1. Introduction

Femtosecond filamentation has attracted significant attention for its multitudinous applications in atmospheric sensing [1], high harmonic generation [2], fabrication [3], biomedical studies [4] and so on. Until now, femtosecond filamentation has been observed in a broad range of transparent materials, such as gases [5], silica [6] and liquids [7]. Recently, femtosecond laser filament was demonstrated to induce condensation in a cloud chamber, which was due to the convection induced by filamentation in air [8–12]. Similar to the filamentation in air, femtosecond filamentation in water originates from the dynamic balance between the optical Kerr self-focusing effect and defocusing effect by plasma which is produced by multiphoton/tunnel ionization of water molecules [13,14]. Nevertheless, reports on femtosecond filamentation induced convection in water are still rare. The much higher value of nonlinearities and low filamentation threshold in water compared to those in air, give rise to a lot of interesting phenomena, such as the conspicuous white-light continuum generation [15], conical emission [16], and bubbles generation (optical cavitation) [17], etc. The bubbles, generated by femtosecond filamentation in water, have been discussed extensively for their formation and growth, which are of abundant physical and chemical processes [18,19]. Now the mechanism of femtosecond filament induced bubbles formation is believed to follow these procedures [20]: first, multiphoton ionization is invoked due to extraordinary peak power (larger than ${10}^{12} \text{W}/c{m}^2$) at the focal domain and the temperature increases strongly locally; second, the plasma expands quickly and results in the breakdown, which is followed by a shock wave propagating into the surrounding medium; finally, the bubbles are formed by homogeneous nucleation when the temperature reaches a critical value. The movements of the generated bubbles in water are driven by the complex mechanics which may include shock waves, Coulomb force, and thermal force induced by temperature difference. On the other hand, the bubbles’ movements can reflect the subtle dynamics in water, revealing the process of laser-filamentation-induced convection.

Recently, with pulses of $0.6 \text{μJ}$ and 130 fs to create the bubbles, Yuki Mizushima et al. [20] have studied the filament-induced single bubble’s formation process on the microsecond time scale via the pump-probe method and stroboscopic photography. While it is intriguing to explore the multitudinous bubbles’ motions on a macroscopic time scale under a stronger laser field. In this work, we investigated the dynamics of the bubbles in water which were induced by femtosecond laser pulses of several millijoules. The movements of the bubbles were investigated by placing a microscope on the top of the filament, which revealed the dynamic motions of the bubbles in a much larger time scale of several seconds. Under a higher input pulse energy, the bubbles were illuminated by the scattered light directly. And the motions of the bubbles were observed to be directional in water. The angles between the bubbles’ moving directions and the laser propagation direction varied at different positions along the filament, exhibiting a fusiform distribution. Besides, by measuring the numbers of bubbles at different positions along the filament, the intensity clamping feature of filamentation in water was obtained.

2. Experimental setup

Our experiments were carried out with the output from an amplified Ti:sapphire laser system (100 fs, 800 nm, 10 Hz), which provided the maximum single pulse energy of 10 mJ with a full width of half maximum (FWHM) diameter of 6 mm. Figure 1 shows the schematic diagram of the experimental setup. The pulse energy was continuously adjusted by a tunable attenuator (fused silica) of 2 mm thickness. The beam was then focused by a lens ($\text{f}=150 \text{mm}$) into a fused silica cuvette. The cuvette was $50 \text{mm} \times 30 \text{mm }\times 20 \text{mm}$ in size, and filled with 25 ml water (Watsons, pure distilled water). The filament was generated in the middle of the cuvette. In the following experiments, we defined the position corresponding to the middle of the cuvette as zero, with its right hand side having a positive value, and its left hand side having a negative value [see Fig. 1]. A microscope ($10\times$ micro objective) with a CCD ($640\times 512$ pixels, $1.3 \text{μm}/\text{pixel}$) was placed on the top of the cuvette to observe the movements of the bubbles in an area of about $820 \text{μm}\times 650 \text{μm}$. The CCD camera was gated with an exposure time of 100 milliseconds which corresponded to the time interval between two sequent laser shots. The microscope was installed on a 2D translation stage in order to cover the top view of the whole filament.

