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.

自由空间中的等速直线传播是光的基本特征，最近使用时空耦合来控制光的传播。在飞行聚焦的方法中，将时间线性调频和纵向色度结合在一起，证明了可调速度，甚至向后传播。我们研究了时空飞行焦点的横向和纵向影响，发现在特定的物理间隔中存在不寻常的往复传播，这与之前的结果有很大不同。通过增加空间中的瑞利长度和时间上的时间chi，所创建的飞行焦点可以沿着纵轴首先向前，其次向后，最后再次向前传播，并且纵向空间分辨率随着时间chi的增加而提高。当在辐射压力模拟中施加该光时，可以相应地产生往复的辐射力。这一发现扩展了对光的控制，并可能实现重要的潜在应用。