Airy wave packets accelerating in space-time

TL;DR

This paper demonstrates the synthesis of an Airy wave packet that propagates without acceleration by manipulating its spatio-temporal spectrum, effectively mimicking a Lorentz boost and revealing a novel 'time-diffraction' phenomenon.

Contribution

It introduces a method to create acceleration-free Airy wave packets through spectral deformation, leveraging relativistic frame transformations.

Findings

Achieved propagation-invariant Airy wave packets with deformed spectra.

Revealed 'time-diffraction' as a new manifestation of wave dynamics.

Demonstrated control over wave acceleration by spectral engineering.

Abstract

Although diffractive spreading is an unavoidable feature of all wave phenomena, certain waveforms can attain propagation-invariance. A lesser-explored strategy for achieving optical selfsimilar propagation exploits the modification of the spatio-temporal field structure when observed in reference frames moving at relativistic speeds. For such an observer, it is predicted that the associated Lorentz boost can bring to a halt the axial dynamics of a wave packet of arbitrary profile. This phenomenon is particularly striking in the case of a self-accelerating beam -- such as an Airy beam -- whose peak normally undergoes a transverse displacement upon free-propagation. Here we synthesize an acceleration-free Airy wave packet that travels in a straight line by deforming its spatio-temporal spectrum to reproduce the impact of a Lorentz boost. The roles of the axial spatial coordinate and time are swapped, leading to `time-diffraction' manifested in self-acceleration observed in the propagating Airy wave-packet frame.