Speed of structured light pulses in free space

A plane monochromatic wave propagates in vacuum at the velocity c. However, wave packets limited in space and time are used to transmit energy and information. Here it has been shown based on the wave approach that the on-axis part of the pulsed beams propagates in free space at a variable speed, exhibiting both subluminal and superluminal behaviours in the region close to the source, and their velocity approaches the value of c with distance. Although the pulse can travel over small distances faster than the speed of light in vacuum, the average on-axis velocity, which is estimated by the arrival time of the pulse at distances z ≫ l_d (l_d is the Rayleigh diffraction range) and z > cτ (τ is the pulse width) is less than c. The total pulsed beam propagates at a constant subluminal velocity over the whole distance. The mutual influence of the spatial distribution of radiation and the temporal shape of the pulse during nonparaxial propagation in vacuum is studied. It is found that the decrease in the width of the incident beam and the increase in the central wavelength of the pulse lead to a decrease in the propagation velocity of the wave packet.