-Davies, and V. T. Tikhonchuk, “Ablation of solids by femtosecond lasers: Ablation mechanism and ablation thresholds for metals and dielectrics,” Phys. Plasmas 9(3), 949 (2002).
[Crossref]

Gaudin, J.

S. Guizard, A. Semerok, J. Gaudin, M. Hashida, P. Martin, and F. Quéré, “Femtosecond laser ablation of transparent dielectrics: measurement and modelisation of crater profiles,” Appl. Surf. Sci. 186(1-4), 364–368 (2002).
[Crossref]

Gawelda, W.

D. Puerto, J. Siegel, W. Gawelda, M. Galvan-Sosa, L. Ehrentraut, J. Bonse, and J. Solis, “Dynamics of plasma formation, relaxation, and topography modification induced by femtosecond laser pulses in crystalline and amorphous dielectrics,” J. Opt. Soc. Am. B 27(5), 1065–1076 (2010).
[Crossref]

J. Siegel, D. Puerto, W. Gawelda, G. Bachelier, J. Solis, L. Ehrentraut, and J. Bonse, “Plasma formation and structural modification below the visible ablation threshold in fused silica upon femtosecond laser irradiation,” Appl. Phys. Lett. 91(8), 082902 (2007).
[Crossref]

Grehn, M.

M. Grehn, F. Reinhardt, J. Bonse, M. Eberstein, and T. Seuthe, “Response to “Comment on 'Femtosecond laser-induced ablation of potassium-magnesium silicate glasses: An analysis of structural changes by near edge x-ray absorption spectroscopy,”' [Appl. Phys. Lett. 102, 196101 (2012)],” Appl. Phys. Lett. 102(19), 196102 (2013).
[Crossref]

T. Seuthe, M. Grehn, A. Mermillod-Blondin, H. J. Eichler, J. Bonse, and M. Eberstein, “Structural modifications of binary lithium silicate glasses upon femtosecond laser pulse irradiation probed by micro-Raman spectroscopy,” Opt. Mater. Express 3(6), 755–764 (2013).
[Crossref]

M. Grehn, T. Seuthe, W.-J. Tsai, M. Höfner, A. W. Achtstein, A. Mermillod-Blondin, M. Eberstein, H. J. Eichler, and J. Bonse, “Nonlinear absorption and refraction of binary and ternary alkaline and alkaline earth silicate glasses,” Opt. Mater. Express 3(12), 2132–2140 (2013).
[Crossref]

T. Seuthe, M. Höfner, F. Reinhardt, W. J. Tsai, J. Bonse, M. Eberstein, H. J. Eichler, and M. Grehn, “Femtosecond laser-induced modification of potassium-magnesium silicate glasses: an analysis of structural changes by near edge x-ray absorption spectroscopy,” Appl. Phys. Lett. 100(22), 224101 (2012).
[Crossref]

M. Grehn, T. Seuthe, F. Reinhardt, M. Höfner, N. Griga, M. Eberstein, and J. Bonse, “Debris of potassium-magnesium silicate glass generated by femtosecond laser-induced ablation in air: an analysis by near edge X-ray absorption spectroscopy, micro Raman and energy dispersive X-ray spectroscopy,” Appl. Surf. Sci. (2013), doi:.
[Crossref]

Griga, N.

M. Grehn, T. Seuthe, F. Reinhardt, M. Höfner, N. Griga, M. Eberstein, and J. Bonse, “Debris of potassium-magnesium silicate glass generated by femtosecond laser-induced ablation in air: an analysis by near edge X-ray absorption spectroscopy, micro Raman and energy dispersive X-ray spectroscopy,” Appl. Surf. Sci. (2013), doi:.
[Crossref]

Gross, S.

D. J. Little, M. Ams, S. Gross, P. Dekker, C. T. Miese, A. Fuerbach, and M. J. Withford, “Structural changes in BK7 glass upon exposure to femtosecond laser pulses,” J. Raman Spectrosc. 42(4), 715–718 (2011).
[Crossref]

Gruzdev, V. E.

V. E. Gruzdev and J. K. Chen, “Laser-induced ionization and intrinsic breakdown of wide band-gap solids,” Appl. Phys., A Mater. Sci. Process. 90(2), 255–261 (2007).
[Crossref]

Guizard, S.

S. S. Mao, F. Quéré, S. Guizard, X. Mao, R. E. Russo, G. Petite, and P. Martin, “Dynamics of femtosecond laser interactions with dielectrics,” Appl. Phys., A Mater. Sci. Process. 79, 1695–1709 (2004).
[Crossref]

S. Guizard, A. Semerok, J. Gaudin, M. Hashida, P. Martin, and F. Quéré, “Femtosecond laser ablation of transparent dielectrics: measurement and modelisation of crater profiles,” Appl. Surf. Sci. 186(1-4), 364–368 (2002).
[Crossref]

Hallo, L.

C. Mézel, A. Bourgeade, and L. Hallo, “Surface structuring by ultrashort laser pulses: A review of photoionization models,” Phys. Plasmas 17(11), 113504 (2010).
[Crossref]

Harkin, A.

A. Ben-Yakar, R. L. Byer, A. Harkin, J. Ashmore, H. A. Stone, M. Shen, and E. Mazur, “Morphology of femtosecond-laser-ablated borosilicate glass surfaces,” Appl. Phys. Lett. 83(15), 3030–3032 (2003).
[Crossref]

Hashida, M.

S. Guizard, A. Semerok, J. Gaudin, M. Hashida, P. Martin, and F. Quéré, “Femtosecond laser ablation of transparent dielectrics: measurement and modelisation of crater profiles,” Appl. Surf. Sci. 186(1-4), 364–368 (2002).
[Crossref]

Herman, S.

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Optical ablation by high-power short-pulse lasers,” J. Opt. Soc. Am. B 13(2), 459–468 (1996).
[Crossref]

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B Condens. Matter 53(4), 1749–1761 (1996).
[Crossref] [PubMed]

Höfner, M.

M. Grehn, T. Seuthe, W.-J. Tsai, M. Höfner, A. W. Achtstein, A. Mermillod-Blondin, M. Eberstein, H. J. Eichler, and J. Bonse, “Nonlinear absorption and refraction of binary and ternary alkaline and alkaline earth silicate glasses,” Opt. Mater. Express 3(12), 2132–2140 (2013).
[Crossref]

T. Seuthe, M. Höfner, F. Reinhardt, W. J. Tsai, J. Bonse, M. Eberstein, H. J. Eichler, and M. Grehn, “Femtosecond laser-induced modification of potassium-magnesium silicate glasses: an analysis of structural changes by near edge x-ray absorption spectroscopy,” Appl. Phys. Lett. 100(22), 224101 (2012).
[Crossref]

M. Grehn, T. Seuthe, F. Reinhardt, M. Höfner, N. Griga, M. Eberstein, and J. Bonse, “Debris of potassium-magnesium silicate glass generated by femtosecond laser-induced ablation in air: an analysis by near edge X-ray absorption spectroscopy, micro Raman and energy dispersive X-ray spectroscopy,” Appl. Surf. Sci. (2013), doi:.
[Crossref]

Huggins, M. L.

