Bessel beams have been extensive studied to date but are always created over a finite region inside the laboratory. Means to overcome this consider multi-element refractive designs to create beams that have a longitudinal dependent cone angle, thereby allowing for a far greater quasi non-diffracting propagation region. Here we outline a generalized approach for the creation of shape-invariant B...

Fourier multiplexed FLIM (FmFLIM) tomography enables multiplexed 3D lifetime imaging of whole embryos. In our previous FmFLIM system, the spatial resolution was limited to 25 μm because of the trade-off between the spatial resolution and the imaging depth. In order to achieve cellular resolution imaging of thick specimens, we built a tomography system with dual-color Bessel beam. In combination...

A beam that resembles a Bessel beam on two scales is generated using a tunable acoustic gradient index of refraction (TAG) lens. The minor scale of the TAG-generated Bessel beam is nondiffracting and self-healing. The major scale of the beam diffracts while still forming a Bessel pattern due to the specific geometry of the TAG lens. The acoustic and optical theory behind the TAG lens is outline...

We consider the exact path sampling of the squared Bessel process and some other continuous-time Markov processes, such as the CIR model, constant elasticity of variance diffusion model, and hypergeometric diffusions, which can all be obtained from a squared Bessel process by using a change of variable, time and scale transformation, and/or change of measure. All these diffusions are broadly us...

n this article, we prove An Lp-Lq-version of Morgan’s theorem for the generalized Bessel transform.

The Sheffer polynomials and the monomiality principle, along with the underlying operational formalism, offer a powerful tool for investigation of the properties of a wide class of polynomials. We present, within such a context, a self-contained theory of such familiar systems of polynomials as the Euler, Bernoulli, Bessel and other clasical polynomials and show how the derivation of some of th...

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 ...