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Abstract
In this study, transient temporal-spatial evolutions of femtosecond (fs) laser pulse-induced filaments and electronic plasma when laser induced damage occurred in fused silica were investigated using fs time-resolved pump-probe shadowgraphy. The transient peak electron density increased and then decreased as delay time of probe beam increased. Its corresponding spatial positions moved from the sample surface to the inside of the sample, but remained at the nonlinear focus for a relatively long time. The maximum electron density increased as pump energies increased and then became saturated at 8 μJ, above which laser-induced material damage occurred. The material damage threshold electron density was approximately 1.27×1020 cm-3. The laser-induced material damage position corresponded to the position of the maximum electron density. Furthermore, the material damage was extended from the nonlinear focus to the deeper parts of the sample at pump energies above 8 μJ. This tendency agreed well with the spatial distribution of the maximum transient electron density at each propagation depth, implying that the fs time-resolved pump-probe shawdowgraphy is a meaningful tool for predicting the distribution of laser-induced microstructures in ultrafast laser micromachining.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Femtosecond (fs) filamentation [1,2] in transparent solid materials has wide applications in micromachining, such as fabrication of gratings and optical memory [1], and the stealth dicing of materials [3]. It is governed by a balance between Kerr self-focusing and electronic plasma defocusing effects. The fs laser-induced electronic plasma depends on the nonlinear ionization process in solid materials, which mainly involved the two processes of photoionization and avalanche ionization when the pulse duration is several hundred femtoseconds [4,5]. Meanwhile, the mechanism of fs laser micromachining is essentially determined by fs laser-electron interactions and the subsequently variation of electronic plasma [6,7]. Hence, the characterization of the temporal-spatial evolution of electronic plasma is helpful for understanding fs laser-material interaction processes.
Fs time-resolved pump-probe shawdowgraphy [8,9] and in-line holographic microscopy [10,11] are two popular methods for studying fs laser-induced electronic plasma evolution in transparent solid materials. Laser-induced transient electron densities can be retrieved from transient absorption in time-resolved pump-probe shawdowgraphy. Pan et al. [8] and Mao et al. [9] measured the time-resolved evolution of a single fs laser pulse-induced electronic plasma in transparent solid materials using pump-probe shadowgraphy. Pan et al. [8] demonstrated that the relationship between electron relaxation time and electron density was inversely proportional in fused silica. Mao et al. [9] demonstrated the distribution of plasma induced by different laser energies in borosilicate glass. However, they studied only the spatiotemporal evolution of the fs laser-induced plasma in fused silica when there was no laser-induced material damage. Meanwhile, fs laser-induced material damage is significantly important in fs laser micromachining. Papazoglou et al. [10] studied the plasma density spatio-temporal dynamics using time-resolved inline holographic microscopy when nanogratings were induced by fs laser in fused silica. They retrieved the electron density information via laser-induced refractive index changes and found the electron density was saturated at approximately 5.0×1019 cm-3 as the pump energy increased. Compared with time-resolved inline holographic microscopy [10,11], fs time-resolved pump-probe shadowgraphy [8,9] has simple experimental configuration. Furthermore, it can directly show the transient plasma distribution and retrieve the electron density without the use of complex algorithms [7]. With the help of this technique, Gawelda et al. [12] revealed that filamentation and prefocal depletion were important energy loss channels in doped phosphate glass for waveguide writting using fs laser, which deteriorated the spatial distribution of the laser-deposited energy.
In this study, transient temporal-spatial evolutions of single fs laser pulse-induced filaments and electronic plasma in fused silica were investigated using fs time-resolved pump-probe shadowgraphy. We demonstrated the temporal-spatial evolution of fs laser-induced electronic plasma and the evolution of the transient absorption at the nonlinear focus when fs laser propagated in fused silica. The results showed that the transient peak electron density increased and then decreased as delay time of probe beam increased, and the corresponding spatial position moved from the sample surface to the inside of the sample, but remained at the nonlinear focus for a relatively long time as fs laser pulse propagated in the sample. Meanwhile, the maximum electron density appeared at the nonlinear focus. Furthermore, when the pump energies increased from 1 to 16 μJ, the maximum electron density increased and then became saturated at 8 μJ, above which laser-induced material damage occurred. The material damage threshold electron density was approximately 1.27×1020 cm-3. The laser-induced material damage position corresponded to the position of the maximum electron density during fs laser propagation. Moreover, the strong damage appeared at the nonlinear focus, which subsequently became extended from the nonlinear focus to the deeper parts of the sample at pump energies above 8 μJ. This tendency agrees well with the spatial distribution of the maximum transient electron density at each propagation depth. The results imply that the fs time-resolved pump-probe shadowgraphy is a useful tool for predicting the distribution of laser-induced microstructures in ultrafast laser micromachining. The distribution characteristisc of microstructure can be seen more clearly from the transient plasma distribution than that observed in optical microscopy. Therefore, this technology may be used for online monitoring fs laser processing process and offer references for obtaining optimal processing parameters in fs laser micromachinining, such as stealth dicing of materials or fabricating microchannels using ultrafast laser.
