  Laser filamentation in transparent material has a wide range of applications,
from three dimensional manufacturing to biological technologies. Various
experimental results showed that femtosecond laser pulse filamentation in fused
silica strongly depends on laser focusing conditions. However, the physical
mechanism governing each regime has not been fully understood. For the first
time, single and multiple re-focusing of the laser pulse in interaction of
femtosecond laser pulse with fused silica, and consequent single and multiple
damage zones (filaments) have been observed in our extensive three-dimensional,
high resolution FDTD (finite-difference time-domain) simulations. We show that
Kerr nonlinearity plays a crucial role loose laser focusing regime, while it is
not an important factor in tight laser focusing regime, where geometrical
focusing becomes important. Our simulation results agree well with existing
experimental findings. In addition, the improved analytical model prediction
gives a reasonable estimate of the shift from Kerr nonlinearity regime to
linear geometrical focusing regime.
