The Talbot effect [1], in which a wave imprinted with transverse periodicity reconstructs itself at regular intervals, is a diffraction phenomenon that occurs in many physical systems. Here we present the first observation of the Talbot effect for electron de Broglie waves behind a nanofabricated transmission grating. This was thought to be difficult because of Coulomb interactions between elec...

Talbot’s self-imaging effect occurrs in near-field diffraction. In the rational paraxial approximation, the Talbot images are formed at distances z = p/q, where p and q are coprimes, and are superpositions of q equally spaced images of the original binary transmission (Ronchi) grating. This interpretation offers the possibility to express the Talbot effect through Gauss sums. Here, we pay atten...

We describe a reciprocal-lattice vector method for analysis of the diffractive self-imaging (or Talbot effect) of a two-dimensional periodic object. Using this method we analyze the fractional Talbot effect of a hexagonal array and deduce a simple analytical expression for calculation of the complex amplitude distribution at any fractional Talbot plane. Based on this new formula, we design a he...

The plasmon analog of the self-imaging Talbot effect is described and theoretically analyzed. Rich plasmon carpets containing hot spots are shown to be produced by a row of periodically-spaced surface features. A row of holes drilled in a metal film and illuminated from the back side is discussed as a realizable implementation of this concept. Self-images of the row are produced, separated from...

We demonstrate a new method to generate second-harmonic Talbot effect through degenerate Cherenkov radiation in one-dimension anomalous-dispersion-like nonlinear photonic crystals. In anomalous-dispersion-like medium, the degenerated nonlinear Cherenkov radiation can be achieved and is parallel to domain walls, of which the intensity is adjusted by the second-order nonlinear coefficient. In thi...

A monochromatic beam of wavelength λ transmitted through a periodic one-dimensional diffraction grating with lattice constant d will be spatially refocused at distances from the grating that are integer multiples of . This self-refocusing phenomena, commonly referred to as the Talbot effect, has been experimentally demonstrated in a variety of systems ranging from optical to matter waves. Theor...

We theoretically study discrete Talbot self-imaging in hexagonal, square, and irregular two-dimensional waveguide arrays. Different from its counterpart in a continuous system, the periods of the input fields must belong to {1, 2, 3, 4, 6} for Talbot self-imaging. Also, the combinations of the input periods cannot be 3 & 4, or 4 & 6 along two different directions, which distinguishes itself fro...

In this paper we show that using optical photolithography it’s possible to obtain submicron features for periodic structures using the Talbot effect. To use the Talbot effect without the need of an absolute distance measurement between the mask and the wafer we integrate over several exposures for varying wafer mask distances. Here we discuss the salient features of ‘integrated Talbot lithograp...

We present a detailed experimental and theoretical study of plasmon Talbot effect. A theoretical model based on simple scattering theory is developed to describe the Talbot self-imaging pattern generated by a linear arrangement of cylindrical nanostructures forming a periodic array. We first show the experimental observation of plasmon Talbot carpets created by propagating surface plasmon polar...