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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We theoretically consider infrared-driven hyperbolic metamaterials able to spatially filtering terahertz radiation. The metamaterial is a slab made of alternating semiconductor and dielectric layers whose homogenized uniaxial response, at terahertz frequencies, shows principal permittivities of different signs. The gap provided by metamaterial hyperbolic dispersion allows the slab to stop spatial frequencies within a bandwidth tunable by changing the infrared radiation intensity. We numerically prove the device functionality by resorting to full wave simulation coupled to the dynamics of charge carries photoexcited by infrared radiation in semiconductor layers.Manipulating terahertz (THz) radiation is generally a difficult task since the most of standard materials simply do not respond to such frequencies. However, the advent of metamaterials has allowed to partially reduce this difficulty since their electromagnetic properties can be artificially manipulated 1 through a suitable design of the underlying constituent unit cells. At the same time a number of setups have been proposed for steering the THz radiation 2 and reconfigurable electrically 3 or opticallydriven metamaterials have been exploited for conceiving active THz devices 6 . The most of the proposed active THz devices are tunable frequency-domain filters since it is relatively simple to control the metamaterial dispersion properties through external stimuli. In this Letter we theoretically propose a way for achieving active and spatial filtering of the THz radiation by means of a suitable hyperbolic metamaterial whose THz response can be tuned by an auxiliary infrared field. Hyperbolic or indefinite media 7 are uniaxially anisotropic metamaterials having principal permittivities of different signs, a remarkable feature leading extraordinary plane waves to be ruled by a hyperbolic dispersion relation. Hyperbolicity is the main physical ingredient leading to unusual optical effects as negative refraction 8 and hyperlensing 9 and supporting a number of proposed devices as beam splitters 10 , spatial 11 and angular filters 12 and optical switches 13 . The tunable hyperbolic metamaterial we consider in the present Letter, together with the fields geometry, is sketched in Fig.1. The metamaterial slab of thickness L is obtained by stacking along the x-axis alternating layers of an intrinsic semiconductor 14 (sc) and a negative dielectric (nd) of thicknesses d sc and d nd , respectively and it is illuminated by an infrared (IR) plane wave linearly polarized along the y-axis and normally impinging onto the slab interface at z = 0. The THz field (TH) is a transverse magnetic (TM or p-polarized) monochromatic plane impinging with incidence angle θ onto the interface.The infrared field within the semiconductor layers photoexcites electrons to the conduction band which dynamically recombine so that the resulting electron density N is described by the rate equationwhere is the Planck constant divided by 2π, ǫ 0 is the absolute vacuum permittivity, ǫ sc (ω IR ) is ...

We predict that a liquid crystal/silver nanoparticles mixture can be designed so that, in a frequency range, its effective ordinary and extraordinary permittivities have real parts of different signs. We exploit this result to design a nano-photonic device obtained by sandwiching a few hundred nanometer thick slab of the proposed mixture between two silica layers. By resorting to full-wave simulations, we show that, by varying the direction of an externally applied electric field, the device can be used as an optical modulator since its transmissivity can be switched between 0.02 and 0.4 at a wavelength close to the frequency range where the medium is indefinite. The device functionality physically stems from the fact the orientation of the hyperbola characterizing extraordinary waves within the indefinite medium follows the applied electric field direction and therefore, if the hyperbola asymptote is nearly normal to the slab, full switch between evanescent and homogeneous propagating waves can be achieved within the medium.PACS numbers:

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