2. Experimental setup
Figure 1 shows the schematic diagram of the fs laser pump-probe shawdowgraphy. An amplified Ti: sapphire laser (Libra-USP-HE, Coherent, USA) generated a train of 1-kHz, 3.5-mJ, and 800-nm horizontally polarized pulses with a Gaussian spatial profile. The repetition rate of the fs laser was decreased to 0.5 kHz by a mechanically optical chopper. Afterward, the fs laser was split into pump beam and probe beam using a beam splitter. A λ/2 retarder plate and Glan prism GP1 placed in the optical path of the pump beam were used to adjust the pump power. The pump beam was then focused into the sample from the side surface using a microscope objective MO1 (10×, NA = 0.3, Nikon). A dam-board was placed on the opposite side of the sample to block the pump beam transmitted from the sample. The sample was a 50 × 5 × 2-mm piece of fused silica with four polished surfaces. It was mounted on a computer-controlled three-dimensional stage and moved parallel to the x-direction at a speed sufficient to ensure no overlapping between each pulse-irradiated zone. The probe pulse passed through the front surface of the sample with a sufficiently low energy to ensure that the material was not modified. Meanwhile, a variable optical path for the probe beam was precisely realized with a delay line comprising two reflecting mirrors (M5 and M7) fixed on a computer-controlled one-dimensional stage. Afterward, Glan prism GP2 was inserted in front of the sample to adjust the polarization state of the probe beam. Another microscope objective MO2 (10×, NA = 0.3, Nikon) imaged the transmitted shadowgraph of plasma on a monochrome charge-coupled device (CCD). The CCD was triggered by synchronized signals generated by the optical chopper, which was synchronized with the fs laser source. Additionally, Glan prism GP3 was placed behind MO2. The axis of GP3 can be set in directions of perpendicular and parallel to that of GP2. When the axis of GP1 was set at the vertical direction, the axis of GP2 was set at 45o to that of GP1, and the axis of GP3 was set perpendicular to that of GP2, the signals record by CCD were ultrafast optical Kerr signals, and the setup was used for time-resolved optical polarigraphy [13]. This setup can be used to visualize the pump beam in a sample and measure the pulse duration. When the axes of all the Glan prisms were set at horizontal direction, the CCD recorded the transmitted shadowgraph of the electronic plasma and the setup was used for pump-probe shawdowgraphy. The spatial resolution of the experimental setup could reach approximately 2 µm and the temporal resolution depended on the fs laser pulse duration. The time-resolved image was attributed to the absorption of the probe beam by the fs laser-induced electronic plasma and other phenomena. The inserted image in Fig. 1 shows the distribution of 3-μJ fs laser pulse laser induced plasma in air. The middle position of the plasma was considered to be the nonlinear focus in air and the pump beam waist was approximately 3 μm.
Fig. 1. Schematic diagram of the fs laser pump-probe shawdowgraphy. BS: beam splitter; MO: microscopic objective (MO1 and MO2); GP: Glan prism (GP1, GP2, and GP3); M: reflecting mirror (M1, M2, M3, M4, M5, M6, M7, and M8). The dotted lines represent trigger lines. The inserted image shows the distribution of fs laser pulse-induced plasma in air.
3. Results and discussion
To evaluate the pulse duration of the fs laser pulse in fused silica, fs time-resolved optical polarigraphy experiments were first carried out. A pump beam with a pulse energy of 1.6 µJ was focused approximately 500 μm into the sample from the side surface. Figure 2(a) shows evolutions of the Kerr signals [14] recorded by the CCD at different delay times, in which the pump beam was transmitted from left to right. For easy description, we defined the left edge of the image as Z = 0 μm. The delay time when a weak Kerr signal appeared on the CCD was defined as 0 fs. The Kerr signal intensity first increased and gradually decreased, and its position gradually propagated into the sample as delay time increased. Figure 2(b) demonstrates that the position of the strongest Kerr signal along the axis of the propagation direction varied with delay time and the relationship between them was almost linear. The slope was approximately 2.2 × 108 m/s, which is slightly higher than the propagation speed (approximately 2.1 × 108 m/s) of the pump pulse in fused silica with refractive index n0 of 1.45. To investigate the pulse duration of the fs laser pulse, the Kerr signal intensities at different delay times were recored where the Kerr signal was strongest and shown in Fig. 2(c). The full-width-at-half-maximums (FWHM) of the optical Kerr signals was approximately 115 fs. Therefore, the pulse duration of the fs laser pulse was calculated to be approximately 94 fs [15].
