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Abstract
The evolution mechanism of femtosecond laser-induced filaments has been widely investigated owing to its application prospects in microprocessing. However, the material dependence of the excitation, stability, and decay of filaments is not well understood despite the importance of their precise utilization. In this study, the spatiotemporal evolution of filaments induced by a single femtosecond laser pulse in sapphire and silica glass was investigated using time-resolved pump-probe shadowgraphy on femtosecond and picosecond timescales. The results revealed that the evolution was significantly different in the two typically transparent dielectrics in terms of the electronic plasma dynamics and filament lifetimes. This difference can be attributed to the self-trapped excitons (STEs) in silica glass. Furthermore, the filament dependence on pump energy and focal position was experimentally analyzed. Divergent filaments were observed when the focal position was near the surface because of the effect of the excited plasma on beam propagation. Moreover, the evolution of filament length in the two materials was discussed. This study contributes to the applications of filaments in precise processing.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Filamentation is formed by the dynamic balance between Kerr self-focusing and electronic plasma defocusing during femtosecond laser pulse propagation in transparent dielectrics [1,2]. It has received extensive attention owing to its potential applications in microprocessing fields [3], such as micro drilling [4–7], micro welding [8], waveguide writing [9,10], grating fabrication [11,12], and scribing [13]. The processing mechanism depends on the interaction between femtosecond laser pulses and matter, and the properties of induced filaments, especially the extended propagation length [6,13] and excited electronic plasma [4,14]. Therefore, understanding the formation rules and characteristics of filaments is useful for the precise control of microprocessing applications of femtosecond lasers.
Several previous studies have focused on the peak intensity and decay time of electrons excited by ultrafast laser pulses. Mao et al. [15] captured time-resolved images of plasma filaments induced by a femtosecond laser pulse in borosilicate glass and measured the spatial variation of the excited electron density. Huang et al. [16] investigated the temporal-spatial dynamics of the peak electron density in a filament induced by a single femtosecond laser pulse in fused silica and calculated the critical electron density of material damage. Pan et al. [17] researched the evolution of electrons excited by double femtosecond pulses and analyzed the influence of the first pulse on subsequent filament formation during the second pulse. Moreover, the relaxation process of excited electron plasma induced by ultrafast lasers in transparent dielectrics was well clarified using the transmissivity measurements of probe beams [18,19]. In addition, the parameter dependence of the filament formation laws was investigated. Wang et al. [20] observed filament splitting during multipulse ablation of fused silica and revealed the effect of pre-pulse-ablated craters on the filaments induced by subsequent pulses. Sun et al. [21] analyzed the influence of pulse duration on the filamentation behavior, which was explained using ionization mechanisms. Nevertheless, the material dependence of the excitation, stability, and decay of filaments has not been well investigated despite the significance of their precise applications.
In this study, a pump-probe setup was constructed to investigate the evolution of filaments induced by a single femtosecond laser pulse in sapphire and silica glass using time-resolved shadowgraphy on femtosecond and picosecond timescales. The material dependence of the evolution was experimentally analyzed in terms of the dynamics of the electronic plasma and the lifetime of the filaments. In addition, experiments were conducted to clarify the dependence of filaments on pump energy and focal position. The characteristics of the filaments are further summarized and discussed.
2. Methods
2.1 Experimental setup
The experimental setup is shown in Fig. 1. A Yb:KGW laser system was used to generate femtosecond pulses with a wavelength of 1030 nm and pulse duration of 170 fs. Each delivered pulse was split into pump and probe pulses using a beam splitter. A quarter-wave plate was used to convert the pump to a circularly polarized wave which was then focused onto a sample using an objective lens OL1 (Mitutoyo; M Plan Apo NIR 10×) with a focal length of 20 mm. The probe pulse was frequency-doubled by a beta barium borate (BBO) crystal, and then illuminated the sample perpendicularly to the pump pulse. The transmitted probe pulse was collected using a second objective lens OL2 (Mitutoyo; M Plan Apo NIR 20×), and the filament shadowgraph was imaged on a cooled charge-coupled device (CCD) (Bitran; BU-55LN). The CCD was synchronized with the femtosecond laser system so that one image corresponded to each pump pulse. Time-resolved imaging was realized using an optical delay line consisting of two reflectors, which enabled a probe pulse delay ranging from femtoseconds to sub-nanoseconds. Images with increasing probe delays were sequentially recorded, which revealed the evolution of the filaments. The short-pass filter (SPF) after the BBO was used to exclude the remained 1030 nm light from the probe pulse, and the SPF in front of the CCD was used to suppress the disturbance caused by the scattered pump pulse and plasma radiation. Two samples with polished surfaces were used in the experiment; one was amorphous silica glass, and the other was single-crystal sapphire. The sample was mounted on a three-directional moving stage; thus, the incidence points and focal positions of the pump pulses on the sample were adjustable. Another CCD was used to find the surface of the sample using white-light illumination.
