Propagating light beams with widths down to and below the optical wavelength require bulky large-aperture lenses and remain focused only for micrometric distances. 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 we observe a non-paraxial propagation of a sub-micrometre-sized beam for over 1,000 diffraction lengths, the narrowest visible beam reported to date. 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. Our findings open the way to high-resolution optics over large depths of focus, and a route to merging bulk optics into nanodevices.
Bibliographical noteFunding Information:
The research leading to these results was supported by funding from the Italian Ministry of Research (MIUR) through the ‘Futuro in Ricerca’ FIRB grant PHOCOS-RBFR08E7VA and from the European Research Council under the European Community Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement no. 201766. Partial funding was received through the SMARTCONFOCAL project of the Regione Lazio and through the PRIN 2012BFNWZ2 and Sapienza 2013PHOTOANDERSON projects. A.J.A. acknowledges support from the Peter Brojde Center for Innovative Engineering.
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