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Related papers: Half-integer order Bessel beams

200 papers

Oblique plane microscopy (OPM) offers 3D optically sectioned imaging with high spatial- and temporal-resolution while enabling conventional sample mounting. The technique uses a concatenation of three microscopes, two for remote focusing…

The transmutation (transformation) operator associated with the perturbed Bessel equation is considered. It is shown that its integral kernel can be uniformly approximated by linear combinations of constructed here generalized wave…

Classical Analysis and ODEs · Mathematics 2018-03-26 Vladislav V. Kravchenko , Sergii M. Torba , Jessica Yu. Santana-Bejarano

In this paper, we develop an ensemble-based time-stepping algorithm to efficiently find numerical solutions to a group of linear, second-order parabolic partial differential equations (PDEs). Particularly, the PDE models in the group could…

Numerical Analysis · Mathematics 2017-10-18 Yan Luo , Zhu Wang

We present a fully relativistic analysis of Bessel beams revealing some noteworthy features that are not explicit in the standard description. It is shown that there is a reference frame in which the field takes a particularly simple form,…

Optics · Physics 2009-11-11 S. Hacyan , R. Jauregui

In this paper, we introduce the Bessel-Struve transform, we establish an inversion theorem of the Weyl integral transform associated with this transform, in the case of half integers, we give a characterization of the range of…

Classical Analysis and ODEs · Mathematics 2010-12-14 Lotfi Kamoun , Selma Negzaoui

A theorem that constructs a path integral solution for general second order partial differential equations is specialized to obtain path integrals that are solutions of elliptic, parabolic, and hyperbolic linear second order partial…

Mathematical Physics · Physics 2012-12-04 J. LaChapelle

The derivation of a function is a fundamental tool for solving problems in calculus. Consequently, the motivations for investigating physical systems capable of performing this task are numerous. Furthermore, the potential to develop an…

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…

Optics · Physics 2024-02-05 Riccardo Borghi

We solve the Cauchy problem for the $n$-dimensional wave equation using elementary properties of the Bessel functions.

Analysis of PDEs · Mathematics 2018-12-24 Alberto Torchinsky

A numerical technique is described that can efficiently compute solutions in interface problems. These are problems with data, such as the coefficients of differential equations, discontinuous or even singular across one or more interfaces.…

Computational Physics · Physics 2015-05-27 Theodoros P. Horikis

Recently, a method for obtaining diffraction-attenuation resistant beams in absorbing media was developed through suitable superposition of ideal zero-order Bessel beams. In this work, we will show that such beams maintain their resistance…

Computation of high frequency solutions to wave equations is important in many applications, and notoriously difficult in resolving wave oscillations. Gaussian beams are asymptotically valid high frequency solutions concentrated on a single…

Analysis of PDEs · Mathematics 2009-05-30 Hailiang Liu , James Ralston

Using acoustic evanescent Bessel beam is analyzed the fundamental properties for the spin and orbital angular momentum. The calculation shows that the transversal spin, the canonical momentum, and the orbital angular momentum are…

Classical Physics · Physics 2021-10-07 Irving Rondon

The problem of light waves interaction with charged particles becomes more and more complex starting with the case of plane waves, where the analytical solution is well known, to more natural, though more complicated situations which…

Plasma Physics · Physics 2024-07-22 Egor Dmitriev , Philipp Korneev

A new set of vector solutions to Maxwell's equations based on solutions to the wave equation in spheroidal coordinates allows laser beams to be described beyond the paraxial approximation. Using these solutions allows us to calculate the…

Optics · Physics 2015-03-13 Martin Zeppenfeld , Pepijn W. H. Pinkse

The edge diffraction of a homogeneously polarized light beam is studied theoretically based on the paraxial optics and Fresnel-Kirchhoff approximation, and the dependence of the diffracted beam pattern of the incident beam polarization is…

Optics · Physics 2017-08-02 Aleksandr Ya. Bekshaev

Computation of high frequency solutions to wave equations is important in many applications, and notoriously difficult in resolving wave oscillations. Gaussian beams are asymptotically valid high frequency solutions concentrated on a single…

Analysis of PDEs · Mathematics 2009-06-17 Hailiang Liu , James Ralston

This paper is devoted to numerical simulation of a charged particle beam submitted to a strong oscillating electric field. For that, we consider a two-scale numerical approach as follows: we first recall the two-scale model which is…

Numerical Analysis · Mathematics 2008-12-22 Alexandre Mouton

We predict that Bessel-like beams of arbitrary integer order can exhibit a tunable self-similar behavior (that take an invariant form under suitable stretching transformations). Specifically, by engineering the amplitude and the phase on…

A wide class of nonuniformly totally polarized beams is introduced that preserve their transverse polarization pattern during paraxial propagation. They are obtained as suitable combinations of Gaussian modes and find applications in…