Related papers: Analytical Solutions for Beams Passing Apertures w…
We present a simple method for calculation of diffraction effects in a beam passing an aperture. It follows the well-known approach of Miyamoto and Wolf, but is simpler and does not lead to singularities. It is thus shown that in the…
When an optical beam propagates through a turbulent medium such as the atmosphere or ocean, the beam will become distorted. It is then natural to seek the best or optimal beam that is distorted least, under some metric such as intensity or…
Paraxial diffraction of monochromatic Gaussian beams by arbitrarily shaped polygonal apertures is analytically explored within the boundary diffraction wave theory framework. Exact closed-form expressions of the diffracted wavefield are…
A semi-analytical computational algorithm to model the wavefield generated by paraxial diffraction of a class of Laguerre-Gauss beams by sharp-edge elliptic apertures is here developed. Thanks to such a powerful computational tool, some…
In this paper, we have developed an analytic method for describing Airy-Type beams truncated by finite apertures. This new approach is based on suitable superposition of exponentially decaying Airy beams. Regarding both theoretical and…
General properties of linear propagation of discretized light in homogeneous and curved waveguide arrays are comprehensively investigated and compared to those of paraxial diffraction in continuous media. In particular, general laws…
A new $z$-stretching finite difference method is established for simulating the paraxial light beam propagation through a lens in a cylindrically symmetric domain. By introducing proper domain transformations, we solve corresponding…
Beam propagation beyond the paraxial approximation is studied in an optically written waveguide structure. The waveguide structure that leads to diffractionless light propagation, is imprinted on a medium consisting of a five-level atomic…
A purely analytical extension of the flattened Gaussian beams [Opt. Commun. \textbf{107,} 335 (1994)] to any values of the beam order, is here proposed. Due to it, the paraxial propagation problem of axially symmetric, coherent flat-top…
We present an algorithm to estimate fast and accurate depth maps from light fields via a sparse set of depth edges and gradients. Our proposed approach is based around the idea that true depth edges are more sensitive than texture edges to…
In this work, the paraxial approximation of the free Dirac equation is examined. The results are first obtained by constructing superpositions of exact solutions with suitable profiles, which are borrowed from paraxial optics. In this…
In practice, Airy beams can only be reproduced in an approximate manner, with a limited spatial extension and hence a finite energy content. To this end, different procedures have been reported in the literature, based on a convenient…
The problem of a beam of quantum particles falling through a diffractive screen is studied. The solutions for single and double slits are obtained explicitly when the potential is approximated by a linear function. It is found that the…
Due to their flexibility, frames of Hilbert spaces are attractive alternatives to bases in approximation schemes for problems where identifying a basis is not straightforward or even feasible. Computing a best approximation using frames,…
We construct pulse-type approximate solutions to nonlinear hyperbolic equations near diffractive points, allowing arbitrary (even infinite) order of grazing. We show that in low regularity spaces and the high frequency limit, such solutions…
We consider the modeling of light beams propagating in highly forward-peaked turbulent media by fractional Fokker-Planck equations and their approximations by fractional Fermi pencil-beam models. We obtain an error estimate in a…
The advantages of convergent beam electron diffraction for symmetry determination at the scale of a few nm are well known. In practice, the approach is often limited due to the restriction on the angular range of the electron beam imposed…
A hidden symmetry of the nonlinear wave equation is exploited to analyse the propagation of paraxial and uniform atom-laser beams in time-independent, quadratic and cylindrical potentials varying smoothly along the propagation axis. The…
We present a class of diffraction-free partially coherent beams each member of which is comprised of a finite power, non-accelerating Airy bump residing on a statistically homogeneous, Gaussian-correlated background. We examine free-space…
Quantitative phase imaging has become a topic of considerable interest in the microscopy community. We have recently described one such technique based on the use of a partitioned detection aperture, which can be operated in a single shot…