We investigate the second-harmonic generation of the nth-order Bessel beam in the nonlinear medium. The analysis is based on the Khokhlov-Zabolotskaya-Kuznetsov wave equation under the second-order approximation in nonlinear acoustics. The theory indicates that for an nth-order Bessel beam, the second-harmonic beam is nearly diffraction-free in the radial direction and behaves as a Bessel beam ...

Non-Gaussian beam profiles such as Bessel or annular beams enable novel approaches to modifying materials through laser-based processing. In this review paper, properties, generation methods and emerging applications for nonconventional beam shapes are discussed, including Bessel, annular, and vortex beams. These intensity profiles have important implications in a number of technologically rele...

We present a method for the realization of radially and azimuthally polarized nonparaxial Bessel beams in a rigorous but simple manner. This result is achieved by using the concept of Hertz vector potential to generate exact vector solutions of Maxwell's equations from scalar Bessel beams. The scalar part of the Hertz potential is built by analogy with the paraxial case as a linear combination ...

Bessel processes play an important role in financial mathematics because of their strong relation to financial processes like geometric Brownian motion or CIR processes. We are interested in the first time Bessel processes and more generally, radial Ornstein–Uhlenbeck processes hit a given barrier. We give explicit expressions of the Laplace transforms of first hitting times by (squared) radial...

We present a simple method using an axicon and spatial light modulator to create multiple parallel Bessel beams and precisely control their individual positions in three dimensions. This technique is tested as an alternative to classical holographic beam shaping commonly used now in optical tweezers. Various applications of precise control of multiple Bessel beams are demonstrated within a sing...

Linear and nonlinear processes of transferring optical singularities from anisotropic crystals onto the wavefront of Bessel light beams (BLBs) are investigated. The generation of high-order vortices at the propagation of BLBs along the optical axes of crystals was studied. Particularly, a nonlinear frequency doubling of Bessel vortices in the conditions of new type synchronism (full conical pha...

Bessel beams are widely used in optical metrology mainly because of their large Rayleigh range (focal length). Radial/azimuthal polarization of such beams is of interest in the fields of material processing, plasma absorption or communication. In this paper an experimental set-up is presented, which generates a Bessel-type vector beam with a spatial polarization, oscillating along the optical a...

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.