Abstract
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 ≫ ld (ld 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.
Highlights
A plane monochromatic wave propagates in vacuum at the velocity c
The wave packet propagates at a group velocity that is different from the velocity of individual harmonic components
Bessel beams are the solutions of the Helmholtz wave equation[32,33]. They can be considered as the modal solutions with azimuthal indices in free space
Summary
A plane monochromatic wave propagates in vacuum at the velocity c. Wave packets limited in space and time are used to transmit energy and information 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. This approach is insufficient, and a rigorous analysis of the problem is possible only www.nature.com/scientificreports within the framework of wave optics, taking into account nonstationary diffraction effects It was shown in[23] that the slowing down of light depends on the magnitude of the orbital momentum of the beam. The group velocities manifested by Laguerre-Gauss (LG) modes in vacuum were investigated, and the subluminal effects arising from the twisted nature of the optical phase front were observed and explained in paraxial approximations. Of particular interest were propagation-invariant localized pulsed waves that exhibit non-diffracting non-spreading propagation over a large distance[31]
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