Numerical Calculation of Self-Focusing and Trapping of a Short Light Pulse in Kerr Liquids

Self-focusing and trapping of an intense, short light pulse is discussed on the basis of a parabolic scalar wave equation which includes a quadratic nonlinear refractive index. When the finite relaxation time of the nonlinear index is taken into account, the propagation properties of the transient solution differ considerably from those of the time-independent solution. Based mainly on the results of our numerical calculations, we show that contraction of the self-focusing pulse stops at a finite radius and that part of the pulse remains trapped beyond this focal point. The limiting radius decreases rather rapidly with increasing input power as well as with pulse width. However, if we assume a cutoff radius, the resulting filament accounts for experiments performed with multimode lasers. Effects of stimulated Raman scattering and dispersion are also discussed.