Multiple foci and a long filament observed with focused femtosecond pulse propagation in fused silica

Multiple foci and a long filament are observed when we focus a femtosecond laser pulse into a fused-silica sample. The dependences of the intensity distribution of the plasma luminescence on the pulse energy and the numerical aperture (NA) of the focusing objective are investigated. Multiple foci are observed when NA of $\le 0.65$. A long filament tail is formed instead of multiple foci when the NA is 0.85. A physical image of femtoseond pulse propagation is given by a model based on the nonlinear Schrödinger equation.