Fig. 2. (a) Time-resolved images of Kerr signals in fused silica with 1.6-µJ pump energy. The black arrow denotes the propagation direction of the pump pulses. The left edge of the image was defined as Z = 0 μm. (b) Variation of the position of the strongest Kerr signal with delay time. The black squares represent the recorded data and the red line represents the linear fit. (c) Variation of the optical Kerr signal intensity with delay time.
Afterward, we studied the time-resolved images of the fs laser-induced electronic plasma in fused silica recorded by the CCD at different delay times, as shown in Fig. 3. The laser pulse energy was 12 µJ. We defined the left edge of the image as Z = 0 μm. At 0 fs, only a weak filament appeared in the image. As the delay time increased, the fs laser-induced filament gradually moved into the deeper part of the sample owing to laser pulse propagation. Additionally, a fork-like structure appeared near the incident surface and then converged to a single filament as the depth increased. The appearance of the fork-like structure near the laser pulse entrance may be due to nonlinear optical and interface spherical aberration effects [16], which lead to pump beam intensity off-axis distribution and the subsequent electronic plasma off-axis distribution. The fork-like structure converged to a single filament at the nonlinear focus owing to the focusing effect. Another interesting phenomenon was that material damage was observed in the nonlinear focus, indicating that the laser pulse intensity reached the sample damage threshold.
Fig. 3. Time-resolved images of fs laser-induced electronic plasma in fused silica recorded by CCD with 12-µJ pump energy. The black arrow denotes the propagation direction of the pump pulses. The left edge of the image was defined as Z = 0 μm. The red arrows denote the damage position.
In addition, images without pump laser irradiation were also recoreded as references. Transmissivities of probe laser at different delay times can be calculated from the ratio of the time-resolved images to reference images. Figure 4 shows the results at the delay of 0.6 ps. The reference image, time-resolved image at a delay time of 0.6 ps, and its corresponding transmissivity distribution image are shown in Fig. 4(a), (b), and (c), respectively. The low transmissivity plasma region with a fork-like structures can be clearly distinguished.
Fig. 4. Reference image, time-resolved image at a delay time of 0.6 ps, and its corresponding transmissivity image.
The decay time of transient absorption is an important parameter for describing the characteristics of electronic plasma. The transient absorption of electronic plasma can be deduced from the transient transmissivity [17]. Considering that the electronic plasma has cylindrical symmetry along the pump beam, the probe beam undergoes absorption, reflection, and refraction when it passes through the plasma region. Meanwhile, the incidence angle of the central part of the probe beam was zero when the probe beam passed through the axis of the plasma region. Hence, the refraction can be neglected. For simplicity, the reflection was also neglected, and only the absorption was considered. The laser intensity It of the central part of the probe beam follows [17]:
The integral of Eq. (1) is described as:
where T is the transmissivity of the probe laser after passing through the plasma region, x is the length of the electronic plasma along probe beam propagation direction, which is perpendicular to the pump beam propagation direction, and α is the absorption coefficient.Further, we can obtain average absorption coefficient αaver as follow:
where xFWHM is FWHM length of electronic plasma in x direction. By assuming the symmetric distribution of electronic plasma in x-y plane, we can obtain that xFWHM equals to yFWHM, which is obtained from transmissivity image.From Eq. (3), the transient average absorption coefficient can be obtained. Owing to free electron recombination and diffusion, absorption generally has an exponential decay profile [18,19]. Figure 5 shows the temporal evolution of the transient average absorption coefficient at the nonlinear focus with 12-µJ pump energy. The black squares and red solid curve represent the measured results and the exponentially fitted curve, respectively. The fitted decay time was 84 fs. The first several decreasing data points were ignored because the electron plasma was still being induced by the fs laser at that time, although the electron density was decreasing. The relaxation of electronic plasma may via self-trapping excitons, and other ultrafast process in fused silica [20,21]. Self-trapping excitons have a fast rise time of approximately 150 fs [22] and two typical absorption peaks at 2.8 eV and 1.9 eV [23]. Because the bandgap of self-trapping excitons are larger than 800-nm photon energy, their process can not be detected in our experiments. Hence, our experiments show the pure electronic plasma evolution process, which is related to the self-trapping excitons and other ultrafast processes.
