Propagating light beams with widths down to and below the optical wavelength require bulky large-aperture lenses and remain focused only for micrometric distances 1,2 . 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 ferroelectrics 3,4 we observe a non-paraxial propagation of a sub-micrometresized beam for over 1,000 diffraction lengths, the narrowest visible beam reported to date [5][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 field 9 . Our findings open the way to high-resolution optics over large depths of focus, and a route to merging bulk optics into nanodevices.As monochromatic light travels through a transparent material its optical field E is governed by the Helmholtz equation (HE) (∇ 2 + n 2 k 2 0 )E = 0, where k 0 = 2π/λ is the wavevector, λ is the wavelength of the beam, and n is the index of refraction 10 . The HE includes diffraction, which smears out the fine details of spatial information. In nanodisordered ferroelectrics, the photorefractive nonlinearity can cause light to obey a Klein-Gordon equation0 )E = 0, which corresponds to a relativistic particle with mass given by the Einstein relation mc 2 = h − n m k 0 c (see Methods). In terms of propagation, a basic signature of the KGE regime is anti-diffraction; that is, diffraction-limited optical spots shrink instead of spreading. The simplest description of anti-diffraction can be formulated in the paraxial approximation, which predicts that(see Supplementary Section 'Beam anti-diffraction law in the paraxial regime'), which connects the beam spot size w(z) at a given distance z along the propagation direction to the minimum spot size w 0 at z = 0 through λ and n and the characteristic length scale L 11 . For L ≪ λ the standard diffraction law holds, so for sufficiently large values of z, the beam has an angular spread that scales as Δθ ≈ λ/nw 0 . In turn, for L > λ, equation (1) predicts beams that converge like funnels into a point-like focus at the critical value z c = (nπ/λ)w 0 2 [(L/λ) 2 -1] -1/2 . Anti-diffraction at λ = 633 nm was observed with the set-up presented in Fig. 1a. To achieve values of L/λ > 1 we applied a rapid change in temperature to the crystal before launching the propagating light (see description of thermal shocks in the Methods). The L ≪ λ (diffraction) and the L > λ (anti-diffraction) cases are shown in Fig. 1b and c, respectively. In Fig. 1b, a round Gaussian beam is focused to its diffraction-limited spot at the input of the sample and naturally diffracts through the sample when standard cooling is performed, a behaviour compatible with L ≪ λ. In this case the beams obey the HE in its paraxial approximation and spread following the basic Gaussian beam law. If a therm...

Using temperature-resolved dielectric spectroscopy in the range 25-320 K we investigate the macroscopic response, phase symmetry, and order/disorder states in bulk ferroelectric K 1−y Li y Ta 1−x Nb x (KLTN). Four longrange symmetry phases are identified with their relative transitions. Directional analysis of the order/disorder states using Fröhlich entropy indicates global symmetry breaking along the growth axis and an anisotropic dipolar effective thermodynamic behavior, which ranges from disordered to ordered at the same temperature for different directions in the sample. Results indicate that the macroscopic polarization, driven by nanosized polar regions, follows a microscopic perovskite eight-sites lattice model.

We demonstrate an electro-optic response that is linear in the\ud amplitude but independent of the sign of the applied electric field. The\ud symmetry-preserving linear electro-optic effect emerges at low applied\ud electric fields in freezing nanodisordered KNTN above the dielectric peak\ud temperature, deep into the nominal paraelectric phase. Strong temperature\ud dependence allows us to attribute the phenomenon to an anomalously\ud reduced thermal agitation in the reorientational response of the underlying\ud polar-nanoregions

Zirconium doped lithium niobate is a promising candidate as a substrate for nonlinear optical applications, since it does not suffer from the so-called “optical damage.” In order to optimize this aspect, the proper Zr concentration has be used, hence the precise determination of the so-called “threshold concentration,” i.e., the concentration above which the photorefractive effect is markedly reduced, is of great importance. In this work, we prepared by Czochralski growth a series of Zr-doped lithium niobate crystals with various Zr content and studied them using structural high-resolution x-ray diffraction and optical birefringence measurements as a function of the dopant content in the melt. Both the approaches pointed out a marked change in the crystal characteristics for a Zr concentration between 1.5 and 2 mol %, a value which is identified as the threshold concentration

Using temperature-resolved dielectric spectroscopy in the range of 75-320 K we have inspected the solid-like and liquid-like arrangements of nanometric dipoles (polar nanoregions) embedded in sodium-enriched potassium-tantalate-niobate (KNTN), a chemically-substituted complex perovskite crystal hosting inherent substitutional disorder. The study of order versus direction is carried out using Fröhlich entropy measurements and indicates the presence of four long-range symmetry phases, two of which are found to display profoundly anisotropic features. Exotic phases are found for which the dipoles at one fixed temperature manifest a liquid reorientational response along one crystal axis and a solid-like behavior along another axis. The macroscopic anisotropy observed in the sequence of different phases is found to match a microscopic order-disorder sequence typical of nominally pure perovskites. Moreover, experimental demonstration of the onset of a frozen state above transitions is provided.

Measurements of birefringence, second-harmonic phase-matching conditions, and nonlinear coefficient d(31) are performed for a set of Hafnium-doped congruent lithium niobate (Hf:cLN) crystals as functions of dopant concentration. The data highlight that the threshold concentration, above which there is a change in the Hf incorporation mechanism, is slightly above 2mol% and that, up to this value of concentration, the efficiency of nonlinear processes is not affected by the dopant insertion. Combining these results with those already present in literature, Hf:cLN crystals appear to be very promising candidates for the development of photorefractivity-free wavelength converters working at room temperature.

Quantum dot solar cells are based on the concept of harvesting different parts of the solar light spectrum with a single, cheap semiconductor by simply changing the size of the nanoparticles. Of the many compositions explored, germanium is one of the most interesting as it has the major advantage of a large Bohr radius, which allows for the fabrication of larger particles. Moreover, germaniums possess very high optical absorption, and a small band gap give it free parameters to optimize the quantum dot solar cell. In a previous work, the germanium quantum dots were used in a Graẗzel type solar cell containing an electrolyte, which is not desirable for applications. In this work instead, the n-doped germanium quantum dots were combined with a p-doped a-Si layer, making it the first all solid-state solar cell made from nanoparticles from a gas aggregation nanoparticle source. Remarkably, the effect of quantum confinement in both the germanium quantum dot assembled layer and a-Si was observed by peaks in the spectral response experiments. This work forms an important step toward realizing a germanium quantum dot based solar cell and studying quantum dot based solids.

We show how the cross-over effect of dipolar glasses can be used to observe diffraction cancellation in composite ferroelectric samples independently of composition. We are able to selectively frustrate the dielectric anomaly of different compositionally disordered photorefractive ferroelectrics to achieve scale-free optical propagation at one same temperature