A phase space description of the fractional Talbot effect, occurring in a one--dimensional Fresnel diffraction from a periodic grating, is presented. Using the phase space formalism a compact summation formula for the Wigner function at rational multiples of the Talbot distance is derived. The summation formula shows that the fractional Talbot image in the phase space is generated by a finite s...

The Talbot effect, epitomized by periodic revivals of a freely evolving field structure, has been observed with waves diverse physical nature in space and separately time, whereby diffraction underlies the former dispersion latter. To date, combined spatio-temporal effect not realized any wave because are independent phenomena, typically unfolding at incommensurable length scales. Here we repor...

We extend the theory of Talbot revivals for planar or rectangular geometry to the case of cylindrical waveguides. We derive a list of conditions that are necessary to obtain revivals in cylindrical waveguides. A phase space approach based on the Wigner and the Kirkwood-Rihaczek functions provides a pictorial representation of TM modes interference associated with the Talbot effect.

The nonlinear Talbot effect, in which self-images are formed by generated parametric light from the nonlinear optical process, is presented in this paper. The comparison is made between the conventional Talbot effect and the newly observed nonlinear case. The essence of such nonlinear self-images is provided and future work on this effect is also discussed. The conceptional extension achieved h...

We propose a new type of scalar wave-mixing optical solitons, Talbot solitons. The soliton consists of sinusoidal and uniform components that are mutually coherent and jointly trapped in one direction. The intensity structure of the soliton oscillates in the propagation direction as a result of the linear Talbot effect and periodic nonlinear energy exchange between the components. Talbot solito...

A laser based technique for microstructuring titanium and tantalum substrates using the Talbot effect and an array of microlenses is presented. By using this hybrid technique; we are able to generate different patterns and geometries on the top surfaces of the biomaterials. The Talbot effect allows us to rapidly make microstructuring, solving the common problems of using microlenses for multipa...

Common microscope objectives have fields of view (FOVs) of less than a few millimeters because of limits imposed by optical aberrations. To scale up the FOVs, additional lens elements and heroic design efforts are required to compensate for the aberrations, leading to reduced transmissions and higher system costs. Such FOV limitations have thus become amajor bottleneck in microscopy for large-s...

We report the first observation of discrete Talbot revivals in one-dimensional waveguide arrays. Unlike continuous systems where the Talbot self-imaging effect always occurs irrespective of the pattern period, in discrete configurations this process is only possible for a specific set of periodicities. Recurrence of different input periodic patterns is observed in good agreement with theory.