Related papers: Generation of Talbot-like fields
The scattering of scalar waves by a set of scatterers is considered. It is proven that the scattered field can be represented as an integral supported by any smooth surface enclosing the scatterers. This is a generalization of the series…
Image composition involves inserting a foreground object into the background while synthesizing environment-consistent effects such as shadows and reflections. Although shadow generation has been extensively studied, reflection generation…
There is significant interest in tailoring wave packets that transversely accelerate during propagation. The first realisation was in the optical domain, the Airy beam. Valid in the paraxial approximation, such beams were shown to…
Decades of work on beam deformation on reflection, and especially on lateral shifts, have spread the idea that a reflected beam is larger than the incident beam. However, when the right conditions are met, a beam reflected by a multilayered…
Optical vector beam generation based on the superposition technique [Phys. Rev. Lett. 107(5), 053601 (2011)] has attracted significant interest in both fundamental and applied optics due to its simplicity and cost-effectiveness. In this…
Gaussian beams are asymptotically valid high frequency solutions concentrated on a single curve through the physical domain, and superposition of Gaussian beams provides a powerful tool to generate more general high frequency solutions to…
The propagation dynamics of two-dimensional (2D) ring-Airy beams is studied in the framework of the fractional Schr\"{o}dinger equation, which includes saturable or cubic self-focusing or defocusing nonlinearity and L\'{e}vy index ((LI)…
We consider four different models of nonlinear diffusion equations involving fractional Laplacians and study the existence and properties of classes of self-similar solutions. Such solutions are an important tool in developing the general…
We discuss the propagation of harmonic and transient waves for systems governed by a wave equation with memory whose integral kernel involves ratios of modified Bessel functions of the first kind in the Laplace domain. In particular, the…
Broadband laser sources based on supercontinuum generation by femtosecond laser filamentation have enabled applications from stand-off sensing and spectroscopy to the generation and self-compression of high-energy few-cycle pulses.…
Infinite-range spin-glass models with Levy-distributed interactions show a freezing transition similar to disordered spin systems on finite connectivity random graphs. It is shown that despite diverging moments of the local field…
In this paper, we experimentally demonstrate reversible wavefront shaping through mimicking gravitational field. A gradient-index micro-structured optical waveguide with special refractive index profile was constructed whose effective index…
We derive analytical expressions for external fields of a charged relativistic bunch with a circular cross section. At distances far from the bunch, the field reduces to the relativistic modified Coulomb form and in the near region,…
Light fields with extraordinary propagation behaviours such as nondiffracting and self-bending are useful in optical delivery for energy, information, and even objects. A kind of helical beams is constructed here based on the caustic…
We show a probabilistic functional limit result for one-dimensional diffusion processes that are reflected at an elastic boundary which is a function of the reflection local time. Such processes are constructed as limits of a sequence of…
Motivated by the notion of isotropic $\alpha$-stable L\'evy processes confined, by reflections, to a bounded open Lipschitz set $D\subset \mathbb{R}^d$, we study some related analytical objects. Thus, we construct the corresponding…
We construct self-adjoint Laplacians and symmetric Markov semigroups on hyperbolic attractors, endowed with Gibbs $u$-measures. If the measure has full support, we can also conclude the existence of an associated symmetric diffusion…
By applying the properties of Fabry-Perot resonance and Rayleigh anomaly, we have shown that a photonic crystal slab can scatter the light from an incident plane wave into a diffracted light with a very large reflection or transmission…
For vectors in $\mathbb{E}_3$ we introduce an associative, commutative and distributive multiplication. We describe the related algebraic and geometrical properties, and hint some applications. Based on properties of hyperbolic (Clifford)…
The displacement of star images by atmospheric refraction observed by an Earth-bound telescope is dominated by a familiar term proportional to the product of the tangent of the zenith angle by the refractivity at the ground. The manuscript…