K. H. Sun and M. L. Huggins, “Energy Additivity in Oxygen-containing Crystals and Glasses,” J. Phys. Colloid Chem. 51(2), 438–443 (1947).
[Crossref] [PubMed]

Hunt, A. J.

A. P. Joglekar, H. H. Liu, E. Meyhöfer, G. Mourou, and A. J. Hunt, “Optics at critical intensity: Applications to nanomorphing,” Proc. Natl. Acad. Sci. U.S.A. 101(16), 5856–5861 (2004).
[Crossref] [PubMed]

Huser, T. R.

J. W. Chan, T. R. Huser, S. H. Risbud, and D. M. Krol, “Modification of the fused silica glass network associated with waveguide fabrication using femtosecond laser pulses,” Appl. Phys., A Mater. Sci. Process. 76(3), 367–372 (2003).
[Crossref]

Itina, T.

B. Chimier, O. Utéza, N. Sanner, M. Sentis, T. Itina, P. Lassonde, F. Legare, F. Vidal, and J. C. Kieffer, “Damage and ablation thresholds of fused-silica in femtosecond regime,” Phys. Rev. B 84(9), 094104 (2011).
[Crossref]

Itina, T. E.

N. S. Shcheblanov, E. P. Silaeva, and T. E. Itina, “Electronic excitation and relaxation processes in wide band gap dielectric materials in the transition region of the Keldysh parameter,” Appl. Surf. Sci. 258(23), 9417–9420 (2012).
[Crossref]

Ito, S.

M. Watanabe, Y. Kuroiwa, and S. Ito, “Study of femtosecond laser ablation of multicomponent glass,” Reports Res. Lab. Asahi Glass 55, 27–31 (2005).

Jia, T. Q.

T. Q. Jia, Z. Z. Xu, R. X. Li, D. H. Feng, X. X. Li, C. F. Cheng, H. Y. Sun, N. S. Xu, and H. Z. Wang, “Mechanisms in fs-laser ablation in fused silica,” J. Appl. Phys. 95(9), 5166–5171 (2004).
[Crossref]

Jiang, L.

L. Jiang and H. L. Tsai, “Energy transport and material removal in wide bandgap materials by a femtosecond laser pulse,” Int. J. Heat Mass Tran. 48(3-4), 487–499 (2005).
[Crossref]

Joglekar, A. P.

A. P. Joglekar, H. H. Liu, E. Meyhöfer, G. Mourou, and A. J. Hunt, “Optics at critical intensity: Applications to nanomorphing,” Proc. Natl. Acad. Sci. U.S.A. 101(16), 5856–5861 (2004).
[Crossref] [PubMed]

Kautek, W.

P. Rudolph, J. Bonse, J. Krüger, and W. Kautek, “Femtosecond-and nanosecond-pulse laser ablation of bariumalumoborosilicate glass,” Appl. Phys., A Mater. Sci. Process. 69(7), S763–S766 (1999).
[Crossref]

M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, C. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond optical breakdown in dielectrics,” Phys. Rev. Lett. 80(18), 4076–4079 (1998).
[Crossref]

Kazansky, P. G.

Keldysh, L. V.

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307–1314 (1965).

Kieffer, J. C.

B. Chimier, O. Utéza, N. Sanner, M. Sentis, T. Itina, P. Lassonde, F. Legare, F. Vidal, and J. C. Kieffer, “Damage and ablation thresholds of fused-silica in femtosecond regime,” Phys. Rev. B 84(9), 094104 (2011).
[Crossref]

N. Sanner, O. Utéza, B. Chimier, M. Sentis, P. Lassonde, F. Légaré, and J. C. Kieffer, “Toward determinism in surface damaging of dielectrics using few-cycle laser pulses,” Appl. Phys. Lett. 96(7), 071111 (2010).
[Crossref]

Kittel, T.

D. Ehrt, T. Kittel, M. Will, S. Nolte, and A. Tünnermann, “Femtosecond-laser-writing in various glasses,” J. Non-Cryst. Solids 345-346, 332–337 (2004).
[Crossref]

Korn, G.

D. Du, X. Liu, G. Korn, J. Squier, and G. Mourou, “Laser‐induced breakdown by impact ionization in SiO2 with pulse widths from 7 ns to 150 fs,” Appl. Phys. Lett. 64(23), 3071–3073 (1994).
[Crossref]

Krausz, F.

M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, C. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond optical breakdown in dielectrics,” Phys. Rev. Lett. 80(18), 4076–4079 (1998).
[Crossref]

Krol, D. M.

J. W. Chan, T. R. Huser, S. H. Risbud, and D. M. Krol, “Modification of the fused silica glass network associated with waveguide fabrication using femtosecond laser pulses,” Appl. Phys., A Mater. Sci. Process. 76(3), 367–372 (2003).
[Crossref]

Krüger, J.

P. Rudolph, J. Bonse, J. Krüger, and W. Kautek, “Femtosecond-and nanosecond-pulse laser ablation of bariumalumoborosilicate glass,” Appl. Phys., A Mater. Sci. Process. 69(7), S763–S766 (1999).
[Crossref]

M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, C. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond optical breakdown in dielectrics,” Phys. Rev. Lett. 80(18), 4076–4079 (1998).
[Crossref]

Kuroiwa, Y.

M. Watanabe, Y. Kuroiwa, and S. Ito, “Study of femtosecond laser ablation of multicomponent glass,” Reports Res. Lab. Asahi Glass 55, 27–31 (2005).

Lancry, M.

Lassonde, P.

B. Chimier, O. Utéza, N. Sanner, M. Sentis, T. Itina, P. Lassonde, F. Legare, F. Vidal, and J. C. Kieffer, “Damage and ablation thresholds of fused-silica in femtosecond regime,” Phys. Rev. B 84(9), 094104 (2011).
[Crossref]

N. Sanner, O. Utéza, B. Chimier, M. Sentis, P. Lassonde, F. Légaré, and J. C. Kieffer, “Toward determinism in surface damaging of dielectrics using few-cycle laser pulses,” Appl. Phys. Lett. 96(7), 071111 (2010).
[Crossref]

Lebugle, M.

N. Varkentina, N. Sanner, M. Lebugle, M. Sentis, and O. Utéza, “Absorption of a single 500 fs laser pulse at the surface of fused silica: Energy balance and ablation efficiency,” J. Appl. Phys. 114(17), 173105 (2013).
[Crossref]

Legare, F.

