Subwavelength anti-diffracting beams propagating over more than 1,000 Rayleigh lengths

Propagating light beams with widths down to and below the optical wavelength require bulky large-aperture lenses and remain focused only for micrometric distances1, 2. Here, we report the observation of light beams that violate this localization/depth-of-focus law by shrinking as they propagate, allowing resolution to be maintained and increased over macroscopic propagation lengths. In nanodisordered ferroelectrics3, 4 we observe a non-paraxial propagation of a sub-micrometre-sized beam for over 1,000 diffraction lengths, the narrowest visible beam reported to date5, 6, 7, 8. This unprecedented effect is caused by the nonlinear response of a dipolar glass, which transforms the leading optical wave equation into a Klein-Gordon-type equation that describes a massive particle field9. Our findings open the way to high-resolution optics over large depths of focus, and a route to merging bulk optics into nanodevices.