Reciprocating propagation of laser pulse intensity in free space

Constant-speed straight-line propagation in free space is a basic characteristic of light, and spatiotemporal couplings recently were used to control light propagation. In the method of flying focus, where temporal chirp and longitudinal chromatism were combined, tunable-velocities and even backward-propagation were demonstrated. We studied the transverse and longitudinal effects of the flying focus in space-time and found in a specific physics interval existing an unusual reciprocating propagation that was quite different from the previous result. By increasing the Rayleigh length in space and the temporal chirp in time, the created flying focus can propagate along a longitudinal axis firstly forward, secondly backward, and lastly forward again, and the longitudinal spatial resolution improves with increasing the temporal chirp. When this light is applied in a radiation pressure simulation, a reciprocating radiation-force can be produced accordingly. This finding extends the control of light and might enable important potential applications. Spatiotemporal control has permitted the creation of velocity- and direction-tuneable light in free space. Here, numerical simulations propose a means to achieve a reciprocating flying focus by increasing the Rayleigh length and temporal chirp.