B. Chimier, O. Utéza, N. Sanner, M. Sentis, T. Itina, P. Lassonde, F. Legare, F. Vidal, and J. C. Kieffer, “Damage and ablation thresholds of fused-silica in femtosecond regime,” Phys. Rev. B 84(9), 094104 (2011).
[Crossref]

Légaré, F.

N. Sanner, O. Utéza, B. Chimier, M. Sentis, P. Lassonde, F. Légaré, and J. C. Kieffer, “Toward determinism in surface damaging of dielectrics using few-cycle laser pulses,” Appl. Phys. Lett. 96(7), 071111 (2010).
[Crossref]

Lenzner, M.

M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, C. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond optical breakdown in dielectrics,” Phys. Rev. Lett. 80(18), 4076–4079 (1998).
[Crossref]

Li, R. X.

T. Q. Jia, Z. Z. Xu, R. X. Li, D. H. Feng, X. X. Li, C. F. Cheng, H. Y. Sun, N. S. Xu, and H. Z. Wang, “Mechanisms in fs-laser ablation in fused silica,” J. Appl. Phys. 95(9), 5166–5171 (2004).
[Crossref]

Li, X. X.

T. Q. Jia, Z. Z. Xu, R. X. Li, D. H. Feng, X. X. Li, C. F. Cheng, H. Y. Sun, N. S. Xu, and H. Z. Wang, “Mechanisms in fs-laser ablation in fused silica,” J. Appl. Phys. 95(9), 5166–5171 (2004).
[Crossref]

Little, D. J.

D. J. Little, M. Ams, S. Gross, P. Dekker, C. T. Miese, A. Fuerbach, and M. J. Withford, “Structural changes in BK7 glass upon exposure to femtosecond laser pulses,” J. Raman Spectrosc. 42(4), 715–718 (2011).
[Crossref]

Liu, H. H.

A. P. Joglekar, H. H. Liu, E. Meyhöfer, G. Mourou, and A. J. Hunt, “Optics at critical intensity: Applications to nanomorphing,” Proc. Natl. Acad. Sci. U.S.A. 101(16), 5856–5861 (2004).
[Crossref] [PubMed]

Liu, J.

M. Mero, J. Liu, W. Rudolph, D. Ristau, and K. Starke, “Scaling laws of femtosecond laser pulse induced breakdown in oxide films,” Phys. Rev. B 71(11), 115109 (2005).
[Crossref]

Liu, J. M.

Liu, X.

D. Du, X. Liu, G. Korn, J. Squier, and G. Mourou, “Laser‐induced breakdown by impact ionization in SiO2 with pulse widths from 7 ns to 150 fs,” Appl. Phys. Lett. 64(23), 3071–3073 (1994).
[Crossref]

Luther-Davies, B.

E. G. Gamaly, A. V. Rode, B. Luther-Davies, and V. T. Tikhonchuk, “Ablation of solids by femtosecond lasers: Ablation mechanism and ablation thresholds for metals and dielectrics,” Phys. Plasmas 9(3), 949 (2002).
[Crossref]

Mao, S. S.

S. S. Mao, F. Quéré, S. Guizard, X. Mao, R. E. Russo, G. Petite, and P. Martin, “Dynamics of femtosecond laser interactions with dielectrics,” Appl. Phys., A Mater. Sci. Process. 79, 1695–1709 (2004).
[Crossref]

Mao, X.

S. S. Mao, F. Quéré, S. Guizard, X. Mao, R. E. Russo, G. Petite, and P. Martin, “Dynamics of femtosecond laser interactions with dielectrics,” Appl. Phys., A Mater. Sci. Process. 79, 1695–1709 (2004).
[Crossref]

Martin, P.

S. S. Mao, F. Quéré, S. Guizard, X. Mao, R. E. Russo, G. Petite, and P. Martin, “Dynamics of femtosecond laser interactions with dielectrics,” Appl. Phys., A Mater. Sci. Process. 79, 1695–1709 (2004).
[Crossref]

S. Guizard, A. Semerok, J. Gaudin, M. Hashida, P. Martin, and F. Quéré, “Femtosecond laser ablation of transparent dielectrics: measurement and modelisation of crater profiles,” Appl. Surf. Sci. 186(1-4), 364–368 (2002).
[Crossref]

Mazur, E.

A. Ben-Yakar, R. L. Byer, A. Harkin, J. Ashmore, H. A. Stone, M. Shen, and E. Mazur, “Morphology of femtosecond-laser-ablated borosilicate glass surfaces,” Appl. Phys. Lett. 83(15), 3030–3032 (2003).
[Crossref]

Mermillod-Blondin, A.

Mero, M.

M. Mero, J. Liu, W. Rudolph, D. Ristau, and K. Starke, “Scaling laws of femtosecond laser pulse induced breakdown in oxide films,” Phys. Rev. B 71(11), 115109 (2005).
[Crossref]

Meyhöfer, E.

A. P. Joglekar, H. H. Liu, E. Meyhöfer, G. Mourou, and A. J. Hunt, “Optics at critical intensity: Applications to nanomorphing,” Proc. Natl. Acad. Sci. U.S.A. 101(16), 5856–5861 (2004).
[Crossref] [PubMed]

Mézel, C.

C. Mézel, A. Bourgeade, and L. Hallo, “Surface structuring by ultrashort laser pulses: A review of photoionization models,” Phys. Plasmas 17(11), 113504 (2010).
[Crossref]

Miese, C. T.

D. J. Little, M. Ams, S. Gross, P. Dekker, C. T. Miese, A. Fuerbach, and M. J. Withford, “Structural changes in BK7 glass upon exposure to femtosecond laser pulses,” J. Raman Spectrosc. 42(4), 715–718 (2011).
[Crossref]

Mourou, G.

A. P. Joglekar, H. H. Liu, E. Meyhöfer, G. Mourou, and A. J. Hunt, “Optics at critical intensity: Applications to nanomorphing,” Proc. Natl. Acad. Sci. U.S.A. 101(16), 5856–5861 (2004).
[Crossref] [PubMed]

M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, C. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond optical breakdown in dielectrics,” Phys. Rev. Lett. 80(18), 4076–4079 (1998).
[Crossref]

D. Du, X. Liu, G. Korn, J. Squier, and G. Mourou, “Laser‐induced breakdown by impact ionization in SiO2 with pulse widths from 7 ns to 150 fs,” Appl. Phys. Lett. 64(23), 3071–3073 (1994).
[Crossref]

Nolte, S.

D. Ehrt, T. Kittel, M. Will, S. Nolte, and A. Tünnermann, “Femtosecond-laser-writing in various glasses,” J. Non-Cryst. Solids 345-346, 332–337 (2004).
[Crossref]

Perry, M. D.

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B Condens. Matter 53(4), 1749–1761 (1996).
[Crossref] [PubMed]

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Optical ablation by high-power short-pulse lasers,” J. Opt. Soc. Am. B 13(2), 459–468 (1996).
[Crossref]

Petite, G.

