Talbot effect in waveforms containing subwavelength multilobe superoscillations.

The self-imaging of periodic light patterns, also known as the Talbot effect, is usually limited to periods that are larger than the wavelength. Here we present, theoretically and experimentally, a method to overcome this limitation by using superoscillating light patterns. The input intensity distribution is a periodic band-limited function with relatively large periods, but it contains regions of multilobe periodic oscillations with periods that are smaller than half of the wavelength. We observe the revival of the input pattern, including the subwavelength superoscillating regions, at large distances of more than 40 times the optical wavelength. Moreover, at fractional Talbot distances, we observe even faster local oscillations, with periods of approximately one-third of the optical wavelength.

Multi-lobe superoscillation and its application to structured illumination microscopy.

Superoscillating function is a band-limited function that is locally oscillating faster than its highest Fourier component. In this work, we study and implement methods to generate multi-lobe optical superoscillating beams, with nearly constant intensity and constant local frequency. We generated superoscillating patterns having up to 12 sub-wavelength oscillations, with local frequency of 20% to 40% above the band-limit. We then test the potential application of these beams to super-resolution structured illumination microscopy. By utilizing the Moiré effect on a fluorescent grating, we have demonstrated experimentally resolution improvement over the conventional sinusoidal illumination. Our simulations show that structured illumination microscopy with super oscillating multi-lobe beams can provide more than twofold improvement in resolution, with respect to the classical diffraction limit and for coherent or incoherent modalities.

Observing the Quantum Wave Nature of Free Electrons through Spontaneous Emission.

We investigate, both experimentally and theoretically, the interpretation of the free-electron wave function using spontaneous emission. We use a transversely wide single-electron wave function to describe the spatial extent of transverse coherence of an electron beam in a standard transmission electron microscope. When the electron beam passes next to a metallic grating, spontaneous Smith-Purcell radiation is emitted. We then examine the effect of the electron wave function transversal size on the emitted radiation. Two interpretations widely used in the literature are considered: (1) radiation by a continuous current density attributed to the quantum probability current, equivalent to the spreading of the electron charge continuously over space; and (2) interpreting the square modulus of the wave function as a probability distribution of finding a point particle at a certain location, wherein the electron charge is always localized in space. We discuss how these two interpretations give contradictory predictions for the radiation pattern in our experiment, comparing the emission from narrow and wide wave functions with respect to the emitted radiation's wavelength. Matching our experiment with a new quantum-electrodynamics derivation, we conclude that the measurements can be explained by the probability distribution approach wherein the electron interacts with the grating as a classical point charge. Our findings clarify the transition between the classical and quantum regimes and shed light on the mechanisms that take part in general light-matter interactions.