Fig. 1. Schematic of the experimental setup. BS: beam splitter; BBO: beta barium borate; SPF: short-pass filter; R: reflector; λ/4: quarter-wave plate; DM: dichroic mirror; OL: objective lens (OL1and OL2); TL: tube lens.
2.2 Definition and parameters
To precisely control the focal positions into the samples, the focuses of the pump pulses were measured at different energies. The surface of the sample was firstly found by the white-light CCD, and the surface position, corresponding to the focus of white light, was defined as Y = 0 µm, as shown in Fig. 2(a). Then, a single pump pulse was used to drill a piece of silicon sample that was opaque to the 1030 nm laser, and numerous holes were obtained by moving the sample along the Y direction with a step size of 5 µm; the sample position where the minimum hole occurred was defined as the focus. The difference of focuses between the pump pulse and white light was YF(E), illustrated in Fig. 2(a), where E was the pump pulse energy, and the results are shown in Fig. 2(b). It indicates that the focuses of the pump pulses were between the objective lens and the focus of white light. The difference increased as the power increased owing to the positive correlation between the self-focusing effect and the energy.
Fig. 2. (a) Schematic of the focuses. (b) Focus difference vs pump pulse energies. (c) Zero delay and delay time in pump-probe imaging.
In the experiments, the focal position inside the sample was changed by moving the sample along the beam propagation direction. The sample surface was firstly adjusted to the focal plane of the pump pulse, and then shifted to the position of YS, where YS = D + YF(E), illustrated in Fig. 2(a). We used the D to indicate the relative positions between pump focuses and sample surface, and the focal position of pump was shifted deeper into the sample as D increased. In addition, the theoretical beam diameter was 5.7 µm when the pump pulse was focused on the sample surface (D = 0 µm) using the objective lens OL1 (NA = 0.26). When D were 30 µm and 60 µm, the calculated diameters on the sample surface were 21.86 µm and 38.01 µm, respectively. Therefore, the laser fluences on the sample surface with different pump energy and D were 274.32 J/cm2 (70 µJ-0 µm), 18.65 J/cm2 (70 µJ-30 µm), 6.17 J/cm2 (70 µJ-60 µm), 195.94 J/cm2 (50 µJ-0 µm), 13.32 J/cm2 (50 µJ-30 µm), 4.41 J/cm2 (50 µJ-60 µm), 117.57 J/cm2 (30 µJ-0 µm), 7.99 J/cm2 (30 µJ-30 µm), 2.64 J/cm2 (30 µJ-60 µm).
The delay time for pump-probe imaging was determined by the difference of optical path lengths (OPLs) between pump and probe pulses, and the difference was changed by moving the delay line. The position of delay line at which the OPLs of pump and probe pulses were the same was defined as the zero-delay position. The probe pulse propagated a distance in the sample before arriving at the plasma because of the sample thickness, and thus, its OPL depended on the refractive index of materials. The OPL of pump pulse was changed by the variation of relative position D, and D was related to the pump energy E. Therefore, the zero-delay position was a function of material, pump energy and relative position, expressed as X0(M, E, D), where M was the material. The reference zero-delay position was determined in sapphire (Sa) when the filament was very weak and short at E = 70 µJ and D = 0 µm, which was expressed using X0(Sa, 70 µJ, 0 µm), as illustrated in Fig. 2(c). The zero-delay positions in other experimental conditions were obtained by calculating the delay change compared to the reference zero delay. Based on the zero-delay position, the delay time of imaging was Δt = 2[X0(M, E, D) - X]/c when the delay line was at the position of X, where c is the light speed.
