Observation of optical de Broglie-Mackinnon wave packets

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.