Related papers: Exact paraxial diffraction theory for polygonal ap…

We describe a generalized formalism, addressing the fundamental problem of reflection and transmission of complex optical waves at a plane dielectric interface. Our formalism involves the application of generalized operator matrices to the…

We show that, contrary to popular belief, non only diffraction-free beams may reconstruct themselves after hitting an opaque obstacle but also, for example, Gaussian beams. We unravel the mathematics and the physics underlying the…

All optical systems, which involve the collimation of a reflected, transmitted or scattered wave subsequent to tight focusing, are subject to two kinds of deviations. One is the wavefront curvature due to inaccurate focal placement of the…

We explore the morphological properties of symmetric Airy beams in the paraxial and nonparaxial regimes. We consider a 2D electromagnetic realization with a single transverse component of the electric field, and in the nonparaxial regime,…

The array of micro-prisms was described by model of multi-period blazed gratings consisting of triangular apertures. The origins of hexagram-shaped diffraction patterns were interpreted based on multiple-beam interference and diffraction…

The paraxial approximation of a classical spinning photon is shown to yield an "exotic particle" in the plane transverse to the propagation. The previously proposed and observed position shift between media with different refractive indices…

The optical aberrations of a system can be described in terms of the wave aberrations, defined as the departure from the ideal spherical wavefront; or the ray aberrations, which are in turn the deviations from the paraxial ray intersection…

Diffraction-free optical beams propagate freely without change in shape and scale. Monochromatic beams that avoid diffractive spreading require two-dimensional transverse profiles, and there are no corresponding solutions for profiles…

In this paper we will analyze the propagation of the angular spectrum of the electromagnetic field through a finite length uniaxial crystal. We solve the boundary conditions of the fields at an interface of an isotropic medium and an…

A general family of structured Gaussian beams naturally emerges from a consideration of families of rays. These ray families, with the property that their transverse profile is invariant upon propagation (except for cycling of the rays and…

We develop a formalism for the calculation of the macroscopic dielectric response of composite systems made of particles of one material embedded periodically within a matrix of another material, each of which is characterized by a well…

Spectral and factorization properties of oscillatory matrices leads to a spectral Favard theorem for bounded banded matrices, that admit a positive bidiagonal factorization, in terms of sequences of mixed multiple orthogonal polynomials…

Reformulation of conventional beam definitions into their bidirectional versions and use of Hertz potentials make beam fields exact vector solutions to Maxwell's equations. This procedure is applied to higher-order elegant Laguerre-Gaussian…

Unique intensity features arising from dynamical diffraction arise in coherent x-ray nanobeam diffraction patterns of crystals having thicknesses larger than the x-ray extinction depth or exhibiting combinations of nanoscale and mesoscale…

Self-similar solutions of the coherent diffusion equation are derived and measured. The set of real similarity solutions is generalized by the introduction of a nonuniform phase surface, based on the elegant Gaussian modes of optical…

Limited-diffraction beams are a class of waves that may be localized in space and time. Theoretically, these beams are propagation invariant and can propagate to an infinite distance without spreading. In practice, when these beams are…

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…

Scalar theory of quantum electron beam optics, at the single-particle level, derived from the Dirac equation using a Foldy-Wouthuysen-like transformation technique is considered. Round magnetic electron lenses with Glaser and power law…

A novel type of discrete basis for paraxial beams is proposed, consisting of monomial vortices times polynomials of Gaussians in the radial variable. These bases have the distinctive property that the effective size of their elements is…

We present an analysis of self-imaging in a regime beyond the paraxial, where deviation from simple paraxial propagation causes apparent self-imaging aberrations. The resulting structures are examples of aberration without rays and are…