# Structured light pulses and their Lorentz-invariant mass

## TL;DR

This paper investigates the Lorentz-invariant mass and propagation velocity of various structured light pulses in vacuum, revealing their dependence on spatial-temporal structure and showing velocities below the speed of light.

## Contribution

It provides analytical solutions for Lorentz-invariant mass and velocity of finite-duration structured light pulses, a novel insight into their relativistic properties.

## Key findings

- Lorentz-invariant mass depends on pulse structure
- Mean velocity is less than the speed of light
- Velocity is independent of pulse energy

## Abstract

Lorentz-invariant mass and mean propagation velocity have been found for structured light pulses in vacuum considered as relativistic objects. We solved the boundary problem for such widely known field configurations as Gauss, Laguerre-Gauss, Bessel-Gauss, Hermite-Gauss, and Airy-Gauss ones. The pulses were taken having the finite duration temporal envelope. We discovered that Lorentz-invariant mass and mean propagation velocity significantly depend on the spatial-temporal structure of pulses. We found that mean propagation velocity is independent of the full energy of the pulse and is smaller than the speed of light.