Filamentation of ultrashort laser pulses in silica glass and KDP crystals: A comparative study

Ionizing 800-nm femtosecond laser pulses propagating in silica glass and in potassium dihydrogen phosphate (KDP) crystal are investigated by means of a unidirectional pulse propagation code. Filamentation in fused silica is compared with the self-channeling of light in KDP accounting for the presence of defect states and electron-hole dynamics. In KDP, laser pulses produce intense filaments with higher clamping intensities up to 200 ${\mathrm{TW}/\mathrm{cm}}^2$ and longer plasma channels with electron densities above ${10}^{16}$ ${\mathrm{cm}}^{-3}$. Despite these differences, the propagation dynamics in silica and KDP are almost identical at equivalent ratios of input power over the critical power for self-focusing.

Figure 1

(a) Schematic illustration of the four ionization channels Eqs. (6) considered for the KDP crystal: 3-photon ionization from a defect state SLG1, 1-photon transition from a defect state SLG2 close to the conduction band (CB), direct 5-photon ionization from the valence band (VB), and avalanche ionization. (b) Comparison of ionization rates for multiphoton transitions at 800 nm. The black curve refers to the Keldysh rate [12] for silica (dashed curve) and for KDP (solid curve). The blue (gray) dash-dotted line shows the rate ${\sigma }_5{I}^5$ used for KDP in Eq. (6g).

Figure 2

Electron densities in the conduction band and partial contributions from different transition channels obtained from Eqs. (4) and (6) using Gaussian pulses $I\left(t\right)=I_{0}exp(-2t^2/t_p^2)$ with $t_p=50$ fs and (a), (b) $I_0=10$ ${\mathrm{TW}/\mathrm{cm}}^2$; (c), (d) $I_0=50$ ${\mathrm{TW}/\mathrm{cm}}^2$; and (e), (f) $I_0=100$ ${\mathrm{TW}/\mathrm{cm}}^2$.

Figure 3

Filamentation dynamics of 50-fs, 60-$\mu \mathrm{m}$ Gaussian pulses propagating in silica (left column) or KDP (right column). Input pulse energies are $0.5$ $\mu \mathrm{J}$ (1 $\mu \mathrm{J}$) for silica and 1 $\mu \mathrm{J}$ (resp. 2 $\mu \mathrm{J}$) for KDP. (a), (b) Maximum pulse intensity; (c), (d) peak electron density; (e), (f) nonlinear on-axis dynamics in the $(t,z)$ plane for the high energy pulses; (g), (h) corresponding $1/e^2$ filament diameters.

Figure 4

On-axis temporal profiles at two different longitudinal distances for the 50-fs pulse propagating in (a) silica and (b) KDP. Insets show the on-axis electric field of the most compressed pulse.

Figure 5

Filamentation dynamics of 500-fs, 60-$\mu \mathrm{m}$ Gaussian pulses propagating in silica (left column) or KDP (right column). Input pulse energies are $5\mu \mathrm{J}$ for silica and 10 $\mu \mathrm{J}$ for KDP. (a), (b) Maximum pulse intensity; (c), (d) peak electron density; (e), (f) nonlinear on-axis dynamics in the $(t,z)$ plane; (g), (h) corresponding $1/e^2$ filament diameters. In (b), (d), (h) the red (gray) dashed curve refers to filamentation in KDP with the 5-photon MPI process only.

Figure 6

On-axis temporal profiles at two different longitudinal distances for the 500-fs pulse propagating in (a) silica and (b) KDP. Insets show the on-axis electric field of the most compressed pulse.

Figure 7

On-axis spectra of the 50-fs and 500-fs long pulses plotted as dashed curves in Fig. 4 and as solid curves in Fig. 6. Propagation distances are (a) $z=4.5$ mm and $z=9$ mm for silica, and (b) $z=4.5$ mm and $z=8$ mm for KDP.

Figure 8

Evolution of the on-axis fluence vs propagation distance for the 50-fs (dashed curves) and 500-fs (solid curves) long pulses shown in Figs. 3 and 5.