3. Results and discussion
3.1 Dependence on materials
Images with and without pump beams were recorded in each experiment, and the background noise was eliminated by calculating the ratio between the two images. The results of filaments in sapphire and silica glass are shown in Figs. 3 and 4, respectively. The pump energy was 50 µJ, and the relative position was D = 60 µm. The interface between the air and the sample was defined as Z = 0 µm. In sapphire, the filament gradually grew along the Z direction from 480 fs to 2.28 ps, and then remained stable from 2.28 to 5.48 ps before slowly decaying from 5.48 ps and disappearing after 72.48 ps. Finally, shock wave propagation was observed from 72.48 ps. In silica glass, the filament grew along the Z direction from 480 fs to 1.48 ps, and then entered the stable state from 2.28 ps. At this point, the filament became bright. Shock waves were observed from 72.48 ps. The lifetime of the filament was 72 ps in sapphire and at least 972 ps in silica glass.
Fig. 3. Filament evolution in sapphire with a pump energy of 50 µJ and a relative position D = 60 µm. The red arrow indicates the laser incidence. The dotted line denotes the interface between the air and the sample.
Fig. 4. Filament evolution in silica glass with a pump energy of 50 µJ and a relative position D = 60 µm. The red arrow indicates the laser incidence. The dotted line denotes the interface between the air and the sample.
The black shadow in the filaments represents probe beam depletion caused by the inverse Bremmstrahlung absorption of free electrons in the conduction band [19]. The plasma density is proportional to the absorption coefficient of the probe beam [16]. The absorption can be described as
where It is the intensity of the probe beam passing through the central part of the filament, α is the absorption coefficient, and x is the width of the filament in the direction of probe beam propagation. The average absorption coefficient is calculated as follows: where I0 and I1 are the intensities of the probe beam before and after the filament, respectively, and d is the average width of the filament. The absorption results are shown in Figs. 5 and 6, which reflect the dynamics of the plasma. The Z = 0 µm position is the interface between the air and the sample, and the fluctuation of absorption near the interface from 72.48 to 972.48 ps was attributed to shock waves and the removal of material.Fig. 5. Transient average absorption coefficient of the probe beam in sapphire at different delay times with a pump energy of 50 µJ and a relative position D = 60 µm.
Fig. 6. Transient average absorption coefficient of the probe beam in silica glass at different delay times with a pump energy of 50 µJ and a relative position D = 60 µm.
The absorption coefficients abruptly increased at 480 fs for sapphire and silica glass. This indicates that the plasma in the two materials was excited after almost the same time delay of approximately 480 fs. Moreover, the results show that the plasma density in sapphire was smaller than that in silica glass from 480 to 680 fs. The plasma formation mechanisms in dielectrics can be described using the rate equation [22–24]
With the propagation of a pump pulse, the excited plasma in the filaments achieved peak density. The saturation speed of the plasma in the two materials is different. The plasma in the sapphire filament saturated at approximately 1.48 ps; thus, the growth time was 1 ps. However, the plasma in the silica glass filament reached its maximum density state at approximately 680 fs; thus, the growth time was 200 fs.
As the free electrons relaxed, the probe beam gradually recovered its intensity and the absorption coefficient decreased. In sapphire, the density of the free electrons decreased from approximately 1.48 ps to approximately 72.48 ps. The decay process lasted for 71 ps, which is similar to previous research, where the lifetime was found to be 100 ps with an uncertainty of the order of 10% [25]. In silica glass, the density of free electrons decreased from 680 fs to approximately 1.48 ps, despite the filament’s continued growth along the Z direction from 680 fs to 1.48 ps. The rapid decay of the free electrons lasted for 800 fs. Finally, the filament became stable in terms of electron density and length from 2.28 to 972.48 ps. The ultrafast plasma relaxation phenomenon in silica glass may be attributed to self-trapped excitons (STEs) [26,27]. Owing to the intense interaction between the excited electrons and the lattice, the electron–hole pairs are rapidly trapped as a result of lattice distortion [28]. In previous studies, the trapping time ranged from 50 to 220 fs [18,29–31], and the rapid reduction of free electrons between 680 fs and 1.48 ps observed in this experiment is in agreement with these reported trapping processes. The high filament stability from 2.28 to 972.48 ps after trapping is due to the long lifetime of STEs [32,33].
