Space-frequency coupling, conical waves, and small-scale filamentation in water

Numerical simulations of fs laser propagation in water have been made to explain the small-scale filaments in water we have observed by a nonlinear fluorescence technique. Some analytical descriptions combined with numerical simulations show that a space-frequency coupling mainly from the interplay among self-phase modulation, dispersion and phase mismatching will reshape the laser beam into a conical wave which plays a major role of energy redistribution and can prevent laser beam from self-guiding over a long distance. An effective group velocity dispersion is introduced to explain the pulse broadening and compression in the filamentation.

Figure 1

(a) Experimental setup for visualization of filamentation. A fs laser beam delivered by a Ti:sapphire laser system passes through the slit and propagates in water. (b) Development of a one-dimension filament array in water behind a slit. The fluorescence is excited by two-photon absorption of the fundamental laser beam and one-photon absorption of white light. The dye is Rhodamine B. ${\lambda }_{\text{absorption}}=556\mathrm{nm}$. (c) Evolution of fluorescence intensity as well as the diameter of the first filament in (b) as a function of propagation distance.

Figure 2

Evolution of maximum on-axis laser intensity, diameter of the laser beam, and two-photon plus one-photon ($556\mathrm{nm}$ for Rhodamine B) fluorescence as a function of propagation distance.

Figure 3

(a) Simulated frequency-dependent curvatures at different distances. (b) Evolution of curvatures of light waves on the anti-Stokes side. (c) Calculated frequency-dependent curvatures at different distances.

Figure 4

(a) Spectra intensity outside the axis $(r=10\mu \mathrm{m})$ and on the axis $(r=0\mu \mathrm{m})$, respectively, at the clamping position. (b) $X$-wave induced by the conical wave after propagation of a distance $10.6\mathrm{mm}$.

Figure 5

(a) Evolution of pulse shape on axis as the laser propagates. (b) Evolution of the chirp coefficient and the effective GVD together with the material NGVD in atomic units.