S. S. Mao, F. Quéré, S. Guizard, X. Mao, R. E. Russo, G. Petite, and P. Martin, “Dynamics of femtosecond laser interactions with dielectrics,” Appl. Phys., A Mater. Sci. Process. 79, 1695–1709 (2004).
[Crossref]

Petrov, G. M.

G. M. Petrov and J. Davis, “Interaction of intense ultra-short laser pulses with dielectrics,” J. Phys. B- At. Mol. Opt. 41(2), 025601 (2008).
[Crossref]

Poumellec, B.

Preuss, S.

S. Preuss, M. Späth, Y. Zhang, and M. Stuke, “Time resolved dynamics of subpicosecond laser ablation,” Appl. Phys. Lett. 62(23), 3049 (1993).
[Crossref]

Priven, A. I.

A. I. Priven, “General method for calculating the properties of oxide glasses and glass forming melts from their composition and temperature,” Glass Technol. 45, 244–254 (2004).

Puerto, D.

D. Puerto, J. Siegel, W. Gawelda, M. Galvan-Sosa, L. Ehrentraut, J. Bonse, and J. Solis, “Dynamics of plasma formation, relaxation, and topography modification induced by femtosecond laser pulses in crystalline and amorphous dielectrics,” J. Opt. Soc. Am. B 27(5), 1065–1076 (2010).
[Crossref]

J. Siegel, D. Puerto, W. Gawelda, G. Bachelier, J. Solis, L. Ehrentraut, and J. Bonse, “Plasma formation and structural modification below the visible ablation threshold in fused silica upon femtosecond laser irradiation,” Appl. Phys. Lett. 91(8), 082902 (2007).
[Crossref]

Quéré, F.

S. S. Mao, F. Quéré, S. Guizard, X. Mao, R. E. Russo, G. Petite, and P. Martin, “Dynamics of femtosecond laser interactions with dielectrics,” Appl. Phys., A Mater. Sci. Process. 79, 1695–1709 (2004).
[Crossref]

S. Guizard, A. Semerok, J. Gaudin, M. Hashida, P. Martin, and F. Quéré, “Femtosecond laser ablation of transparent dielectrics: measurement and modelisation of crater profiles,” Appl. Surf. Sci. 186(1-4), 364–368 (2002).
[Crossref]

Reinhardt, F.

M. Grehn, F. Reinhardt, J. Bonse, M. Eberstein, and T. Seuthe, “Response to “Comment on 'Femtosecond laser-induced ablation of potassium-magnesium silicate glasses: An analysis of structural changes by near edge x-ray absorption spectroscopy,”' [Appl. Phys. Lett. 102, 196101 (2012)],” Appl. Phys. Lett. 102(19), 196102 (2013).
[Crossref]

T. Seuthe, M. Höfner, F. Reinhardt, W. J. Tsai, J. Bonse, M. Eberstein, H. J. Eichler, and M. Grehn, “Femtosecond laser-induced modification of potassium-magnesium silicate glasses: an analysis of structural changes by near edge x-ray absorption spectroscopy,” Appl. Phys. Lett. 100(22), 224101 (2012).
[Crossref]

M. Grehn, T. Seuthe, F. Reinhardt, M. Höfner, N. Griga, M. Eberstein, and J. Bonse, “Debris of potassium-magnesium silicate glass generated by femtosecond laser-induced ablation in air: an analysis by near edge X-ray absorption spectroscopy, micro Raman and energy dispersive X-ray spectroscopy,” Appl. Surf. Sci. (2013), doi:.
[Crossref]

Rethfeld, B.

B. Rethfeld, “Free-electron generation in laser-irradiated dielectrics,” Phys. Rev. B 73(3), 035101 (2006).
[Crossref]

Risbud, S. H.

J. W. Chan, T. R. Huser, S. H. Risbud, and D. M. Krol, “Modification of the fused silica glass network associated with waveguide fabrication using femtosecond laser pulses,” Appl. Phys., A Mater. Sci. Process. 76(3), 367–372 (2003).
[Crossref]

Ristau, D.

M. Mero, J. Liu, W. Rudolph, D. Ristau, and K. Starke, “Scaling laws of femtosecond laser pulse induced breakdown in oxide films,” Phys. Rev. B 71(11), 115109 (2005).
[Crossref]

Rode, A. V.

E. G. Gamaly, A. V. Rode, B. Luther-Davies, and V. T. Tikhonchuk, “Ablation of solids by femtosecond lasers: Ablation mechanism and ablation thresholds for metals and dielectrics,” Phys. Plasmas 9(3), 949 (2002).
[Crossref]

Rubenchik, A. M.

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Optical ablation by high-power short-pulse lasers,” J. Opt. Soc. Am. B 13(2), 459–468 (1996).
[Crossref]

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B Condens. Matter 53(4), 1749–1761 (1996).
[Crossref] [PubMed]

Rudolph, P.

P. Rudolph, J. Bonse, J. Krüger, and W. Kautek, “Femtosecond-and nanosecond-pulse laser ablation of bariumalumoborosilicate glass,” Appl. Phys., A Mater. Sci. Process. 69(7), S763–S766 (1999).
[Crossref]

Rudolph, W.

M. Mero, J. Liu, W. Rudolph, D. Ristau, and K. Starke, “Scaling laws of femtosecond laser pulse induced breakdown in oxide films,” Phys. Rev. B 71(11), 115109 (2005).
[Crossref]

Russo, R. E.

S. S. Mao, F. Quéré, S. Guizard, X. Mao, R. E. Russo, G. Petite, and P. Martin, “Dynamics of femtosecond laser interactions with dielectrics,” Appl. Phys., A Mater. Sci. Process. 79, 1695–1709 (2004).
[Crossref]

Sanner, N.

N. Varkentina, N. Sanner, M. Lebugle, M. Sentis, and O. Utéza, “Absorption of a single 500 fs laser pulse at the surface of fused silica: Energy balance and ablation efficiency,” J. Appl. Phys. 114(17), 173105 (2013).
[Crossref]

B. Chimier, O. Utéza, N. Sanner, M. Sentis, T. Itina, P. Lassonde, F. Legare, F. Vidal, and J. C. Kieffer, “Damage and ablation thresholds of fused-silica in femtosecond regime,” Phys. Rev. B 84(9), 094104 (2011).
[Crossref]

N. Sanner, O. Utéza, B. Chimier, M. Sentis, P. Lassonde, F. Légaré, and J. C. Kieffer, “Toward determinism in surface damaging of dielectrics using few-cycle laser pulses,” Appl. Phys. Lett. 96(7), 071111 (2010).
[Crossref]

Sartania, S.

M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, C. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond optical breakdown in dielectrics,” Phys. Rev. Lett. 80(18), 4076–4079 (1998).
[Crossref]

Schou, J.

P. Balling and J. Schou, “Femtosecond-laser ablation dynamics of dielectrics: basics and applications for thin films,” Rep. Prog. Phys. 76(3), 036502 (2013).
[Crossref] [PubMed]

Schüler, H.