In addition, the STE absorption band is larger than the photon energy of the probe beam, and the intensity of the unfocused probe is too weak to achieve multiphoton absorption; thus, the STEs do not absorb the probe beam. The appearance of bright silica glass filaments from 2.28 ps immediately after trapping may be caused by changes in the refractive index or the increase in transmission; however, this requires further investigation. The radiative recombination of STEs accompanied by visible luminescence only occurs at temperatures below 220 K [34–37], and the luminescence characteristic of the direct recombination of electron–hole pairs from the conduction band to the valence band is outside the visible range and cannot be captured by the CCD camera. Therefore, the radiation argument was excluded.
The evolution laws of filaments in sapphire and silica glass are essentially different; this determines what concrete methods are utilized in filamentation-assisted microfabrication. The sapphire plasma remains at the conduction band for a relatively long duration; thus, the use of filaments is flexible. In silica glass, the time window is critically small to fully utilize the plasma, but STEs can be treated as seed electrons [38] and are easily re-excited to the conduction band using a lower energy value than in initial multiphoton ionization. In summary, the temporal evolution results are useful to control precise processing.
3.2 Dependence on laser parameters
The processing parameters are important in femtosecond laser applications; therefore, the influence of pump energies (30, 50, and 70 µJ) and relative positions (D = 0, 30, and 60 µm) on the filament evolution of sapphire and silica glass were further investigated. As shown in Figs. 7(a), 7(b), 7(d) and 7(e), small divergent filaments appeared on the subsurface of the samples when the pump beams were focused near the surface. This indicates that the propagation of the pump pulses was influenced when entering the materials, which may be attributed to the high density of excited plasma on the surface. As the focal position was shifted deeper into the samples, the high-intensity areas were located inside the sample and the excitation of the surface materials decreased; thus, the single filaments in Figs. 7(c) and 7(f) were observed. In addition, the filaments became longer with increasing the depth of focal position owing to the lower consumption of energy on the surface areas. Long and noncontinuous filament tails appeared when the pump energy was 70 µJ and D was larger than 30 µm, as shown in Figs. 7(b), 7(c), 7(e), and 7(f). This implies that more energy was supplied during the dynamic balance process of the Kerr effect and plasma defocusing to significantly extend the filaments.
Fig. 7. Filaments of sapphire and silica glass with a 70 µJ pump energy. Sapphire with a relative position of (a) D = 0 µm, (b) D = 30 µm, and (c) D = 60 µm. Silica glass with a relative position of (d) D = 0 µm, (e) D = 30 µm, and (f) D = 60 µm. The red arrow indicates the laser incidence direction. The dotted line denotes the interface between the air and the sample.
Furthermore, the length of the filaments during temporal evolution is also important for precise processing applications. These lengths were measured, excluding the filament tails, and the results are shown in Fig. 8. First, the filament lengths in both materials rapidly increased before reaching their saturation states. Then, the sapphire filaments decreased after a short stable stage, whereas the silica glass filaments maintained a stable state until at least 972.48 ps. The filament lengths in the two materials increased as the depth of focal position and laser energy increased. The stable filament length of sapphire was 1.1–1.7 times larger than that of silica glass, and the length ratio was approximately 1.1–1.25 when the focal position was not at the surface of samples. This range is close to the ratio of the refractive indexes of the two materials. Moreover, the dependence of maximum filament length in two materials on the pump energy is shown in Fig. 8(g). The maximum lengths increased as the depth of focal position and pump energy increased. It provides the basic information for the control of filament lengths. Besides, the sample surface was damaged in all the experimental conditions used in this work, which indicates that the pump energy was not fully utilized for the filament formation inside the materials, and the filament length can be increased by shifting the focal position deeper into the samples. However, it is worth noting that the starting position of filaments will shift into the samples from the surface if the focal position is too deep.
Fig. 8. Filament length evolution at different pump pulse energies and relative positions. Sapphire: (a) 30 µJ, (b) 50 µJ, and (c) 70 µJ. Silica glass: (d) 30 µJ, (e) 50 µJ, and (f) 70 µJ. (g) Dependence of maximum filament length on the pulse energy. In the legend, Sa and S represents sapphire and silica glass respectively, and the numbers are the values of relative position D.
