Stiff traps using super-oscillating optical beams

When an optical lens is illuminated by a plane wave, the generated focal spot is given by the Abbe diffraction limit. However, arbitrary small spots, surrounded by additional lobes, can be obtained by illuminating the lens with a suitable light pattern. This is a manifestation of super-oscillation (SO), since the far field intensity pattern is band-limited by the ratio of the lens numerical aperture and the wavelength, but nevertheless the light beam at the focal plane can oscillate locally at much higher frequency. Here, we investigate a systematic method to structure the small lobes of SO function, by using Gaussian, Hermite-Gaussian, Laguerre-Gaussian and Airy functions. After experimentally realizing the sub-wavelength focusing of these structured super-oscillating optical beams we showed their capabilities to achieve high localization of nano-meter sized particles and observed unprecedented localization accuracy and trapping stiffness, significantly exceeding those provided by standard diffraction limited beams. Further, we envisage that the method of structuring super-oscillating functions shown here can be used in other fields, e.g. STED microscopy, nonlinear frequency conversion, lithography, plasmonics as well as in the time domain for structuring light pulses for super-transmission and for time-dependent focusing.