# Non-invariance of the speed of light in free-space

## TL;DR

This paper demonstrates that the on-axis velocity of pulsed laser beams in free space can vary, exhibiting subluminal and superluminal behaviors near the source, but the average velocity over long distances remains less than the speed of light.

## Contribution

It reveals the non-invariance of light speed in free space for pulsed beams and analyzes how beam properties influence propagation velocity.

## Key findings

- On-axis pulse velocity varies near the source.
- Average pulse velocity over long distances is less than c.
- Beam properties like width and wavelength affect propagation speed.

## Abstract

A plane monochromatic wave propagates in vacuum at the velocity of 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 > ct (t is the pulse width) is less than c. The total pulse beam propagates at a constant subluminal velocity through the whole distance. The mutual influence of the spatial distribution of radiation and 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. It is shown that the velocities of the Bessel-Gauss and Laguerre-Gauss pulsed beams decrease with increasing orbital angular momentum (OAM). The results obtained are in good agreement with subluminal and superluminal measurements in free space.

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Source: https://tomesphere.com/paper/1902.08563