 

Fig. 1 Experimental setup for observing the movements of the bubbles generated by femtosecond filamentation in water.

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3. Results and discussion

The top view of the filament-induced bubbles generation is shown in Fig. 2(a). We adjusted the distance between the objective and the filament in order to have the best resolution for the moving bubbles. Most of the bubbles were spherical. Concentric circle stripes were observed on them with microscope direct observation, which may result from the diffraction of the scattered laser light. Here we focus on the dynamic motions of the bubbles and don’t discuss the concentric circle stripes. The lifetime of a bubble was measured to be several seconds. By averaging the displacement of the bubble on two sequent slides of the CCD images, the speed of the bubble was estimated to be at the order of ${10}^{-4} m/s$. To reveal the origin of the scattered light on the bubbles, a band pass filter with central wavelength of 800 nm and FWHM bandwidth of 40 nm (Andover 800FS40-25) was placed between the microscope and the surface of water. And in this way the bubbles were still observed [see Fig. 2(b)]. The background brightness dimed a bit, which was due to the filtration of the generated continuum. It demonstrated that the light shined the bubbles was mainly the fundmental beam at 800 nm.

 

Fig. 2 Top view of the filament-induced bubbles generation in water. The input pulse energy was 3.0 mJ, without (a) and with (b) a band pass filter of 800 nm under the micro objective.

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It should be pointed out that the lowest pulse energy corresponding to the bubbles generation on the CCD image was about $20 \text{μJ}$. As the pulse energy increased, the number of the bubbles increased accordingly, and more light was scattered on the surface of the bubbles. When the pulse energy was more than 5 mJ, the bubbles generation and moving dynamics on the CCD images became very fierce and the bubbles overlapped with each other. To reveal an intuitive physical picture, three different input pulse energy (0.5, 1.7, and 3.0 mJ) were chosen for the following experimental investigations.

With the microscope moving along the filament, we observed that the moving directions of the bubbles at different geometric positions along the filament were different. And a set of videos at three different positions along the filament were recorded, corresponding to the cases of $\text{θ}>{90}^{°}$ [Fig. 3(a)], $\text{θ}\approx {90}^{°}$ [Fig. 3(b)] and $\text{θ}<{90}^{°}$ [Fig. 3(c)], respectively, where $\text{θ}$ was defined as the angle between the bubble moving direction and the laser propagation direction. As we can see, the bubbles moved upward from the bottom of the CCD picture in a certain direction, which corresponded to the bubbles moving across the filament in the cuvette. As the exposure time of the CCD was set as 100 ms in our experimental observation, we could see the moving track of a bubble on the CCD image clearly. The bubbles’ motions mainly appeared in a range of about $500 \text{μm}$ from the filament on both sides. Note that in Figs. 3(a)-3(c) the bubbles’ motion was not symmetrical with the filament, but from one side to the other side. And we found it was related to the relative location of the filament to the silica cuvette. Actually, the bubbles always move from the cramped side to the largo one, as the diagram shown in Fig. 4(a). The movements of the generated bubbles in water are mainly driven by the filament-induced shock waves, Coulomb force and the pressure force induced by water density gradient. The filament ionizes the water molecules. The resulted electrons are then accelerated and collide with other electrons/molecules, which heats the surrounding water. As a result, the water temperature gradient is induced along the filament within hundreds of micrometers. Thus it results in the water density gradient, which probably takes the dominate role here. The specific procedures of bubbles’ motion can be expressed as the following four steps: (1) bubbles are generated by femtosecond filamentation in water and the pressures towards the surrounding water are created. As a result, the water on both sides of the filament is pushed towards the side walls of the cuvette. It creates a low water density region at the filament position; (2) the water below the filament flows upwards to fill the space at the filament. Here we drew a schematic diagram to show the water flowing loops on both sides of the filament, as shown in Fig. 4(b). It is a phenomenon similar to the “ocean currents” in geophysics, as hot water always flows upwards; (3) due to the viscous resistance of water, the water flowing on the largo side suffers a longer distance for one loop, resulting that its speed damps more than that of the cramped side. Thus the cramped side possesses faster water flowing speed and higher water pressure; (4) the bubbles are driven by the difference of the water pressure between the two sides, and finally flow to the tenuous one. Besides, by using one 45°high reflectivity mirror at 800 nm, we were able to observe the side view of the bubbles’ motion, as shown in Fig. 3(d). The bubbles were also moving upwards in water, which was probably due to buoyancy and the local hot water rising. However, the speed for bubbles moving upwards was much smaller than that of the horizontal motion. This implies that the filament induced water pressure difference between two sides takes the dominant role for bubbles’ motion.

