1. Introduction

The filamentary damage is a plasma channel resulting from the dynamic balance between optical Kerr effect and self-induced ionization. During its forming process, the beam shrinks and maintains a narrow diameter in the transverse diffraction plane [1,2]. In different pulse durations and media, the filament length is in the order of micron to kilometer [3,4], while its diameter is on micron scale [5]. For these advantages, the filament has been employed in the practical application field of remote sensing [6], weather control [7], and surgery [8]. In order to control the filament length and initial position, more attention has focused on the physical mechanism of filamentary damage process.

For the experimental study of filament in the square sample, more works focused on the laser ablation on the rear surface or bulk rather than the front surface, because of the pulse defocusing by the surface plasma. In these works, different filament propagations have been found. Shen et al. [9] found the filament initialed at the rear surface and gradually grew towards the incident laser flux, when the 1064 nm nanosecond laser focused behind the sample. And the filament was no independent on the surface damage. For the independent filament, Nguyen et al. [10] reported filament was initialed at the laser focus and propagating opposite to laser in a sub-nanosecond filamentary damage process. In above experiment, the filament only grew opposite to the laser while the focus was not on the surface, and the filament propagated in the other direction was not found. But in another work, Gridin et al. [11] reported a different filament propagation induced by a single 1064 nm pulse ablation of potassium dihydrogen phosphate (KDP) crystal, with a pulse duration of 4 ps. The filament initialed in the focal region, and grew both along the laser propagation and the opposite directions. However, there was no explanation of the filamentary damage process. So, it is necessary to find the reason of different direction propagation in theory. About the theory of filament formation, and self-channeling model (SCM) and moving focus model (MFM) have been reported. In the SCM, the filament was interpreted as a plasma channel resulting from the balance of pulse self-focusing and plasma defocusing [3,12]. But for the MFM, the filament resulted from the continuous succession of foci, which was arising from the self-focusing of the several pulse slices [13]. The MFM connected the filament with the temporal profile of pulse, which was a better explanation for the dynamics of filamentary damage over time. But in the nanosecond regime, the MFM was not well agreement with the experimental result. Shen et al. [14] found the MFM mostly overestimated the experimental filament length and could not explain the increase in the filamentary damage length at the end of the pump pulse. And the opposite result was reported that the MFM underestimated the filamentary damage length recently [10].

In our work, the filamentary damage appeared under the condition of the laser ablation of front surface. It initialed at the most obvious damage point called the main damage point and grew both along the laser propagation direction and the opposite direction successively. Compared with a previous work [15], it had a different propagating direction. The physical mechanism of filamentary damage was explored and the improved moving focus model were presented, which is in good agreement with experimental result.

2. Experimental setup

The Q-switched Nd: YAG laser (Spectra-Physics LAB 190–10) served as the single longitude mode pump light source, which operated at a repetition rate of 10 Hz, a center wavelength of 532 nm, a single pulse energy of 25 mJ, and the full width at half maxima (FWHM) of 14 ns. The diameter of beam waist was approximately 100 µm and the laser fluence was about $\textrm{2}\textrm{.37} \times 1{\textrm{0}^{\textrm{10}}}\,\textrm{W/c}{\textrm{m}^\textrm{2}}$. The Rayleigh length is experimentally estimated to be ∼59 mm in air. The titanium-doped sapphire femtosecond laser acted as a probe light source, with a central wavelength of 800 nm, a repetition rate of 10 Hz, and a pulse duration of 50 fs. The pump light passed through a splitter and was divided into two parts. One part was focused on the front surface of the sample by a lens, and the other part was incident to the photodiode. The probe light, which was passed through a beta-barium borate (BBO) crystal, an attenuation slice, and a filter, was perpendicular to the pump laser light and transmitted to a CCD camera (Princeton Instruments, ES3200). The attenuation slice prevented the femtosecond laser from damaging the CCD. The filter with a center wavelength of 400 nm transmitted the probe light, while simultaneously repressing other light from laser-induced plasma. The two photodiodes received the pump and probe lights and converted them into electrical signals. The accurate time delay was taken as the time interval between the peak values of the probe light and the pump light formed waveforms on the oscilloscope (LeCroy WaveSurfer 104Xs) screen. The two shutters ensured that only one probe light and one pump light passed the corresponding optical paths every time. The fused silica sample was polished for each side, and its size was 100 mm × 7 mm × 2 mm. To avoid repeated damage, the sample was moved to a new position every time of ablation. The temporal shape of pulse and more detailed information about the experimental setup can be found in our previous work [16].

3. Results and discussion

3.1 Pressure wave

Figure 1(a) shows the temporal plume outside and inside the fused silica at a delay time of 92.2 ns. The first, second, and third waves were generated from air breakdown, sample breakdown, and a reflection of the backward moving gas on the sample surface, respectively [17]. Accordingly, the temporal characteristics of the first and the second bulk waves were recorded at the same time. The first bulk wave and the filament pressure wave were generated from the photothermal effect as thermoelastic waves, while the second bulk wave was generated from the photomechanical effect as a mechanical wave. In Fig. 1(b), the wave front radii dynamics of two bulk waves and the filament pressure wave with the delay time is depicted. Their velocities reached $\textrm{5}\textrm{.91} \times 1{\textrm{0}^\textrm{3}}$ m/s, $\textrm{5}\textrm{.64} \times 1{\textrm{0}^\textrm{3}}$ m/s, and $\textrm{3}\textrm{.78} \times 1{\textrm{0}^\textrm{3}}$ m/s, respectively. It also indicates that, for the generation mechanism, the second bulk wave is different from the first bulk wave or the filament pressure wave.

