Related papers: Half-integer order Bessel beams
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…
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…
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,…
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…
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…
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…
We solve the Cauchy problem for the $n$-dimensional wave equation using elementary properties of the Bessel functions.
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.…
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…
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…
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…
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…
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…
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…
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…
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…