Underwater acoustic wave generation by filamentation of terawatt ultrashort laser pulses

Acoustic signals generated by filamentation of ultrashort terawatt laser pulses in water are characterized experimentally. Measurements reveal a strong influence of input pulse duration on the shape and intensity of the acoustic wave. Numerical simulations of the laser pulse nonlinear propagation and the subsequent water hydrodynamics and acoustic wave generation show that the strong acoustic emission is related to the mechanism of superfilamention in water. The elongated shape of the plasma volume where energy is deposited drives the far-field profile of the acoustic signal, which takes the form of a radially directed pressure wave with a single oscillation and a very broad spectrum.

Figure 1

Experimental setup for generation of acoustic waves with a laser beam and recording them with a hydrophone. $h$ is the distance between the surface of water and the lens while $z$ defines the direction of hydrophone displacement for spatiotemporal acoustic wave analysis.

Figure 2

Typical acoustic wave profile registered by a hydrophone. The focusing lens was 30 cm above the surface of water and the pulse duration was 5 ps. The two dashed curves represent the profiles of the two spherical acoustic waves emitted from point sources located at the depths $z=0$ and 297 mm (corresponding to the position of the top of the hyperbolic branches). These locations clearly correspond to the water tank surface and to the laser focal region, respectively.

Figure 3

Comparison of amplitude profiles for the acoustic waves generated by 290 mJ laser pulses with initial duration of (a) 0.25 ps, (b) 0.5 ps, and (c) 5 ps. The lens was positioned at $h$ = 13 cm above the surface of water corresponding to a focus depth of $z_0\sim$ 500 mm. Acoustic waves are registered by moving the hydrophone along a vertical axis at distance $d$ = 38 cm from the laser propagation axis.

Figure 4

Fluence profiles (cross section along a single transverse dimension $x$) for nonlinear propagation of laser pulses in water. The focus of the lens is at $z$ = 488 mm. Input pulse energy 290 mJ. Pulse duration: (a) 0.5 ps; (b) 5ps. Maximum fluence values are (a) 13 and (b) 114 mJ/${\mathrm{mm}}^2$.

Figure 5

Plasma density, ${\rho }_e$, profiles in the same conditions as in Fig. 4 is depicted in (a) and (b), i.e., when input pulse energy 290 mJ and pulse duration: (a) 0.5 ps; (b) 5 ps. While (b), (c), and (d) are for the cases when input beam peak power was the same for pulse durations 5, 0.5, and 0.25 ps, respectively. Maximum plasma densities are 12.4 $\times {10}^{21}, 31\times {10}^{21}, 9.5\times {10}^{21}$, and $4.9\times {10}^{21}{\mathrm{m}}^{-3}$ for (a), (b), (c), and (d), respectively.

Figure 6

(a) Absorbed energy, $\langle U\rangle$, and (b) rate of nonlinear energy losses, $d\langle U\rangle /dz$, as a function of propagation distance. The curves correspond to different input pulse energies and pulse durations: 290 mJ, 5 ps (dotted blue); 290 mJ, 0.5 ps (solid red), 29 mJ, 0.5 ps (dashed green), and 14.5 mJ, 0.25 ps (dash-dot black). The dotted blue and solid red curves correspond to pulses with the same energy while the dotted blue, dashed green and dash-dot black curves correspond to beams with the same peak power.

Figure 7

Plasma density, ${\rho }_e$, distribution from the simulation of pulse propagation with initial energy of 290 mJ and duration of 5 ps (a). The solid green curve represents the boundary of the focal (plasma) volume. (b) Spectrally filtered plasma density distribution for the same conditions. A log scale is used for both figures.

Figure 8

Absorbed energy density, $U_m$, versus propagation distance. Different initial beam energies and pulse durations are represented with different colors and are the same as described in the caption of Fig 6. The thin gray horizontal line represents an approximate threshold value (40 $\mu \text{J}/{\mathrm{mm}}^3$) for pressure wave to be registered by the hydrophone (see Fig. 1).

Figure 9

Initial (a) temperature and (b) pressure distributions for peak heatings of $\mathrm{\Delta }{T}_{\text{max}}\equiv max\{T(r,z,t=0)-T_0\}$ = 6 K (leftmost color bars) and $\mathrm{\Delta }{T}_{\text{max}}$ = 70 K (rightmost colorbars). The contours are at 1/10, 1/20, and 1/50 of the difference between the maximum and background levels, $p_0=1.023\times {10}^5$ Pa (corresponding to a depth of the order of 10 cm in water of background density ${\rho }_0$ = 998.2 kg/${\mathrm{m}}^3$), and $T_0=300$ K. Same criterion for contours is applied to Figs. 10 and 11.

Figure 10

(a, d) Temperature, $\mathrm{\Delta }T$, (b, e) pressure, $p$, and (c, f) density, $\mathrm{\Delta }\rho \equiv \rho -{\rho }_0$, distributions in water 10 $\mu \mathrm{s}$ after the pulse heating. (a–c) $\mathrm{\Delta }{T}_{\text{max}}=6$ K, (d–f) $\mathrm{\Delta }{T}_{\text{max}}=70$ K. ${\rho }_0$ = 998.2 kg/${\mathrm{m}}^3$ and $T_0=300$ K.

Figure 11

Simulated pressure vs. time signal recorded at an offset of 5 mm from the pulse propagation axis, $z$. Simulations show (a) linear (Eqs. (6)) and (b, c) nonlinear (Eqs. (7)) calculations, the latter for (b) $\mathrm{\Delta }{T}_{\text{max}}=6$ K and (c) $\mathrm{\Delta }{T}_{\text{max}}=70$ K.

Figure 12

Sound-wave directivity measured from experiments (from Ref. [13], black curves) and numerical simulations with $\mathrm{\Delta }=70$ K (at 50 mm from the source, blue (gray) curves) for (a) 0.5 MHz, (b) 2 MHz, and (c) 4.5 MHz. The maximum pressure recorded numerically at this distance is of 2 MPa above the background $\sim 0.1$ MPa and the maximum amplitudes for the selected frequencies correspond to (a) $5.3\times {10}^5$ Pa/MHz, (b) $2.88\times {10}^5$ Pa/MHz, and (c) $0.98\times {10}^5$ Pa/MHz. (d) Shows spectrally integrated angular distributions corresponding to distances of 38 cm [solid blue (gray)], 10 m (dotted), and 100 m (dashed) away from the source. In (d), directivity plots are scaled to 1, and the relative ratios are 0.57 (10 m to 38 cm) and 0.22 (100 m to 38 cm). In all figures, $\theta$ is measured from the $z$ axis: $0^{\circ }({180}^{\circ }$) corresponds to the forward (backward) laser propagation direction.