Semerok, A.

S. Guizard, A. Semerok, J. Gaudin, M. Hashida, P. Martin, and F. Quéré, “Femtosecond laser ablation of transparent dielectrics: measurement and modelisation of crater profiles,” Appl. Surf. Sci. 186(1-4), 364–368 (2002).
[Crossref]

Sentis, M.

N. Varkentina, N. Sanner, M. Lebugle, M. Sentis, and O. Utéza, “Absorption of a single 500 fs laser pulse at the surface of fused silica: Energy balance and ablation efficiency,” J. Appl. Phys. 114(17), 173105 (2013).
[Crossref]

B. Chimier, O. Utéza, N. Sanner, M. Sentis, T. Itina, P. Lassonde, F. Legare, F. Vidal, and J. C. Kieffer, “Damage and ablation thresholds of fused-silica in femtosecond regime,” Phys. Rev. B 84(9), 094104 (2011).
[Crossref]

N. Sanner, O. Utéza, B. Chimier, M. Sentis, P. Lassonde, F. Légaré, and J. C. Kieffer, “Toward determinism in surface damaging of dielectrics using few-cycle laser pulses,” Appl. Phys. Lett. 96(7), 071111 (2010).
[Crossref]

Seuthe, T.

T. Seuthe, M. Grehn, A. Mermillod-Blondin, H. J. Eichler, J. Bonse, and M. Eberstein, “Structural modifications of binary lithium silicate glasses upon femtosecond laser pulse irradiation probed by micro-Raman spectroscopy,” Opt. Mater. Express 3(6), 755–764 (2013).
[Crossref]

M. Grehn, F. Reinhardt, J. Bonse, M. Eberstein, and T. Seuthe, “Response to “Comment on 'Femtosecond laser-induced ablation of potassium-magnesium silicate glasses: An analysis of structural changes by near edge x-ray absorption spectroscopy,”' [Appl. Phys. Lett. 102, 196101 (2012)],” Appl. Phys. Lett. 102(19), 196102 (2013).
[Crossref]

M. Grehn, T. Seuthe, W.-J. Tsai, M. Höfner, A. W. Achtstein, A. Mermillod-Blondin, M. Eberstein, H. J. Eichler, and J. Bonse, “Nonlinear absorption and refraction of binary and ternary alkaline and alkaline earth silicate glasses,” Opt. Mater. Express 3(12), 2132–2140 (2013).
[Crossref]

T. Seuthe, M. Höfner, F. Reinhardt, W. J. Tsai, J. Bonse, M. Eberstein, H. J. Eichler, and M. Grehn, “Femtosecond laser-induced modification of potassium-magnesium silicate glasses: an analysis of structural changes by near edge x-ray absorption spectroscopy,” Appl. Phys. Lett. 100(22), 224101 (2012).
[Crossref]

M. Grehn, T. Seuthe, F. Reinhardt, M. Höfner, N. Griga, M. Eberstein, and J. Bonse, “Debris of potassium-magnesium silicate glass generated by femtosecond laser-induced ablation in air: an analysis by near edge X-ray absorption spectroscopy, micro Raman and energy dispersive X-ray spectroscopy,” Appl. Surf. Sci. (2013), doi:.
[Crossref]

Shcheblanov, N. S.

N. S. Shcheblanov, E. P. Silaeva, and T. E. Itina, “Electronic excitation and relaxation processes in wide band gap dielectric materials in the transition region of the Keldysh parameter,” Appl. Surf. Sci. 258(23), 9417–9420 (2012).
[Crossref]

Shen, M.

A. Ben-Yakar, R. L. Byer, A. Harkin, J. Ashmore, H. A. Stone, M. Shen, and E. Mazur, “Morphology of femtosecond-laser-ablated borosilicate glass surfaces,” Appl. Phys. Lett. 83(15), 3030–3032 (2003).
[Crossref]

Shore, B. W.

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Optical ablation by high-power short-pulse lasers,” J. Opt. Soc. Am. B 13(2), 459–468 (1996).
[Crossref]

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B Condens. Matter 53(4), 1749–1761 (1996).
[Crossref] [PubMed]

Siegel, J.

D. Puerto, J. Siegel, W. Gawelda, M. Galvan-Sosa, L. Ehrentraut, J. Bonse, and J. Solis, “Dynamics of plasma formation, relaxation, and topography modification induced by femtosecond laser pulses in crystalline and amorphous dielectrics,” J. Opt. Soc. Am. B 27(5), 1065–1076 (2010).
[Crossref]

J. Siegel, D. Puerto, W. Gawelda, G. Bachelier, J. Solis, L. Ehrentraut, and J. Bonse, “Plasma formation and structural modification below the visible ablation threshold in fused silica upon femtosecond laser irradiation,” Appl. Phys. Lett. 91(8), 082902 (2007).
[Crossref]

Silaeva, E. P.

N. S. Shcheblanov, E. P. Silaeva, and T. E. Itina, “Electronic excitation and relaxation processes in wide band gap dielectric materials in the transition region of the Keldysh parameter,” Appl. Surf. Sci. 258(23), 9417–9420 (2012).
[Crossref]

Solis, J.

D. Puerto, J. Siegel, W. Gawelda, M. Galvan-Sosa, L. Ehrentraut, J. Bonse, and J. Solis, “Dynamics of plasma formation, relaxation, and topography modification induced by femtosecond laser pulses in crystalline and amorphous dielectrics,” J. Opt. Soc. Am. B 27(5), 1065–1076 (2010).
[Crossref]

J. Siegel, D. Puerto, W. Gawelda, G. Bachelier, J. Solis, L. Ehrentraut, and J. Bonse, “Plasma formation and structural modification below the visible ablation threshold in fused silica upon femtosecond laser irradiation,” Appl. Phys. Lett. 91(8), 082902 (2007).
[Crossref]

Späth, M.

S. Preuss, M. Späth, Y. Zhang, and M. Stuke, “Time resolved dynamics of subpicosecond laser ablation,” Appl. Phys. Lett. 62(23), 3049 (1993).
[Crossref]

Spielmann, C.

M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, C. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond optical breakdown in dielectrics,” Phys. Rev. Lett. 80(18), 4076–4079 (1998).
[Crossref]

Squier, J.

D. Du, X. Liu, G. Korn, J. Squier, and G. Mourou, “Laser‐induced breakdown by impact ionization in SiO2 with pulse widths from 7 ns to 150 fs,” Appl. Phys. Lett. 64(23), 3071–3073 (1994).
[Crossref]

Starke, K.

M. Mero, J. Liu, W. Rudolph, D. Ristau, and K. Starke, “Scaling laws of femtosecond laser pulse induced breakdown in oxide films,” Phys. Rev. B 71(11), 115109 (2005).
[Crossref]

Stone, H. A.

