The scintillation index is formulated for modified Bessel-Gaussian beams propagating in weakly turbulent media. Numerical calculations applied directly to the derived triple integral show that, for off-axis positions, the modified Bessel-Gaussian beams of higher than zero order scintillate less than Gaussian beams at large input beam sizes and low beam orders with the increasing width parameter...

Abstra t: In the early 1950's, Emil Grosswald began investigating the irredu ibility of the Bessel polynomials yn(x) and onje tured the irredu ibility of yn(x) over the rationals for all positive integers n. This paper resolves the onje ture by establishing the irredu ibility of a lass of polynomials that in ludes the Bessel polynomials.

We find the high energy asymptotics for the singular Weyl–Titchmarsh m-functions and the associated spectral measures of perturbed spherical Schrödinger operators (also known as Bessel operators). We apply this result to establish an improved local Borg–Marchenko theorem for Bessel operators as well as uniqueness theorems for the radial quantum scattering problem with nontrivial angular momentum.

We investigate the ultraslow motion of polychromatic Bessel beams in unbounded, nondispersive media. Control over the group velocity is exercised by means of the angular dispersion of pulsed Bessel beams of invariant transverse spatial frequency, which spontaneously emerge from near-field generators. Temporal dynamics in transients and resonances over homogeneous delay lines (dielectric slabs) ...

Some estimates are proved for the generalized Fourier-Bessel transform in the space (L^2) (alpha,n)-index certain classes of functions characterized by the generalized continuity modulus.

Bessel functions of matrix argument appeared as a subject of studies in the work of Herz [6]. One can find in the multivariate statistics literature some applications of these functions (see [11]). The main tool of Herz’s work was the Laplace transform and its inverse in the space of real symmetric matrices. He obtained several properties but a “good” differential system was lacking. This was t...

Abstract Discrete analogues of the index transforms, involving Bessel and modified functions, are introduced investigated. The corresponding inversion theorems for suitable classes functions sequences established.

Nondiffracting Bessel beams have been recently applied to single shot ultrafast laser processing of high aspect ratio nanochannels. We review the principles and benefits of nondiffracting Bessel beams for material processing, and we compare experimental results with numerical simulations. We show how the stationarity of nonlinear propagation of ultrafast laser pulses allows high aspect ratio ma...

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, the wave appearing to rotate in circles. The concepts of polarization and angular momentum for Bessel beams is also reanalyzed.

We model the propagation of Gaussian and Bessel beams from ground through 22kmaltitude of atmospheric turbulence. We observe the Bessel beam has better performance based onRMS intensity error and the captured beam power.OCIS codes: (010.1300) Atmospheric propagation; (000.1330) Atmospheric turbulence.