 

Fig. 1. (a) Temporal plume outside and inside the fused silica at a delay time of 92.2 ns. (b) Development in time of the wave front radii of the first bulk wave, the second bulk wave, and the filament pressure wave.

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3.2 Filament evolution

The filament formation process experiences three stages, the single filament (SF), double filaments (DFs), and long filament (LF) stages, as shown in Figs. 2(a) to (c), respectively. During the filamentary damage process in Fig. 2, the most obvious damage point which is the symmetric center of the filament pressure wave is regarded as the main damage point. In the stage of SF at 10.6 ns, for the rising edge of the laser pulse, one main damage point appeared with an obvious surrounding the filament pressure wave, which attached an elongated filament channel on the right. The initial portion of the filament was caused by the balance between self-focusing in the sample and defocusing of plasma. As the laser power increased, the filament grew from right to left. Up to the peak laser power, the main damage point was created and the filament pressure wave was formed immediately. In the DFs stage at 71 ns, for the filling edge of the laser pulse, there was an obvious plasma born in front of the sample that focused the laser beam to form an extra filament appearing on the left side of the main damage point, and the whole filament length was double that of SF. Compared with the opinion of the main damage point as the focus point [18,19], on the contrary, the main damage point appeared in the bulk, while the laser focused on the front surface of fused silica. In the LF stage at 244 ns, the main damage point disappeared and a uniformly symmetric filament channel was formed.

 

Fig. 2. Time-resolved shadowgraph images of nanosecond laser (532 nm, 25 mJ) ablation of the front surface of fused silica at three stages of filament forming process, (a) SF stage, (b) DFs stage, and (c) LF stage.

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The filamentary damage morphology was captured by using an optical microscope (Leica DFC550) in Fig. 3(a), and the front surface of the sample corresponded to the left axis in (b). Compared with 355 nm laser, 532 nm laser induces a straight filament without the obvious thermal explosion, since thermo-mechanical phenomena are not predominant. And it can also find this regular in the study of surface damage [20]. The diameter of the filament edge was approximately 3 µm, while the middle part reached 6 µm. Compared with the filament induced by femtosecond laser, it had a wider diameter because of the explosion induced by the thermal effect. Figure 3(b) shows the spatial filament distribution in the bulk sample with the delay time. The transverse axis represents the sample thickness (2 mm).

 

Fig. 3. (a) Side view of filamentary and front surface damage morphology in fused silica. (b) Filamentary distribution in fused silica as a function of delay time.

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The value of the main damage point location relative to the front surface is in the range of 735–942 µm. The variable location was caused by the mechanical deformation of the sample and the laser energy fluctuation. SF, DFs, and LF took place before 10.6 ns, 10.6 −198 ns, after 198 ns, respectively. There was an obvious increase in the filament length after 10.6 ns, resulting in an extra filament formed on the left of the main damage point. In the DFs stage, the filament length was twice as long as that in SF. The damage of the fused silica was due to the abnormal absorption of laser energy by the surface and the subsurface defects, which caused the local temperature to rise sharply. Then, a micro-explosion occurred resulting in the destruction of the material structure. Therefore, after the early laser energy deposition, the material on the left side of the main damage point was more likely to cause damage in a short time because of the subsequent laser pulse. That is why the filament length jumped from 200 µm to 500 µm around a delay time of 10.6 ns.

3.3 Improved theoretical model of filament

This model is presented by the following three conditions. (1) The laser peak power and the critical power for self-focusing [12] are $\textrm{1}\textrm{.78} \times 1{\textrm{0}^\textrm{6}}\; \textrm{W}$ and $\textrm{9}\textrm{.48} \times 1{\textrm{0}^\textrm{5}}\; \textrm{W}$, respectively, which means the self-focusing could happen in the sample. (2) The time scale of the extra filament appearing was close to that of the FWHM of the pump pulse. Many obvious damage dots can be observed in Fig. 3(a), similar to a series of foci. (3) The plasma appearing in front of the sample reflected and defocused the laser pulse, which caused focus of the laser far away from the front surface. Therefore, it needs the improved moving focus model based on the self-focusing theory and the moving focus model to explain the whole process of the filament.

According to the improved moving focus model, the reflection of the laser on the plasma was considered [21], which is called a plasma mirror. It′s like a mirror that the low-intensity pulse of the laser pulse transmits directly, while the high-intensity pulse ablates the glass to produce a plasma larger than the critical density to reflect the pulse. The critical density can be calculated as in [22]:

Figure 4 presents the entire filament process of the improved moving focus model. The left column shows the pulse profile in different stages, while the right column represents filamentary damage during the corresponding stages as follows:

 

Fig. 4. Schematic of the improved moving focus model. The left column is laser pulse profile and right is filamentary damage in different pulse energies, (a) rising edge of pulse, (b) peak power, (c) filling edge of pulse, and (d) end of pulse.

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4. Conclusions

In summary, we investigated the filament process in fused silica irradiated by a 532 nm nanosecond laser. The entire process included three stages of SF, DFs, and LF, and resulted in the filament length doubling from the SF to DFs stage, while a new filament appeared at the left side of the main damage point. During the entire process, the location of the main damage point was relatively stable and was confined within the range from 735 µm to 942 µm. The rising edge of the laser created the right filament by self-focus, while the plasma in the main damage point reflected the filling edge to form the left one, and the peak power of the laser pulse corresponded to the main damage point, which is in agreement with the improved moving focus model. The evolution of filamentary damage can help us understand the mechanism of laser-induced filamentary damage in transparent media.