Next, the transient electron density can be deduced from transient average absorption coefficient as:
where ne is the electronic plasma density, and σ is the absorption cross-section for inverse bremsstrahlung according to the Drude model [18]: k = 2πn0/λ, where λ is the vacuum wavelength of the probe laser, n0 is the refractive index of fused silica, and me, ε0, ω and τ are the electron mass, vacuum dielectric constant, laser frequency, and electron relaxation time, respectively. Here τ was estimated to be approximately 0.2 fs [24].According to Eq. (3) and Eq. (4), the electron density is described as:
The electron density can be calculated from Eq. (6). Figure 6(a) shows the spatial distributions of transient electron densities at the plasma axis at delay times of 200, 400, 600, 800, and 1000 fs with 12-µJ pump energy. The transient peak electron densities in spatial and their corresponding spatial positions at different delay times were clearly observed. From Fig. 6(b), the transient peak electron density increased and then decreased as delay time increased, implying variations in the focused pump pulse intensity. The electron density reached the maximum at the nonlinear focus and was approximately 1.29 × 1020 cm-3. Furthermore, the spatial position of the transient peak electron density gradually moved from the sample surface to the inside of the sample as delay time increased. Interestingly, it remained at the nonlinear focus for a relatively long time.
Fig. 6. (a) Spatial distributions of transient electron densities at the plasma axis at different delay times with 12-µJ pump energy. (b) Temporal-spatial evolution of the transient peak electron density.
The evolutions of the fs laser-induced electronic plasma at different pump energies (1, 2, 4, 8, 12, and 16 µJ) were also studied. The time-resolved images of the fs laser-induced electronic plasma were recorded as delay time ranged from 0 to 1.6 ps. Figure 7 shows the time-resolved images at different pump energies at a delay time of 0.6 ps. The starting point of the filament was extended toward the laser source as the pump energy increased. Moreover, only a single filament was observed at pump energies of 1, 2, and 4 µJ, whereas a fork-like structure first appeared and then converged to a single filament at the nonlinear focus for pump energies above 8 µJ. Additionally, material damage appeared in the nonlinear focus above 8 µJ and became more obvious as the pump energy increased.
Fig. 7. Time-resolved images at different pump energies recorded by the CCD at a delay time of 0.6 ps. The black arrow denotes the propagation direction of the pump pulses. The left edge of the image was defined as Z = 0 μm. The red arrows denote the material damage positions.
Furthermore, the influence of pump energy on the temporal-spatial evolutions of transient electron densities during pump pulses propagation in fused silica was studied. Figures 8(a)–(e) show the transient peak electron densities and their corresponding spatial positions varied with delay time for pump energies of 1, 2, 4, 8, and 16 µJ, respectively. The transient peak electron densities increased and then decreased as delay time increased. For all pump energies, the positions of the transient peak electron density gradually moved from the sample surface to the inside of the sample as delay time increased but remained at the nonlinear focus for a relatively long time. The phenomena was similar to that of the 12-µJ pump energy. The maximum electron densities, i.e., the highest measured values at any delay time and any position in the plasma region, were 0.37 × 1020, 0.93 × 1020, 1.12 × 1020, 1.27 × 1020, 1.29 × 1020, and 1.28 × 1020 cm-3 at delay times of 1.35, 0.85, 0.75, 0.65, 0.6, and 0.65 ps for 1, 2, 4, 8, 12, and 16 µJ, respectively. This implies that a short time was needed to reach the nonlinear focus as the pump energy increased due to increasing self-focusing effect.
Fig. 8. Temporal-spatial evolutions of the transient peak electron density. (a) 1 µJ, (b) 2 µJ, (c) 4 µJ, (d) 8 µJ, and (e) 16 µJ. (f) Variation of maximum electron density with pump energy.
