A simple theory is given to explain the many different features of small-scale filaments under various experimental conditions. It is shown that the observed filaments are the consequences of moving foci. Under appropriate conditions, a focal spot can move in the forward direction with a speed faster than light. As a result, the light pulse emitted from the filament at the end of the nonlinear medium has a much shorter duration than the input pulse, and shows a characteristic spectral broadening. Because of its high intensity, a moving focal spot also leaves behind it a temporary track of field-induced refractive index. Light trailing after the focal spot can then be partially trapped in the track. Trapping over an appreciable distance is possible if the velocity of the forward-moving focal spot is not much higher than the light velocity.

• Received 4 December 1970

DOI:https://doi.org/10.1103/PhysRevA.3.2099