Relativistic transformations of quasi-monochromatic optical beams

TL;DR

This paper studies how a quasi-monochromatic optical beam transforms under Lorentz transformations when observed from a moving frame, revealing it becomes a pulsed wave packet traveling at the relative velocity.

Contribution

It demonstrates that Lorentz transformations convert monochromatic beams into space-time wave packets, a novel insight into relativistic optical beam behavior.

Findings

Monochromatic beams become pulsed wave packets under Lorentz transformations.

The transformed wave packets travel at the relative velocity of the observer.

The predicted effects are observable at terrestrial speeds.

Abstract

A monochromatic plane wave recorded by an observer moving with respect to the source undergoes a Doppler shift and spatial aberration. We investigate here the transformation undergone by a generic, paraxial, spectrally coherent quasi-monochromatic optical \textit{beam} (of finite transverse width) when recorded by a moving detector. Because of the space-time coupling engendered by the Lorentz transformation, the monochromatic beam is converted into a propagation-invariant pulsed beam traveling at a group velocity equal to that of the relative motion, and which belongs to the recently studied family of `space-time wave packets'. We show that the predicted transformation from a quasi-monochromatic beam to a pulsed wave packet can be observed even at terrestrial speeds.