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 intensity(1-14). 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 ferroelectric(15-17). This demonstrates that diffraction can be cancelled, and not merely compensated, thus leading to a completely new paradigm for ultraresolved imaging and microscopy

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One of the most controversial phenomena in nonlinear dynamics is the reappearance of initial conditions. Celebrated as the Fermi-Pasta-Ulam-Tsingou problem, the attempt to understand how these recurrences form during the complex evolution that leads to equilibrium has deeply influenced the entire development of nonlinear science. The enigma is rendered even more intriguing by the fact that integrable models predict recurrence as exact solutions, but the difficulties involved in upholding integrability for a sufficiently long dynamic has not allowed a quantitative experimental validation. In natural processes, coupling with the environment rapidly leads to thermalization, and finding nonlinear multimodal systems presenting multiple returns is a long-standing open challenge. Here, we report the observation of more than three Fermi-Pasta-Ulam-Tsingou recurrences for nonlinear optical spatial waves and demonstrate the control of the recurrent behavior through the phase and amplitude of the initial field. The recurrence period and phase shift are found to be in remarkable agreement with the exact recurrent solution of the nonlinear Schrödinger equation, while the recurrent behavior disappears as integrability is lost. These results identify the origin of the recurrence in the integrability of the underlying dynamics and allow us to achieve one of the basic aspirations of nonlinear dynamics: the reconstruction, after several return cycles, of the exact initial condition of the system, ultimately proving that the complex evolution can be accurately predicted in experimental conditions.

Recent studies of the minute morphology of the skin by optical coherence tomography revealed that the sweat ducts in human skin are helically shaped tubes, filled with a conductive aqueous solution. This, together with the fact that the dielectric permittivity of the dermis is higher than that of the epidermis, brings forward the supposition that as electromagnetic entities, the sweat ducts could be regarded as low Q helical antennas. The implications of this statement were further investigated by electromagnetic simulation and experiment of the in vivo reflectivity of the skin of subjects under varying physiological conditions (Feldman et al 2008 Phys. Rev. Lett. 100 128102). The simulation and experimental results are in a good agreement and both demonstrate that sweat ducts in the skin could indeed behave as low Q antennas. Thus, the skin spectral response in the sub-Terahertz region is governed by the level of activity of the perspiration system and shows the minimum of reflectivity at some frequencies in the frequency band of 75-110 GHz. It is also correlated to physiological stress as manifested by the pulse rate and the systolic blood pressure. As such, it has the potential to become the underlying principle for remote sensing of the physiological parameters and the mental state of the examined subject.