A. Ben-Yakar, R. L. Byer, A. Harkin, J. Ashmore, H. A. Stone, M. Shen, and E. Mazur, “Morphology of femtosecond-laser-ablated borosilicate glass surfaces,” Appl. Phys. Lett. 83(15), 3030–3032 (2003).
[Crossref]

Stuart, B. C.

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B Condens. Matter 53(4), 1749–1761 (1996).
[Crossref] [PubMed]

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Optical ablation by high-power short-pulse lasers,” J. Opt. Soc. Am. B 13(2), 459–468 (1996).
[Crossref]

Stuke, M.

S. Preuss, M. Späth, Y. Zhang, and M. Stuke, “Time resolved dynamics of subpicosecond laser ablation,” Appl. Phys. Lett. 62(23), 3049 (1993).
[Crossref]

Sun, H. Y.

T. Q. Jia, Z. Z. Xu, R. X. Li, D. H. Feng, X. X. Li, C. F. Cheng, H. Y. Sun, N. S. Xu, and H. Z. Wang, “Mechanisms in fs-laser ablation in fused silica,” J. Appl. Phys. 95(9), 5166–5171 (2004).
[Crossref]

Sun, K. H.

K. H. Sun, “Fundamental condition of glass formation,” J. Am. Ceram. Soc. 30(9), 277–281 (1947).
[Crossref]

K. H. Sun and M. L. Huggins, “Energy Additivity in Oxygen-containing Crystals and Glasses,” J. Phys. Colloid Chem. 51(2), 438–443 (1947).
[Crossref] [PubMed]

Tikhonchuk, V. T.

E. G. Gamaly, A. V. Rode, B. Luther-Davies, and V. T. Tikhonchuk, “Ablation of solids by femtosecond lasers: Ablation mechanism and ablation thresholds for metals and dielectrics,” Phys. Plasmas 9(3), 949 (2002).
[Crossref]

Tsai, H. L.

L. Jiang and H. L. Tsai, “Energy transport and material removal in wide bandgap materials by a femtosecond laser pulse,” Int. J. Heat Mass Tran. 48(3-4), 487–499 (2005).
[Crossref]

Tsai, W. J.

T. Seuthe, M. Höfner, F. Reinhardt, W. J. Tsai, J. Bonse, M. Eberstein, H. J. Eichler, and M. Grehn, “Femtosecond laser-induced modification of potassium-magnesium silicate glasses: an analysis of structural changes by near edge x-ray absorption spectroscopy,” Appl. Phys. Lett. 100(22), 224101 (2012).
[Crossref]

Tsai, W.-J.

Tünnermann, A.

D. Ehrt, T. Kittel, M. Will, S. Nolte, and A. Tünnermann, “Femtosecond-laser-writing in various glasses,” J. Non-Cryst. Solids 345-346, 332–337 (2004).
[Crossref]

Utéza, O.

N. Varkentina, N. Sanner, M. Lebugle, M. Sentis, and O. Utéza, “Absorption of a single 500 fs laser pulse at the surface of fused silica: Energy balance and ablation efficiency,” J. Appl. Phys. 114(17), 173105 (2013).
[Crossref]

B. Chimier, O. Utéza, N. Sanner, M. Sentis, T. Itina, P. Lassonde, F. Legare, F. Vidal, and J. C. Kieffer, “Damage and ablation thresholds of fused-silica in femtosecond regime,” Phys. Rev. B 84(9), 094104 (2011).
[Crossref]

N. Sanner, O. Utéza, B. Chimier, M. Sentis, P. Lassonde, F. Légaré, and J. C. Kieffer, “Toward determinism in surface damaging of dielectrics using few-cycle laser pulses,” Appl. Phys. Lett. 96(7), 071111 (2010).
[Crossref]

Varkentina, N.

N. Varkentina, N. Sanner, M. Lebugle, M. Sentis, and O. Utéza, “Absorption of a single 500 fs laser pulse at the surface of fused silica: Energy balance and ablation efficiency,” J. Appl. Phys. 114(17), 173105 (2013).
[Crossref]

Vidal, F.

B. Chimier, O. Utéza, N. Sanner, M. Sentis, T. Itina, P. Lassonde, F. Legare, F. Vidal, and J. C. Kieffer, “Damage and ablation thresholds of fused-silica in femtosecond regime,” Phys. Rev. B 84(9), 094104 (2011).
[Crossref]

von der Linde, D.

Wang, H. Z.

T. Q. Jia, Z. Z. Xu, R. X. Li, D. H. Feng, X. X. Li, C. F. Cheng, H. Y. Sun, N. S. Xu, and H. Z. Wang, “Mechanisms in fs-laser ablation in fused silica,” J. Appl. Phys. 95(9), 5166–5171 (2004).
[Crossref]

Watanabe, M.

M. Watanabe, Y. Kuroiwa, and S. Ito, “Study of femtosecond laser ablation of multicomponent glass,” Reports Res. Lab. Asahi Glass 55, 27–31 (2005).

Will, M.

D. Ehrt, T. Kittel, M. Will, S. Nolte, and A. Tünnermann, “Femtosecond-laser-writing in various glasses,” J. Non-Cryst. Solids 345-346, 332–337 (2004).
[Crossref]

Withford, M. J.

D. J. Little, M. Ams, S. Gross, P. Dekker, C. T. Miese, A. Fuerbach, and M. J. Withford, “Structural changes in BK7 glass upon exposure to femtosecond laser pulses,” J. Raman Spectrosc. 42(4), 715–718 (2011).
[Crossref]

Wu, A. Q.

A. Q. Wu, I. H. Chowdhury, and X. Xu, “Femtosecond laser absorption in fused silica: Numerical and experimental investigation,” Phys. Rev. B 72(8), 085128 (2005).
[Crossref]

Xu, N. S.

T. Q. Jia, Z. Z. Xu, R. X. Li, D. H. Feng, X. X. Li, C. F. Cheng, H. Y. Sun, N. S. Xu, and H. Z. Wang, “Mechanisms in fs-laser ablation in fused silica,” J. Appl. Phys. 95(9), 5166–5171 (2004).
[Crossref]

Xu, X.

A. Q. Wu, I. H. Chowdhury, and X. Xu, “Femtosecond laser absorption in fused silica: Numerical and experimental investigation,” Phys. Rev. B 72(8), 085128 (2005).
[Crossref]

Xu, Z. Z.

T. Q. Jia, Z. Z. Xu, R. X. Li, D. H. Feng, X. X. Li, C. F. Cheng, H. Y. Sun, N. S. Xu, and H. Z. Wang, “Mechanisms in fs-laser ablation in fused silica,” J. Appl. Phys. 95(9), 5166–5171 (2004).
[Crossref]

Zhang, Y.

