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.

Fractional Bessel processes are defined and considering the processes associated with fractional Bessel processes 1 2 1 ), ( )) ( ( ) ( 0 < < = ∫ H t dB s B sign t X H t H H ) ( ) ( ) ( 1 0 s dB s R B t Y j H d

The transformation from a time-dependent random walk to quantum mechanics converts a modi­ fied Bessel function into an ordinary one together with a phase factor e,ir/2 for each time the electron flips both direction and handedness. Causality requires the argument to be greater than the order of the Bessel function. Assuming equal probabilities for jumps ± 1 , the normalized modified Bessel fun...

In this paper, using a generalized translation operator, we prove theestimates for the generalized Fourier-Bessel transform in the space L2 on certainclasses of functions.