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The numerical analysis of the diffraction features rendered by transmission electron microscopy (TEM) typically relies either on classical approximations (Monte Carlo simulations) or quantum paraxial tomography (the multislice method and…
Recent interest in structure solution and refinement using electron diffraction (ED) has been fuelled by its inherent advantages when applied to crystals of sub-micron size, as well as a better sensitivity to light elements. Currently, data…
We discuss in detail the Bloch waves method for calculation of energy and orientation dependent scattering cross-section for inelastic scattering of electrons on crystals. Convergence properties are investigated and a new algorithm with…
Further development of the method of quantum hydrodynamics in application for Bose-Einstein condensates (BECs) is presented. To consider evolution of polarization direction along with particles movement we have developed corresponding set…
A photonic realization of Bloch oscillations (BOs) of two correlated electrons that move on a one-dimensional periodic lattice, based on spatial light transport in a square waveguide array with a defect line, is theoretically proposed. The…
We apply a Bloch-bands approach to the analysis of pulsed optical standing wave diffractive elements in optics and interferometry with ultracold atoms. We verify our method by comparison to a series of experiments with Bose-Einstein…
We investigate the eigenstructure of matrix formulations used for modeling scattering processes within materials in transmission electron microscopy. Dynamical scattering is crucial for describing the interaction between an electron wave…
Bloch oscillations, the oscillatory motion of a quantum particle in a periodic potential, are one of the most fascinating effects of coherent quantum transport. Originally studied in the context of electrons in crystals, Bloch oscillations…
Coherent electrons such as those in electron microscopes, exhibit wave phenomena and may be described by the paraxial wave equation. In analogy to light-waves, governed by the same equation, these electrons share many of the fundamental…
We investigate the electromagnetic propagation in two-dimensional photonic crystals, formed by parallel dielectric cylinders embedded a uniform medium. The frequency band structure is computed using the standard plane-wave expansion method,…
Nanobeam electron diffraction can probe local structural properties of complex crystalline materials including phase, orientation, tilt, strain, and polarization. Ideally, each diffraction pattern from a projected area of a few unit cells…
Bloch wavefunctions are used to derive dispersion relations for water wave propagation in the presence of an infinite array of periodically arranged surface scatterers. For one dimensional periodicity (stripes), band gaps for wavevectors in…
In this work we report on a detailed analysis of the propagation of high energy electron beams having different shapes in a model system, namely [100] oriented zincblende GaN crystal. The analyses are based on the comparison between a…
The multiple scattering formalism is proposed describing the guided modes in the optical waveguide array within the framework of macroscopic electrodynamics. It is shown that, under sufficiently general assumptions, our approach justifies…
The general method to obtain solutions of the Maxwellian equations from scalar representatives is developed and applied to the diffraction of electromagnetic waves. Kirchhoff's integral is modified to provide explicit expressions for these…
An electron beam traversing a structured plasmonic field is shown to undergo diffraction with characteristic angular patterns of both elastic and inelastic outgoing electron components. In particular, a plasmonic {\it grating} (e.g., a…
The effects of thermal diffuse scattering on the transmission and eventual diffraction of highly accelerated electrons are investigated with a method that incorporates the frozen phonon approximation to the exact numerical solution of the…
By introducing concepts of beam shaping into quantum mechanics, we show how interference effects of the quantum wavefunction describing multiple electrons can exactly balance the repulsion among the electrons. With proper shaping of the…
We ask the question 'what happens to Bloch waves in gratings synthetically moving at near the speed of light?'. First we define a constant refractive index (CRI) model in which Bloch waves remain well defined as they break the light…
We present a flexible method that can calculate Bloch modes, complex band structures, and impedances of two-dimensional photonic crystals from scattering data produced by widely available numerical tools. The method generalizes previous…