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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.

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Figure 1: Scale-free beam propagation at different cooling rates.
Figure 2: Interaction and generation of scale-free beams under rapid cooling.
Figure 3: Training the scale-free behaviour to have polarization selectivity.


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The research leading to these results was supported by funding from the European Research Council under the European Community's Seventh Framework Program (FP7/2007-2013)/ERC grant agreement no. 201766, and from the Italian Ministry of Research (MIUR) through the ‘Futuro in Ricerca’ FIRB grant PHOCOS-RBFR08E7VA. Partial funding was received through the SMARTCONFOCAL project of the Regione Lazio. A.J.A. acknowledges the support of the Peter Brojde Center for Innovative Engineering.

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E.D. and C.C. conceived and developed the experiments and theory. R.A. designed and fabricated the KTN:Li samples and participated in the analysis and interpretation of results. E.S. participated in the experiments and data analysis.

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Correspondence to E. DelRe.

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The authors declare no competing financial interests.

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DelRe, E., Spinozzi, E., Agranat, A. et al. Scale-free optics and diffractionless waves in nanodisordered ferroelectrics. Nature Photon 5, 39–42 (2011).

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