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A freely propagating optical field having a periodic transverse spatial profile undergoes periodic axial revivals - a well-known phenomenon known as the Talbot effect or self-imaging. We show here that introducing tight spatio-temporal spectral correlations into an ultrafast pulsed optical field with a periodic transverse spatial profile eliminates all axial dynamics in physical space while revealing a novel space-time Talbot effect that can be observed only when carrying out time-resolved measurements. Indeed, time-diffraction is observed whereupon the temporal profile of the field envelope at a fixed axial plane corresponds to a segment of the spatial propagation profile of a monochromatic field sharing the initial spatial profile and observed at the same axial plane. Time-averaging, which is intrinsic to observing the intensity, altogether veils this effect.
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By modulating transmission function of a weak probe field via a strong control standing wave, an electromagnetically induced grating can be created in the probe channel. Such a nonmaterial grating may lead to self-imaging of ultra-cold atoms or molecules in the Fresnel near-field regime. This work may offer a nondestructive and lensless way to image ultra-cold atoms or molecules.
We demonstrate the fractional Talbot effect of nonpraxial accelerating beams, theoretically and numerically. It is based on the interference of nonparaxial accelerating solutions of the Helmholtz equation in two dimensions. The effect originates from the interfering lobes of a superposition of the solutions that accelerate along concentric semicircular trajectories with different radii. Talbot images form along certain central angles, which are referred to as the Talbot angles. The fractional nonparaxial Talbot effect is obtained by choosing the coefficients of beam components properly. A single nonparaxial accelerating beam possesses duality --- it can be viewed as a Talbot effect of itself with an infinite or zero Talbot angle. These results improve the understanding of nonparaxial accelerating beams and the Talbot effect among them.
We report a simple, novel sub-diffraction method, i.e. diffraction interference induced super-focusing in second-harmonic (SH) Talbot effect, to achieve focusing size of less than {lambda}_pump/8 without involving evanescent waves or sub-wavelength apertures. By tailoring point spread functions with Fresnel diffraction interference, we observe periodic SH sub-diffracted spots over a hundred of micrometers away from the sample. Our demonstration is the first experimental realization of the proposal by Toraldo Di Francia pioneered 60 years ago for super-resolution imaging.
We introduce an idea of producing an optical lattice relied on the Talbot effect. Our alternative scheme is based on the interference of light behind a diffraction grating in the near-field regime. We demonstrate 1-D and 2-D optical lattices with the simulations and experiments. This Talbot optical lattice can be broadly used from quantum simulations to quantum information. The Talbot effect is usually used in lensless optical systems, therefore it provides small aberrations.
In this study, we report on the fractional Talbot effect of nonparaxial self-accelerating beams in a multilevel electromagnetically induced transparency (EIT) atomic configuration, which, to the best of our knowledge, is the first study on this subject. The Talbot effect originates from superposed eigenmodes of the Helmholtz equation and forms in the EIT window in the presence of both linear and cubic susceptibilities. The Talbot effect can be realized by appropriately selecting the coefficients of the beam components. Our results indicate that the larger the radial ifference between beam components, the stronger the interference between them, the smaller the Talbot angle is. The results of this study can be useful when studying optical imaging, optical measurements, and optical computing.
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