An electron Talbot interferometer

The Talbot effect, 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 electrons and nanostructure gratings, yet we were able to map out the entire near-field interference pattern, the "Talbot carpet", behind a grating. We did this using a Talbot interferometer, in which Talbot interference fringes from one grating are moire'-filtered by a 2nd grating. This arrangement has served for optical, X-ray, and atom interferometry, but never before for electrons. Talbot interferometers are particularly sensitive to distortions of the incident wavefronts, and to illustrate this we used our Talbot interferometer to measure the wavefront curvature of a weakly focused electron beam. Here we report how this wavefront curvature demagnified the Talbot revivals, and we discuss applications for electron Talbot interferometers.Comment: 5 pages, 5 figures, updated version with abstrac

Subwavelength fractional Talbot effect in layered heterostructures of composite metamaterials

We demonstrate that under certain conditions, fractional Talbot revivals can occur in heterostructures of composite metamaterials, such as multilayer positive and negative index media, metallodielectric stacks, and one-dimensional dielectric photonic crystals. Most importantly, without using the paraxial approximation we obtain Talbot images for the feature sizes of transverse patterns smaller than the illumination wavelength. A general expression for the Talbot distance in such structures is derived, and the conditions favorable for observing Talbot effects in layered heterostructures is discussed.Comment: To be published in Phys. Rev.

Talbot effect for dispersion in linear optical fibers and a wavelet approach

We shortly recall the mathematical and physical aspects of Talbot's self-imaging effect occurring 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 attention to the Talbot effect in the case of dispersion in optical fibers presenting our considerations based on the close relationships of the mathematical representations of diffraction and dispersion. Although dispersion deals with continuous functions, such as gaussian and supergaussian pulses, whereas in diffraction one frequently deals with discontinuous functions, the mathematical correspondence enables one to characterize the Talbot effect in the two cases with minor differences. In addition, we apply, for the first time to our knowledge, the wavelet transform to the fractal Talbot effect in both diffraction and fiber dispersion. In the first case, the self similar character of the transverse paraxial field at irrational multiples of the Talbot distance is confirmed, whereas in the second case it is shown that the field is not self similar for supergaussian pulses. Finally, a high-precision measurement of irrational distances employing the fractal index determined with the wavelet transform is pointed outComment: 15 text pages + 7 gif figs, accepted at Int. J. Mod. Phys. B, final version of a contribution at ICSSUR-Besancon (May/05). Color figs available from the first autho

The Same Person

How can we conceptualize curriculum and school knowledge to better address important questions of social change, contingency of knowledge, life in mediated worlds, and inequalities? This question was given to me by Dr. Brent Talbot for my final presentation in Music 149, Social Foundations of Music Education. The purpose of this assignment was to synthesize the knowledge of various philosophies and models of music education covered in this course while utilizing the course material given to us throughout the semester. After Dr. Talbot’s emphasis on creativity and having already written too many papers to count, I decided to write and perform a short play. I drew upon the fact that many considered Dr. Talbot and I to be doppelgängers. In this scene, I play both myself and Dr. Talbot, who is the voice in my head. I often considered what Dr. Talbot would say in regards to my projects for the class, so his voice in my head was all too familiar. This format made the most sense as a summation of my experiences and research in Social Foundations of Music Education

Demonstration of the temporal matter-wave Talbot effect for trapped matter waves

We demonstrate the temporal Talbot effect for trapped matter waves using ultracold atoms in an optical lattice. We investigate the phase evolution of an array of essentially non-interacting matter waves and observe matter-wave collapse and revival in the form of a Talbot interference pattern. By using long expansion times, we image momentum space with sub-recoil resolution, allowing us to observe fractional Talbot fringes up to 10th order.Comment: 17 pages, 7 figure