S. Preuss, M. Späth, Y. Zhang, and M. Stuke, “Time resolved dynamics of subpicosecond laser ablation,” Appl. Phys. Lett. 62(23), 3049 (1993).
[Crossref]

Appl. Phys. Lett. (7)

D. Du, X. Liu, G. Korn, J. Squier, and G. Mourou, “Laser‐induced breakdown by impact ionization in SiO2 with pulse widths from 7 ns to 150 fs,” Appl. Phys. Lett. 64(23), 3071–3073 (1994).
[Crossref]

N. Sanner, O. Utéza, B. Chimier, M. Sentis, P. Lassonde, F. Légaré, and J. C. Kieffer, “Toward determinism in surface damaging of dielectrics using few-cycle laser pulses,” Appl. Phys. Lett. 96(7), 071111 (2010).
[Crossref]

A. Ben-Yakar, R. L. Byer, A. Harkin, J. Ashmore, H. A. Stone, M. Shen, and E. Mazur, “Morphology of femtosecond-laser-ablated borosilicate glass surfaces,” Appl. Phys. Lett. 83(15), 3030–3032 (2003).
[Crossref]

J. Siegel, D. Puerto, W. Gawelda, G. Bachelier, J. Solis, L. Ehrentraut, and J. Bonse, “Plasma formation and structural modification below the visible ablation threshold in fused silica upon femtosecond laser irradiation,” Appl. Phys. Lett. 91(8), 082902 (2007).
[Crossref]

M. Grehn, F. Reinhardt, J. Bonse, M. Eberstein, and T. Seuthe, “Response to “Comment on 'Femtosecond laser-induced ablation of potassium-magnesium silicate glasses: An analysis of structural changes by near edge x-ray absorption spectroscopy,”' [Appl. Phys. Lett. 102, 196101 (2012)],” Appl. Phys. Lett. 102(19), 196102 (2013).
[Crossref]

T. Seuthe, M. Höfner, F. Reinhardt, W. J. Tsai, J. Bonse, M. Eberstein, H. J. Eichler, and M. Grehn, “Femtosecond laser-induced modification of potassium-magnesium silicate glasses: an analysis of structural changes by near edge x-ray absorption spectroscopy,” Appl. Phys. Lett. 100(22), 224101 (2012).
[Crossref]

S. Preuss, M. Späth, Y. Zhang, and M. Stuke, “Time resolved dynamics of subpicosecond laser ablation,” Appl. Phys. Lett. 62(23), 3049 (1993).
[Crossref]

Appl. Phys., A Mater. Sci. Process. (4)

J. W. Chan, T. R. Huser, S. H. Risbud, and D. M. Krol, “Modification of the fused silica glass network associated with waveguide fabrication using femtosecond laser pulses,” Appl. Phys., A Mater. Sci. Process. 76(3), 367–372 (2003).
[Crossref]

V. E. Gruzdev and J. K. Chen, “Laser-induced ionization and intrinsic breakdown of wide band-gap solids,” Appl. Phys., A Mater. Sci. Process. 90(2), 255–261 (2007).
[Crossref]

P. Rudolph, J. Bonse, J. Krüger, and W. Kautek, “Femtosecond-and nanosecond-pulse laser ablation of bariumalumoborosilicate glass,” Appl. Phys., A Mater. Sci. Process. 69(7), S763–S766 (1999).
[Crossref]

S. S. Mao, F. Quéré, S. Guizard, X. Mao, R. E. Russo, G. Petite, and P. Martin, “Dynamics of femtosecond laser interactions with dielectrics,” Appl. Phys., A Mater. Sci. Process. 79, 1695–1709 (2004).
[Crossref]

Appl. Surf. Sci. (2)

N. S. Shcheblanov, E. P. Silaeva, and T. E. Itina, “Electronic excitation and relaxation processes in wide band gap dielectric materials in the transition region of the Keldysh parameter,” Appl. Surf. Sci. 258(23), 9417–9420 (2012).
[Crossref]

S. Guizard, A. Semerok, J. Gaudin, M. Hashida, P. Martin, and F. Quéré, “Femtosecond laser ablation of transparent dielectrics: measurement and modelisation of crater profiles,” Appl. Surf. Sci. 186(1-4), 364–368 (2002).
[Crossref]

Glass Technol. (1)

A. I. Priven, “General method for calculating the properties of oxide glasses and glass forming melts from their composition and temperature,” Glass Technol. 45, 244–254 (2004).

Int. J. Heat Mass Tran. (1)

L. Jiang and H. L. Tsai, “Energy transport and material removal in wide bandgap materials by a femtosecond laser pulse,” Int. J. Heat Mass Tran. 48(3-4), 487–499 (2005).
[Crossref]

J. Am. Ceram. Soc. (1)

K. H. Sun, “Fundamental condition of glass formation,” J. Am. Ceram. Soc. 30(9), 277–281 (1947).
[Crossref]

J. Appl. Phys. (3)

A. Ben-Yakar and R. L. Byer, “Femtosecond laser ablation properties of borosilicate glass,” J. Appl. Phys. 96(9), 5316–5323 (2004).
[Crossref]

N. Varkentina, N. Sanner, M. Lebugle, M. Sentis, and O. Utéza, “Absorption of a single 500 fs laser pulse at the surface of fused silica: Energy balance and ablation efficiency,” J. Appl. Phys. 114(17), 173105 (2013).
[Crossref]

T. Q. Jia, Z. Z. Xu, R. X. Li, D. H. Feng, X. X. Li, C. F. Cheng, H. Y. Sun, N. S. Xu, and H. Z. Wang, “Mechanisms in fs-laser ablation in fused silica,” J. Appl. Phys. 95(9), 5166–5171 (2004).
[Crossref]

J. Non-Cryst. Solids (1)

D. Ehrt, T. Kittel, M. Will, S. Nolte, and A. Tünnermann, “Femtosecond-laser-writing in various glasses,” J. Non-Cryst. Solids 345-346, 332–337 (2004).
[Crossref]

J. Opt. Soc. Am. B (3)

J. Phys. B- At. Mol. Opt. (1)

G. M. Petrov and J. Davis, “Interaction of intense ultra-short laser pulses with dielectrics,” J. Phys. B- At. Mol. Opt. 41(2), 025601 (2008).
[Crossref]

J. Phys. Colloid Chem. (1)

K. H. Sun and M. L. Huggins, “Energy Additivity in Oxygen-containing Crystals and Glasses,” J. Phys. Colloid Chem. 51(2), 438–443 (1947).
[Crossref] [PubMed]

J. Raman Spectrosc. (1)

D. J. Little, M. Ams, S. Gross, P. Dekker, C. T. Miese, A. Fuerbach, and M. J. Withford, “Structural changes in BK7 glass upon exposure to femtosecond laser pulses,” J. Raman Spectrosc. 42(4), 715–718 (2011).
[Crossref]

Opt. Lett. (1)

Opt. Mater. Express (3)

Phys. Plasmas (2)

