# Observation of optical de Broglie-Mackinnon wave packets

## TL;DR

This paper reports the experimental observation of optical de Broglie-Mackinnon wave packets, demonstrating their non-dispersive, circularly symmetric profiles in a dispersive medium, and exploring their relation to particle mass and velocity.

## Contribution

First experimental realization of optical de Broglie-Mackinnon wave packets, confirming their theoretical properties and unique O-shaped spatio-temporal profiles in a dispersive medium.

## Key findings

- Observed non-dispersive, circularly symmetric wave packets.
- Produced dispersion-free wave packets by spectral shaping.
- Tuned parameters to relate wave packet properties to particle mass and velocity.

## Abstract

de Broglie wave packets accompanying moving particles are dispersive and lack an intrinsic length scale dictated solely by the particle mass and velocity. Mackinnon proposed almost 45~years ago a localized non-dispersive wave packet constructed out of dispersive de Broglie phase waves via a Copernican inversion of the roles of particle and observer, whereupon an intrinsic length scale emerges by accounting for every possible observer -- rather than by introducing an \textit{ad hoc} uncertainty in the particle velocity. The de Broglie-Mackinnon (dBM) wave packet has nevertheless remained to date a theoretical entity. Here, we report the observation of optical dBM wave packets using paraxial space-time-coupled pulsed laser fields in presence of anomalous group-velocity dispersion. Crucially, the bandwidth of dBM wave packets has an upper limit that is compatible with the wave-packet group velocity and equivalent mass. In contrast to previously observed linear propagation-invariant wave packets whose spatio-temporal profiles at any axial plane are X-shaped, those for dBM wave packets are uniquely O-shaped (circularly symmetric with respect to space and time). By sculpting their spatio-temporal spectral structure, we produce dispersion-free dBM wave packets in the dispersive medium, observe their circularly symmetric spatio-temporal profiles, and tune the field parameters corresponding to particle mass and velocity that uniquely determine the wave-packet length scale.