In both sapphire and silica glass, the earliest filament inducement occurred when the pump was focused on the surface compared with other focal position conditions; this inducement occurred earlier with increasing laser energy. This phenomenon can be attributed to the spatial-temporal differences in laser beam intensities under different focal positions. In the temporal dimension, the pump beams are first incident on the surface and then enter the samples. In the spatial dimension, the position corresponding to the peak intensity of each pulse is the focal point; therefore, when a pump pulse is incident on the surface, the light intensity is higher with smaller depth of focal positions. Thus, plasma was produced earliest when the pump was focused on the surface. In Fig. 8(d), the beginning time of filaments in silica glass at different focal positions was the same. It was because the filament was too small to measure at the beginning stage when the pump power was 30 µJ and D was 0 µm, and its length was regarded as 0 µm. Besides, the delay intervals were incremental, which slightly influenced the precision of the measured beginning time, especially for D = 30 µm and D = 60 µm, where the beginning stage corresponding to larger delay intervals. Additionally, the light intensity reaches the threshold of plasma excitation earlier at the temporally rising stage of the pulse if the pulse energy is larger and the pulse widths are the same. The saturation time of the filament length in the two materials did not significantly change at different pulse energies.
4. Conclusion
In this study, the evolution of filaments induced by a single femtosecond laser pulse in sapphire and silica glass was investigated using pump-probe shadowgraphy. The results showed that the plasma in the two materials appeared after almost the same time delay. The plasma in the sapphire filament reached the saturation state after 1 ps of excitation and then experienced a 71 ps decay course. The plasma in the silica glass filament took 200 fs to reach saturation, and the decay course was approximately 800 fs. The lifetime of the sapphire filament was 72 ps, whereas it was at least 972 ps for that of the silica glass filament. The apparent decay difference can be attributed to the effect of STEs in silica glass. In addition, the influence of the focal position and pulse energy on the filaments was investigated. Divergent filaments were observed when the pump was focused near the surface owing to the effect of the excited plasma on pump propagation. Long tails appeared when the pump energy was 70 µJ and the relative position was larger than 30 µm because the energy supply was sufficient for filament extension. The geometrical length of the filaments in both materials increased as the pulse energy and depth of focal position increased. The stable length in sapphire was 1.1–1.7 times larger than that in silica glass, and the length ratio was approximately 1.1–1.25 when the pump was focused inside the samples, which was caused by the difference in refractive index. Moreover, plasma excitation occurred earlier with smaller depth of focal position and larger pulse energy. This research clarified the material and laser parameter dependence of filaments, and the results contribute to the microprocessing applications of femtosecond laser filamentation.
Funding
Japan Society for the Promotion of Science (21K18667).
Acknowledgements
We would like to thank Dr. Yoshizaki for constructive discussions.
Disclosures
The authors declare no conflict of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441(2-4), 47–189 (2007). [CrossRef]
2. S. L. Chin, Femtosecond Laser Filamentation (Springer, 2010).
3. W. Watanabe, T. Tamaki, Y. Ozeki, and K. Itoh, “Filamentation in ultrafast laser material processing,” in Progress in Ultrafast Intense Laser Science VI, K. Yamanouchi, G. Gerber, and A. D. Bandrauk, eds. (Springer-Verlag, 2010).
