![]() ![]() ![]() 26, 27 (originally named “flying focus”), respectively, which can propagate at an arbitrary group velocity in free space including all motion forms of superluminal or subluminal, accelerating or decelerating, and forward or backward propagations. 24, 25 (originally named “sliding focus”) and Froula et al. ![]() The first example is the three-dimensional (3-D) flying focus (FLFO) within the extended Rayleigh length independently demonstrated by Quéré, et al. For example, a Bessel beam can propagate along a straight-line trajectory at a superluminal velocity governed by c/cos α in free space, where α is the half conical angle of the conical superposition 13, 14 an Airy beam can propagate along a parabolic trajectory at an accelerating superluminal group velocity in free space 15, 16, 17, 18, 19, 20, 21, 22 an Airy-Bessel pulsed beam (called light bullet) can propagate along a straight-line trajectory at an accelerating superluminal group velocity in a dispersion medium 23.Ĭurrently, spatiotemporal (ST) couplings are frequently used to modulate the propagation or structure of a pulsed beam, which permits both velocity control (i.e., superluminal or subluminal, and accelerating or decelerating) and direction control (i.e., forward or backward) 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38. Another approach is by shaping beam in space or pulse in time to change the propagating velocity (e.g., superluminal or accelerating velocity) and direction (e.g., straight-line or bended trajectory) in free space 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23. However, this kind of method cannot be directly applied in free space, where the refractive index is constant n = 1. In this case, the propagating velocity and/or direction can be controlled by crafting the spectrum- and space-dependent refractive index n λ( x, y, z) 7, 8, 9, 10, 11, 12. In linear physics, an optical pulse propagates along a straight-line trajectory at the group velocity of c/ n g, where c is the speed of light in the vacuum and n g is the group refractive index in the medium. Optical pulse propagation, including velocity and direction, is a very basic characteristic for applications like optical information/communication, laser-matter interaction, and so on 1, 2, 3, 4, 5, 6. This finding extends the control of light and might enable important potential applications. When this light is applied in a radiation pressure simulation, a reciprocating radiation-force can be produced accordingly. 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. 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. In the method of flying focus, where temporal chirp and longitudinal chromatism were combined, tunable-velocities and even backward-propagation were demonstrated. ![]() Constant-speed straight-line propagation in free space is a basic characteristic of light, and spatiotemporal couplings recently were used to control light propagation. ![]()
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