Figure 8(f) shows the maximum electron density varied with pump energy. The maximum electron density increased as the pump energy increased and then became saturated at 8 µJ. This implied that when the pump energy reached the material damage threshold, the maximum electron density exhibited almost no variation. The influence of reflection of high density electron plasma was evaluated. The difference of refractive index caused by electronic plasma according to the Drude model [18] was estimated to be: Δn = ne/2nc ≈ 0.04 (nc = ε0meω2/e2 is critical plasma density). The reflectivity of probe beam R ≈ (Δn/2n0)2 ≈ 0.02%. This implies the reflection induced by electronic plasma in our case can be neglected. The maximum electron density saturation at high pump energy may be attributed to that the plasma defocusing effect locally balanced the optical self-focusing effect [24]. Therefore, the damage threshold electron density was defined as the maximum electron density at 8-µJ pump energy and was approximately 1.27×1020 cm-3, which has the same order with that obtained by Couairon et al. [24].
Further, we studied the relation of distrbutions of transient electron density and laser-induced damage. Figure 9(a) shows the spatial distribution of the maximum transient electron density at each propagation depth for pump energies of 8, 12, and 16 µJ. The gray images show the transient images at a delay time of 0.6 ps, in which the separated damage points induced by previous pulses could be observed. The maximum transient electron densities of the fork-like-structure portions were not plotted for simplicity. With the increase of laser propagation depth, the maximum transient electron densities rapidly increased, then reached the maximum value at the nonlinear focus, and finally gradually decreased. Figure 9(a) clearly shows that the maximum electron density in the laser-affected zone, the nonlinear focus, and the material damage are at the same position. This indicates that the position of the material damage can be inferred from the position of the maximum electron density. Figure 9(b) shows typical morphologies of damage structures induced by fs laser with different pump energies, which were observed in a 50× microscope objective (NA = 0.8, Olympus). Strong damage appeared at the nonlinear focus, which was subsequently extended from the nonlinear focus to the deeper parts of the sample at pump energies above 8 μJ. The tendency of the material damage agreed well with the spatial distribution of the maximum transient electron density, which was the length of laser-induced plasma zone after the nonlinear focus was longer than that before the nonlinear focus. It is worth noting that the distribution characteristisc of microstructure can be seen more clearly from the transient plasma distribution than that in optical microscopy. The above results imply that time-resolved pump-probe shawdowgraphy can be an helpful online tool to predict the distribution of laser-induced material microstructures in practical micromachining. This will be great significance to stealth dicing of materials, fabricating microchannels and other field of fs micromachinining. For example, the length of laser induced microstructres is aimed to be increased by using filamentation and optimizing processing parameters.
Fig. 9. (a) Spatial distribution of maximum transient electron density at each propagation depth for 8, 12, and 16 µJ. (b) Typical morphologies of damage structures induced by different pump energies observed in a 50× microscope objective(NA = 0.8, Olympus). (c) Typical morphologies of damage structures after annealing at 1000 °C.
In addition, the fused silica was placed in a tube furnace and annealed at 1000 °C for 6 hours to identify the type of fs laser-induced microstructures. Figure 9(c) shows the typical morphologies of damage structures observed in a 50× microscope objective after annealing at 1000 °C. Fs laser-induced microstructures were not erased. Therefore this structure damage may be the type II damage [24], for example laser induced microcavities.
4. Conclusion
In this study, fs filamentation and electronic plasma induced by a single fs laser pulse in a polished fused silica at different pump energies was investigated with pump-probe shadowgraphy. The temporal-spatial evolution of fs laser-induced electronic plasma when fs laser propagated in fused silica was demonstrated, and the results showed that the transient peak electron densities increased and then decreased as delay time increased, and the positions of which moved from the sample surface to the inside of the sample, but remained at the nonlinear focus for a relatively long time. Meanwhile, the maximum electron density increased as pump energies increased and then became saturated at 8 μJ, above which laser-induced material damage occurred. The material damage threshold electron density was approximately 1.27×1020 cm-3. Furthermore, maximum electron density in the laser-affected zone, the nonlinear focus, and the material damage are at the same position. The spatial distribution of maximum transient electron density at each propagation depth also agreed well with the tendency of the material damage being extended from the nonlinear focus to the deeper parts of the sample at pump energies above 8 μJ. These results imply that the time-resolved pump-probe shawdowgraphy can provide a detailed and quantitative distribution of fs laser-induced transient electronic plasma and the technology can be a useful tool for predicting the distribution of laser-induced material microstructures in micromachining.
Funding
National Key Research and Development Program of China (2017YFB1104600); Key Research and Development Program of Shaanxi province (2017ZDXM-GY-120).
Disclosures
The authors declare no conflicts of interest.