4. Y. Ito, R. Yoshizaki, N. Miyamoto, and N. Sugita, “Ultrafast and precision drilling of glass by selective absorption of fiber-laser pulse into femtosecond-laser-induced filament,” Appl. Phys. Lett. 113(6), 061101 (2018). [CrossRef]
5. S. Butkus, D. Paipulas, R. Sirutkaitis, E. Gaižauskas, and V. Sirutkaitis, “Rapid cutting and drilling of transparent materials via femtosecond laser filamentation,” J. Laser Micro/Nanoeng. 9(3), 213–220 (2014). [CrossRef]
6. M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, R. Salut, L. Furfaro, and J. M. Dudley, “High aspect ratio nanochannel machining using single shot femtosecond Bessel beams,” Appl. Phys. Lett. 97(8), 081102 (2010). [CrossRef]
7. J. del Hoyo, R. Meyer, L. Furfaro, and F. Courvoisier, “Nanoscale confinement of energy deposition in glass by double ultrafast Bessel pulses,” Nanophotonics 10(3), 1089–1097 (2020). [CrossRef]
8. D. Hélie, M. Bégin, F. Lacroix, and R. Vallée, “Reinforced direct bonding of optical materials by femtosecond laser welding,” Appl. Opt. 51(12), 2098–2106 (2012). [CrossRef]
9. W. Watanabe, T. Asano, K. Yamada, K. Itoh, and J. Nishii, “Wavelength division with three-dimensional couplers fabricated by filamentation of femtosecond laser pulses,” Opt. Lett. 28(24), 2491–2493 (2003). [CrossRef]
10. A. Saliminia, R. Vallee, and S. L. Chin, “Waveguide writing in silica glass with femtosecond pulses from an optical parametric amplifier at 1.5 um,” Opt. Commun. 256(4-6), 422 (2005). [CrossRef]
11. E. Ertorer, M. Haque, J. Li, and P. R. Herman, “Femtosecond laser filaments for rapid and flexible writing of fiber Bragg grating,” Opt. Express 26(7), 9323–9331 (2018). [CrossRef]
12. X. Xu, J. He, J. He, B. Xu, R. Chen, Y. Wang, Y. Yang, and Y. Wang, “Efficient point-by-point Bragg grating inscription in sapphire fiber using femtosecond laser filaments,” Opt. Lett. 46(11), 2742–2745 (2021). [CrossRef]
13. J. Li, E. Ertorer, and P. R. Herman, “Ultrafast laser burst-train filamentation for non-contact scribing of optical glasses,” Opt. Express 27(18), 25078–25090 (2019). [CrossRef]
14. N. Miyamoto, Y. Ito, C. Wei, R. Yoshizaki, A. Shibata, I. Nagasawa, K. Nagato, and N. Sugita, “Ultrafast internal modification of glass by selective absorption of a continuous-wave laser into excited electrons,” Opt. Lett. 45(11), 3171–3174 (2020). [CrossRef]
15. X. Mao, S. S. Mao, and R. E. Russo, “Imaging femtosecond laser-induced electronic excitation in glass,” Appl. Phys. Lett. 82(5), 697–699 (2003). [CrossRef]
16. F. Huang, J. Si, T. Chen, T. Shen, M. Shi, and X. Hou, “Temporal-spatial dynamics of electronic plasma in femtosecond laser induced damage,” Opt. Express 29(10), 14658–14667 (2021). [CrossRef]
17. C. Pan, L. Jiang, J. Sun, Q. Wang, F. Wang, and Y. Lu, “The temporal-spatial evolution of electron dynamics induced by femtosecond double pulses,” Jpn. J. Appl. Phys. 58(3), 030901 (2019). [CrossRef]
18. C. Pan, L. Jiang, Q. Wang, J. Sun, G. Wang, and Y. Lu, “Temporal-spatial measurement of electron relaxation time in femtosecond laser induced plasma using two-color pump-probe imaging technique,” Appl. Phys. Lett. 112(19), 191101 (2018). [CrossRef]
19. Q. Sun, H. Jiang, Y. Liu, Y. Zhou, H. Yang, and Q. Gong, “Relaxation of dense electron plasma induced by femtosecond laser in dielectric materials,” Chin. Phys. Lett. 23(1), 189–192 (2006). [CrossRef]
20. F. Wang, C. Pan, J. Sun, Q. Wang, Y. Lu, and L. Jiang, “Direct observation of structure-assisted filament splitting during ultrafast multiple-pulse laser ablation,” Opt. Express 27(7), 10050–10057 (2019). [CrossRef]
21. Q. Sun, H. Asahi, Y. Nishijima, N. Murazawa, K. Ueno, and H. Misawa, “Pulse duration dependent nonlinear propagation of a focused femtosecond laser pulse in fused silica,” Opt. Express 18(24), 24495–24503 (2010). [CrossRef]
