We theoretically investigate the use of Bessel light beams generated using axicons for creating optical dipole traps for cold atoms and atomic waveguiding. Zeroth-order Bessel beams can be used to produce highly elongated dipole traps allowing for the study of one-dimensional trapped gases and realization of a Tonks gas of impentrable bosons. First-order Bessel beams are shown to be able to pro...

Abstract. The series expansion of a power of the modified Bessel function of the first kind is studied. This expansion involves a family of polynomials introduced by C. Bender et al. New results on these polynomials established here include recurrences in terms of Bell polynomials evaluated at values of the Bessel zeta function. A probabilistic version of an identity of Euler yields additional ...

X iv :0 90 5. 40 67 v1 [ m at h. FA ] 2 5 M ay 2 00 9 BESSEL TYPE INEQUALITIES IN HILBERT C-MODULES S. S. DRAGOMIR, M. KHOSRAVI AND M. S. MOSLEHIAN Abstract. Regarding the generalizations of the Bessel inequality in Hilbert spaces which are due to Bombiari and Boas–Bellman, we obtain a version of the Bessel inequality and some generalizations of this inequality in the framework of Hilbert C∗-mo...

Infinite integrals involving Bessel functions are recast, by means of an Abel transform, in terms of Fourier integrals. As there are many efficient numerical methods for computing Fourier integrals, this leads to a convenient way of approximating Bessel function integrals.

The general properties of two-dimensional generalized Bessel functions are discussed. Various asymptotic approximations are derived and applied to analyze the basic structure of the two-dimensional Bessel functions as well as their nodal lines.

We study the existence of weak solutions to (E) (−∆)u+g(u) = ν in a bounded regular domain Ω in R (N ≥ 2) which vanish in R \Ω, where (−∆) denotes the fractional Laplacian with α ∈ (0, 1), ν is a Radon measure and g is a nondecreasing function satisfying some extra hypotheses. When g satisfies a subcritical integrability condition, we prove the existence and uniqueness of a weak solution for pr...

A vector-wave analysis of nondiffracting beams propagating along a birefringent chiral crystal for the case of tensor character of both the optical activity and linear birefringence is presented. We have written characteristic equations and found propagation constants and amplitude parameters of the eigenmodes. The characteristic curves have anomalous zones described by an isotropic point or a ...

Bessel beams are of great interest due to their unique non-diffractive properties. Using a conical prism or an objective paired with an annular aperture are two typical approaches to generating zeroth order Bessel beams. However, the former approach has a limited numerical aperture (NA), and the latter suffers from low efficiency since most of the incident light is blocked by the aperture. Furt...