Time-frequency analysis of light-bullet dynamics during femtosecond filamentation in the anomalous dispersion regime

In this paper, we investigate the light-bullet dynamics during femtosecond laser filamenation in an anomalous dispersion regime based on the experimentally observed blueshifted resonant radiation (RR) in fused silica. A numerical simulation is performed and well reproduces the pronounced asymmetric feature of the RR spectra. By applying a time-frequency analysis to the propagating laser field, this specific spectral feature is found to be closely connected to the positively chirped property of RR in the time domain. In the context of the effective three-wave mixing model, this temporal chirp character of the RR is ascribed to the variable phase-matching conditions, which can be traced back to the accelerative propagation of the light bullet during its formation. Our work provides a deep understanding of the spatiotemporal dynamics of femtosecond laser-pulse propagation in condensed media.

Figure 1

Schematic representation of our experimental setup for femtosecond laser filamentation in fused silica: OPA, optical parametric amplifier; M1, M2, silver mirrors; $\lambda$/2, half-wave plate; G-T, Glan-Taylor polarizer; L, plano-convex lens; Hole, an aperture; Attenuator, different neutral filters.

Figure 2

Spectra in the visible region measured on the laser propagation axis; the black solid line (red dashed line) corresponds to input pulse energy of $31\mu \mathrm{J}$ ($34\mu \mathrm{J}$). The inset shows the conical emission at $31\mu \mathrm{J}$.

Figure 3

Numerical simulation results. The intensity of the initial pulse is $3.5\times {10}^{11}\mathrm{W}/{\mathrm{cm}}^2$. (a) The axial intensity at different positions of the sample. (b) Electric-field envelope and (c) corresponding spectral intensity of the laser pulse after propagating at two positions of the medium. The red solid line (blue dashed line) represents the laser pulse arriving at 18.5 mm (19.2 mm). (d) The axial intensity spectrum at 20 mm; the inset displays an asymmetrical structure of RR.

Figure 4

Time-frequency spectra of the electric field propagating through the medium at (a) 17.5, (b) 18.8, (c) 19.2, and (d) 20 mm. The colors shown are in logarithmic scale.

Figure 5

(a) The laser intensity (blue solid line) and the time corresponding to the peak intensity (red dashed line) on the axis along with the propagation direction. (b) The calculated wavelengths of RRs at different propagation distances using the phase-matching condition according to Eq. (1).

Figure 6

Time-frequency spectra of the electric field propagating through the medium at 22 mm.