Scale-free optics and diffractionless waves in nanodisordered ferroelectrics

Wavelength rigidly fixes the diffraction that distorts waves during propagation, and poses fundamental limits to imaging, microscopy and communication. This distortion can be avoided by using waveguides or nonlinearity to produce solitons. In both cases, however, diffraction is only compensated, so the wavelength still imposes rigid laws on wave shape, size and soliton intensity1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14. Nonlinearity, in turn, can introduce new spatial scales. In principle, if one is able to identify a nonlinearity that introduces an intensity-independent scale that cancels the wavelength, 'scale-free' propagation can occur. In this regime, diffraction ceases, and waveforms will naturally propagate without distortion, forming solitons of any size and intensity, even arbitrarily low. Here we provide the first experimental evidence of scale-free optical propagation in supercooled copper-doped KTN:Li, a recently developed out-of-equilibrium ferroelectric15, 16, 17. This demonstrates that diffraction can be cancelled, and not merely compensated, thus leading to a completely new paradigm for ultraresolved imaging and microscopy.