E. G. Gamaly, A. V. Rode, B. Luther-Davies, and V. T. Tikhonchuk, “Ablation of solids by femtosecond lasers: Ablation mechanism and ablation thresholds for metals and dielectrics,” Phys. Plasmas 9(3), 949 (2002).
[Crossref]

C. Mézel, A. Bourgeade, and L. Hallo, “Surface structuring by ultrashort laser pulses: A review of photoionization models,” Phys. Plasmas 17(11), 113504 (2010).
[Crossref]

Phys. Rev. B (5)

M. Mero, J. Liu, W. Rudolph, D. Ristau, and K. Starke, “Scaling laws of femtosecond laser pulse induced breakdown in oxide films,” Phys. Rev. B 71(11), 115109 (2005).
[Crossref]

B. H. Christensen and P. Balling, “Modeling ultrashort-pulse laser ablation of dielectric materials,” Phys. Rev. B 79(15), 155424 (2009).
[Crossref]

B. Chimier, O. Utéza, N. Sanner, M. Sentis, T. Itina, P. Lassonde, F. Legare, F. Vidal, and J. C. Kieffer, “Damage and ablation thresholds of fused-silica in femtosecond regime,” Phys. Rev. B 84(9), 094104 (2011).
[Crossref]

B. Rethfeld, “Free-electron generation in laser-irradiated dielectrics,” Phys. Rev. B 73(3), 035101 (2006).
[Crossref]

A. Q. Wu, I. H. Chowdhury, and X. Xu, “Femtosecond laser absorption in fused silica: Numerical and experimental investigation,” Phys. Rev. B 72(8), 085128 (2005).
[Crossref]

Phys. Rev. B Condens. Matter (1)

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B Condens. Matter 53(4), 1749–1761 (1996).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, C. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond optical breakdown in dielectrics,” Phys. Rev. Lett. 80(18), 4076–4079 (1998).
[Crossref]

Proc. Natl. Acad. Sci. U.S.A. (1)

A. P. Joglekar, H. H. Liu, E. Meyhöfer, G. Mourou, and A. J. Hunt, “Optics at critical intensity: Applications to nanomorphing,” Proc. Natl. Acad. Sci. U.S.A. 101(16), 5856–5861 (2004).
[Crossref] [PubMed]

Rep. Prog. Phys. (1)

P. Balling and J. Schou, “Femtosecond-laser ablation dynamics of dielectrics: basics and applications for thin films,” Rep. Prog. Phys. 76(3), 036502 (2013).
[Crossref] [PubMed]

Reports Res. Lab. Asahi Glass (1)

M. Watanabe, Y. Kuroiwa, and S. Ito, “Study of femtosecond laser ablation of multicomponent glass,” Reports Res. Lab. Asahi Glass 55, 27–31 (2005).

Sov. Phys. JETP (1)

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307–1314 (1965).

Other (2)

M. Grehn, T. Seuthe, F. Reinhardt, M. Höfner, N. Griga, M. Eberstein, and J. Bonse, “Debris of potassium-magnesium silicate glass generated by femtosecond laser-induced ablation in air: an analysis by near edge X-ray absorption spectroscopy, micro Raman and energy dispersive X-ray spectroscopy,” Appl. Surf. Sci. (2013), doi:.
[Crossref]

D. Bäuerle, Laser Processing and Chemistry, 4th ed. (Springer-Verlag, 2011)

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Figures (5)

Fig. 1
Fig. 1 Plot of the squared ablation diameter D2 vs. the peak fluence F0 for LiGe50Si25 (red triangles) and Borofloat glass (black squares). Note the semi-logarithmic data representation. The solid lines correspond to least-squares-fits with the method proposed in [37]. The arrows indicate the ablation threshold obtained from the fits. The horizontal and vertical bars correspond to the statistical errors.
Fig. 2
Fig. 2 Maximum depth of the ablation craters dmax vs. the incident peak fluence F0 for LiGe50Si25 (red circles) and Borofloat glass (black squares). The solid lines correspond to a least-squares-fit using Eq. (3).
Fig. 3
Fig. 3 SFM surface topography of a selection of laser-induced ablation craters on Borofloat (upper row) and LiGe50Si25 (lower row) glasses. The corresponding horizontal cross-sectional profiles (open symbols) along with the plots of Eq. (4) (solid lines) are shown on the right hand side.
Fig. 4
Fig. 4 Ablation threshold fluence Φ th , d i a vs. the calculated dissociation energy E d i s s c a l c for the investigated silicate glasses (black squares), Fused silica (green triangle) [17] and sapphire (blue rhomb) [17]. Additionally, values for tellurite and bismuthate glasses (red circles) from [33] are presented.
Fig. 5
Fig. 5 Absorbed energy density at the ablation threshold vs. the calculated dissociation energy density for the investigated silicate glasses (black squares), Fused silica (green triangle) and Sapphire (blue rhomb). The solid (red) line represents the identity of both entities.

Tables (6)

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Table 1 Stoichiometric batch composition of the glass samples

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Table 2 Incident ablation threshold fluences Fth,dia obtained by the D2-method along with the ablation threshold fluence Φth,dia corrected by the reflection losses (R). All error bars are derived from the fitting procedure. The refractive indexes nd are taken from [40]. The Fresnel reflectivity is calculated neglecting the difference in n of the two wavelengths 589 and 800 nm, which is not significantly affecting the values of R here

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Table 3 Ablation threshold fluences Fth,dia and 3-PA coefficients α3dep of the glasses derived from fits of the crater depth vs. the applied laser fluence F0 (Eq. (3)) and ablation threshold fluences Φth,dia with the considered reflection losses of the air-glass interface. Additionally, nonlinear absorption coefficients from z-scan technique are listed [42]. Error values are statistical deviations obtained from the least-squares-fitting procedure

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Table 4 Ablation threshold fluences F th , d e p and multiphoton absorption (m-PA) coefficients α m d e p of fused silica and sapphire derived from fits of the crater depth vs. the incident laser fluence F0 (taken from Ref [17].) and the ablation threshold fluences Φ th , d e p with the considered reflection losses of the air-glass interface. Additionally, the band gap energies and the refractive indices are listed

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Table 5 Molar mass and dissociation energy of the glass oxides

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Table 6 Density, molar mass, dissociation energy, and band gap energy of the investigated glasses

Equations (7)

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

dI(z) dz = α m I m (z).
dF(z) dz = α m τ m1 (1R) m1 F m (z).
d max = τ m1 (m1) α m dep (1R) m1 [ 1 F th,dep m1 1 F 0 m1 ].
d(r)= τ² 2 α 3 (1R)² [ 1 F th ² exp{4r²/ w 0 ²} F 0 ² ],
ε b = i mol % i ε i MeO
E diss calc = ε b ρ i mol % i M i = ε b ρ M
E th m-PA = d Φ dep d z | z0 = α m τ m1 [ Φ th,dep ] m

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