References
1. A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441(2-4), 47–189 (2007). [CrossRef]
2. N. T. Nguyen, A. Saliminia, W. Liu, S. L. Chin, and R. Vallée, “Optical breakdown versus filamentation in fused silica by use of femtosecond infrared laser pulses,” Opt. Lett. 28(17), 1591–1593 (2003). [CrossRef]
3. C. Gaudiuso, A. Volpe, and A. Ancona, “One-step femtosecond laser stealth dicing of quartz,” Micromachines 11(3), 327 (2020). [CrossRef]
4. F. Quéré, S. Guizard, and P. Martin, “Time-resolved study of laser-induced breakdown in dielectrics,” Europhys. Lett. 56(1), 138–144 (2001). [CrossRef]
5. 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]
6. L. Jiang, A. Wang, B. Li, T. Cui, and Y. Lu, “Electrons dynamics control by shaping femtosecond laser pulses in micro/nanofabrication: modeling, method, measurement and application,” Light: Sci. Appl. 7(2), 17134 (2018). [CrossRef]
7. B. Guo, J. Sun, Y. Lu, and L. Jiang, “Ultrafast dynamics observation during femtosecond laser-material interaction,” Int. J. Extreme Manuf. 1(3), 032004 (2019). [CrossRef]
8. 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]
9. 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]
10. D. G. Papazoglou, D. Abdollahpour, and S. Tzortzakis, “Ultrafast electron and material dynamics following femtosecond filamentation induced excitation of transparent solids,” Appl. Phys. A 114(1), 161–168 (2014). [CrossRef]
11. D. Abdollahpour, D. G. Papazoglou, and S. Tzortzakis, “Four-dimensional visualization of single and multiple laser filaments using in-line holographic microscopy,” Phys. Rev. A 84(5), 053809 (2011). [CrossRef]
12. W. Gawelda, D. Puerto, J. Siegel, A. Ferrer, A. Ruiz de la Cruz, H. Fernández, and J. Solis, “Ultrafast imaging of transient electronic plasmas produced in conditions of femtosecond waveguide writing in dielectrics,” Appl. Phys. Lett. 93(12), 121109 (2008). [CrossRef]
13. M. Fujimoto, S. Aoshima, M. Hosoda, and Y. Tsuchiya, “Femtosecond time-resolved optical polarigraphy: imaging of the propagation dynamics of intense light in a medium,” Opt. Lett. 24(12), 850–852 (1999). [CrossRef]
14. L. Yan, J. Si, F. Chen, S. Jia, Y. Zhang, and X. Hou, “Pump power dependence of Kerr signals in femtosecond cross pump-probe optical Kerr measurements,” Opt. Express 17(24), 21509–21514 (2009). [CrossRef]
15. J. Collier, C. Hernandez-Gomez, R. Allott, C. Danson, and A. Hall, “A single-shot third-order autocorrelator for pulse contrast and pulse shape measurements,” Laser Part. Beams 19(2), 231–235 (2001). [CrossRef]
16. J. Song, X. Wang, X. Hu, Y. Dai, J. Qiu, Y. Cheng, and Z. Xu, “Formation mechanism of self-organized voids in dielectrics induced by tightly focused femtosecond laser pulses,” Appl. Phys. Lett. 92(9), 092904 (2008). [CrossRef]
17. 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]
18. 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 53(4), 1749–1761 (1996). [CrossRef]
19. M. Li, S. Menon, J. P. Nibarger, and G. N. Gibson, “Ultrafast electron dynamics in femtosecond optical breakdown of dielectrics,” Phys. Rev. Lett. 82(11), 2394–2397 (1999). [CrossRef]
20. 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 79(7), 1695–1709 (2004). [CrossRef]
21. N. M. Bulgakova, R. Stoian, and A. Rosenfeld, “Laser-induced modification of transparent crystals and glasses,” Quantum Electron. 40(11), 966–985 (2010). [CrossRef]
22. S. Guizard, P. Martin, G. Petite, P. D’Oliveira, and P. Meynadier, “Time-resolved study of laser-induced colour centres in SiO2,” J. Phys.: Condens. Matter 8(9), 1281–1290 (1996). [CrossRef]
23. D. G. Papazoglou and S. Tzortzakis, “Physical mechanisms of fused silica restructuring and densification after femtosecond laser excitation,” Opt. Mater. Express 1(4), 625–632 (2011). [CrossRef]
24. A. Couairon, L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Filamentation and damage in fused silica induced by tightly focused femtosecond laser pulses,” Phys. Rev. B 71(12), 125435 (2005). [CrossRef]