 

Fig. 3 The top view videos corresponding to the cases of (a) $\text{θ}<{90}^{°}$, at the position of 16 mm (see Visualization 1); (b) $\text{θ}\approx {90}^{°}$, at the position of 1 mm (see Visualization 2); (c) $\text{θ}>{90}^{°}$, at the position of −14 mm (see Visualization 3). (d) The side view video of the bubbles’ motion, at the position of −5 mm (see Visualization 4). The input pulse energy was set as 3.0 mJ. The geometric position of laser filamentation and the moving direction of bubbles are indicated.

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Fig. 4 (a) The bubbles move from the cramped side to the largo side. (b) Profile schematic of the convection process in water. The red dot refers to the profile of the laser beam, and the white dashed curves are guidelines for the water flowing.

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Then we measured the number of the bubbles at different positions along the filament with the input pulse energy of 0.5, 1.7, and 3.0 mJ, respectively, as shown in Fig. 5(a). As we can see, at the beginning the number of bubbles increased as the laser propagated, which was due to the focusing of the laser beam and the increased filament intensity. Then it began to stay relatively constant in the middle part of the filament, corresponding to the intensity clamping for filamentation in water. And as the laser pulse energy increased, the number of the bubbles at the clamping domain increased accordingly. It should be attributed to a larger plasma volume for filamentation generated by pulses with higher energy, as according to the principle of bubble’s formation mentioned in the introduction part, the number of bubbles is proportional to plasma volume.

 

Fig. 5 (a) Bubbles number at different positions along the filament, with the input pulse energy of 0.5 mJ (black squares), 1.7 mJ (red circles), and 3.0 mJ (olive triangles). The number of bubbles were averaged over 5 random laser shots. (b) Bubbles moving directions at different positions along the filament, with the input pulse energy of 0.5 mJ (black squares), 1.7 mJ (red circles), and 3.0 mJ (green triangles). The red arrows represent the laser propagation direction.

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The moving direction with respect to the geometric positions along the filament with pulse energy of 0.5, 1.7, and 3.0 mJ are plotted in Fig. 5(b). As we can see, the angle increased as the laser propagated, implying that the bubbles all trended to move to the middle of the cuvette. The moving traces of the bubbles along the filament exhibited a fusiform shape [see Fig. 4(a)]. Despite the intensity clamping of the filament, there exists the position with the biggest plasma volume, which corresponds to the position with the bubbles moving direction of ${90}^{°}$. The larger number of bubbles indicates more cavities there and more fierce local convection. Thus the local water pressure on the largo side is even lower. The bubbles always trend to move in a direction that possesses the biggest pressure gradient. And this explains the directional movements of the bubbles at different positions along the filament. Actually, with pulse energy up to several millijoules in our experiment, the beam undergoes multi-filamentation in water, and all these child filaments undergo intensity clamping [21]. The results are that the biggest plasma volume is formed around the geometrical focus. As for the small deviations of the positions corresponding to the ${90}^{°}$ motion in three different pulse energy cases, they are due to the measuring errors in our experiments.

4. Conclusion

In summary, we investigated the movements of femtosecond filamentation induced bubbles in water on a macroscopic time scale. The movements of the bubbles were observed to be directional, exhibiting a fusiform distribution along the filament, which indirectly indicates the intensity-dependent convection phenomenon caused by femtosecond filamentation in water. The details of the dynamic processes of convection await to be explored in succeeding experiments. Nevertheless, it opens up possibilities for investigations on the micro fluid dynamics induced by ultrashort laser in liquid.