22. M. Sun, U. Eppelt, S. Russ, C. Hartmann, C. Siebert, J. Zhu, and W. Schulz, “Numerical analysis of laser ablation and damage in glass with multiple picosecond laser pulses,” Opt. Express 21(7), 7858 (2013). [CrossRef]
23. A. Vogel, J. Noack, G. Hüttman, and G. Paltauf, “Mechanisms of femtosecond laser nanosurgery of cells and tissues,” Appl. Phys. B: Lasers Opt. 81(8), 1015–1047 (2005). [CrossRef]
24. P. K. Kennedy, “A First-Order Model for Computation of Laser-Induced Breakdown Thresholds in Ocular and Aqueous Media: Part I—Theory,” IEEE J. Quantum Electron. 31(12), 2241–2249 (1995). [CrossRef]
25. S. Guizard, P. Martin, P. Daguzan, G. Petite, P. Audebert, J. P. Geindre, A. Dos Santos, and A. Antonnetti, “Contrasted behaviour of an electron gas in MgO, Al2O3 and SiO2,” Europhys. Lett. 29(5), 401 (1995). [CrossRef]
26. P. Martin, S. Guizard, P. Daguzan, G. Petite, P. D’Oliveira, P. Meynadier, and M. Perdrix, “Subpicosecond study of carrier trapping dynamics in wide-band-gap crystals,” Phys. Rev. B 55(9), 5799–5810 (1997). [CrossRef]
27. P. Audebert, P. Daguzan, A. Dos Santos, J. Gauthier, J. Geindre, S. Guizard, G. Hamoniaux, K. Krastev, P. Martin, G. Petite, and A. Antonetti, “Space-time observation of an electron gas in SiO2,” Phys. Rev. Lett. 73(14), 1990–1993 (1994). [CrossRef]
28. T. E. Tsai and D. L. Griscom, “Experimental-evidence for excitonic mechanism of defect generation in high-purity silica,” Phys. Rev. Lett. 67, 2517–2520 (1991). [CrossRef]
29. Q. Sun, H. Jiang, Y. Liu, Z. Wu, H. Yang, and Q. Gong, “Measurement of the collision time of dense electronic plasma induced by a femtosecond laser in fused silica,” Opt. Lett. 30(3), 320–322 (2005). [CrossRef]
30. M. Mero, J. Liu, A. Sabbah, J. C. Jasapara, K. Starke, D. Ristau, J. K. McIver, and W. G. Rudolph, “Femtosecond pulse damage and predamage behavior of dielectric thin films,” Proc. SPIE 4932, 202–212 (2003). [CrossRef]
31. P. Jürgens, M.J.J. Vrakking, A. Husakou, R. Stoian, and A. Mermillod-Blondin, “Plasma formation and relaxation dynamics in fused silica driven by femtosecond short-wavelength infrared laser pulses,” Appl. Phys. Lett. 115(19), 191903 (2019). [CrossRef]
32. D. Grojo, M. Gertsvolf, S. Lei, D. M. Rayner, and P. B. Corkum, “Time-Evolution of Carriers after Multiphoton Ionization of Bulk Dielectrics,” in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper IThI3.
33. S. Lei, D. Grojo, T. Barillot, M. Gertsvolf, Z. Chang, D. M. Rayner, and P. B. Corkum, “From Carrier Dynamics inside Fused Silica to Control of Multiphoton-Avalanche Ionization for Laser Machining,” in Conference on Lasers and Electro-Optics 2010, OSA Technical Digest (CD) (Optical Society of America, 2010), paper CMLL6.
34. C. Itoh, T. Suzuki, and N. Itoh, “Luminescence and defect formation in undensified and densified amorphous SiO2,” Phys. Rev. B 41(6), 3794–3799 (1990). [CrossRef]
35. C. Itoh, K. Tanimura, N. Itoh, and M. Itoh, “Threshold energy for photogeneration of self-trapped excitons in SiO2,” Phys. Rev. B 39(15), 11183–11186 (1989). [CrossRef]
36. K. Tanimura, T. Tanaka, and N. Itoh, “Creation of quasistable lattice defects by electronic excitation in SiO2,” Phys. Rev. Lett. 51(5), 423–426 (1983). [CrossRef]
37. S. Richter, M. Heinrich, S. Döring, A. Tünnermann, S. Nolte, and U. Peschel, “Nanogratings in fused silica: formation, control, and applications,” J. Laser Appl. 24(4), 042008 (2012). [CrossRef]
38. D. Grojo, M. Gertsvolf, S. Lei, T. Barillot, D. M. Rayner, and P. B. Corkum, “Exciton-seeded multiphoton ionization in bulk SiO2,” Phys. Rev. B 81(21), 212301 (2010). [CrossRef]
