We present direct measurements of the spatiotemporal electric field of an ultrashort Bessel-X pulse generated using a conical lens (axicon). These measurements were made using the linear-optical interferometric technique SEA TADPOLE, which has micrometer spatial resolution and femtosecond temporal resolution. From our measurements, both the superluminal velocity of the Bessel pulse and the prop...

We experimentally demonstrate a class of tractor beams created by coherently superposing coaxial Bessel beams. These optical conveyors have periodic intensity variations along their axes that act as highly effective optical traps for micrometer-scale objects. Trapped objects can be moved selectively upstream or downstream along the conveyor by appropriately changing the Bessel beams' relative p...

We utilize a plasmonic vortex lens (PVL) to retrieve the orbital angular momentum (OAM) distribution of light. The OAM modes are coupled to the surface plasmon polaritons (SPPs) in the form of various Bessel functions respectively. By decomposing the interference pattern of SPPs into these Bessel functions, we can retrieve the relative amplitude and the relative phase of input OAM modes simulta...

We provide information and explicit formulae for a class of integrals involving Bessel functions and Gegenbauer polynomials. We present a simple proof of an old formula of Gegenbauer. Some interesting special cases and applications of this result are obtained. In particular, we give a short proof of a recent result of A. A. R. Neves et al. regarding the analytical evaluation of an integral of a...

The authors apply a certain novel technique based on the combined use of operational methods and of some special multivariable and multiindex polynomials to derive several families of generating functions involving the products of Bessel and related functions. The possibility of extending this technique to the derivation of generating functions of hybrid nature (involving, for example, the prod...

We provide information and explicit formulae for a class of integrals involving Bessel functions and Gegenbauer polynomials. We present a simple proof of an old formula of Gegenbauer. Some interesting special cases and applications of this result are obtained. In particular, we give a short proof of a recent result of A. A. R. Neves et al. regarding the analytical evaluation of an integral of a...

An increasing attention has been concentrated on nondiffracting Bessel beams, due to their novel properties and prospective applications. In order to study their properties entirely, including the transverse modes, the polarization states and the flow of energy, vector analyses are necessary. In this paper, based on auxiliary functions of Hertzian vector potential, nondiffracting Bessel beams a...

For a delta operator aD − bD we find the corresponding polynomial sequence of binomial type and relations with Fuss numbers. In the case of D − 1 2D 2 we show that the corresponding Bessel–Carlitz polynomials are moments of the convolution semigroup of inverse Gaussian distributions. We also find probability distributions νt, t > 0, for which {yn(t)}, the Bessel polynomials at t, is the moment ...

A common environment in which to place Bessel and circular functions is envisaged. We show, by the use of operational methods, that the Gaussian provides the umbral image of these functions. We emphasize the role of the spherical Bessel functions and a family of associated auxiliary polynomials, as transition elements between these families of functions. The consequences of this point of view a...

In this work, we extend the analytic treatment of Bessel functions of large order and/or argument. We examine uniform asymptotic Bessel function expansions and show their accuracy and range of validity. Such situations arise in a variety of applications, in particular the Fourier transform of the gravitational wave signal from a pulsar. The uniform expansion we consider here is found to be vali...