Spatiotemporal moving focus of long femtosecond-laser filaments in air

The characteristics of filaments formed by femtosecond-laser pulses freely propagating in air are different from those of filaments generated with a focal lens. A scheme combining (2D+1) modeling of the nonlinear Schrödinger equation and ray-tracing method is proposed to provide a fast estimate of the long-range filamentation process in a single-filament regime. A filament with a length of more than 100 m is formed by a 10-mJ, negative chirped 350-fs laser pulse freely propagating in air. A ray-tracing calculation based on the refractive index field obtained from the nonlinear Schrödinger simulation shows that, in the 100-m propagation range, the main mechanism of filamentation is the spatiotemporal moving focus induced by the initial distribution of the laser intensity. The analysis of ray trajectories suggests that the energy exchange between background and filament core due to refocusing of light rays can be induced by Kerr self-focusing without the help of the ionization effect. The plasma defocusing can be observed only at a very short distance on the propagation track, and it prevents the collapse of the laser field.