Search results for "Bessel function"
showing 10 items of 61 documents
Accurate expansion of cylindrical paraxial waves for its straightforward implementation in electromagnetic scattering
2017
Abstract The evaluation of vector wave fields can be accurately performed by means of diffraction integrals, differential equations and also series expansions. In this paper, a Bessel series expansion which basis relies on the exact solution of the Helmholtz equation in cylindrical coordinates is theoretically developed for the straightforward yet accurate description of low-numerical-aperture focal waves. The validity of this approach is confirmed by explicit application to Gaussian beams and apertured focused fields in the paraxial regime. Finally we discuss how our procedure can be favorably implemented in scattering problems.
Nondiffracting Bessel plasmons.
2011
We report on the existence of nondiffracting Bessel surface plasmon polaritons (SPPs), advancing at either superluminal or subluminal phase velocities. These wave fields feature deep subwavelength FWHM, but are supported by high-order homogeneous SPPs of a metal/dielectric (MD) superlattice. The beam axis can be relocated to any MD interface, by interfering multiple converging SPPs with controlled phase matching. Dissipative effects in metals lead to a diffraction-free regime that is limited by the energy attenuation length. However, the ultra-localization of the diffracted wave field might still be maintained by more than one order of magnitude. This research was funded by the Spanish Mini…
Subwavelength beams with polarization singularities in plasmonic metamaterials
2014
We investigated the diffraction behavior of plasmonic Bessel beams propagating in metal-dielectric stratified materials and wire media. Our results reveal various regimes in which polarization singularities are selectively maintained. This polarization-pass effect can be controlled by appropriately setting the filling factor of the metallic inclusions and its internal periodic distribution. These results may have implications in the development of devices at the nanoscale level for manipulation of polarization and angular momentum of cylindrical vector beams. This research was funded by the Spanish Ministry of Economy and Competitiveness under the project TEC2011-29120-C05-01.
Diffraction-free beams in thin films
2009
The propagation and transmission of Bessel beams through nano-layered structures has been discussed recently. Within this framework we recognize the formation of unguided diffraction-free waves with the spot size approaching and occasionally surpassing the limit of a wavelength when a Bessel beam of any order n is launched onto a thin material slab with grazing incidence. On the basis of the plane-wave representation of cylindrical waves, a simple model is introduced providing an exact description of the transverse pattern of this type of diffraction-suppressed localized wave. Potential applications in surface science are put forward for consideration. Ministerio de Ciencia e Innovación (MI…
Unconditionally convergent multipliers and Bessel sequences
2016
Abstract We prove that every unconditionally summable sequence in a Hilbert space can be factorized as the product of a square summable scalar sequence and a Bessel sequence. Some consequences on the representation of unconditionally convergent multipliers are obtained, thus providing positive answers to a conjecture by Balazs and Stoeva in some particular cases.
Quantum extensions of semigroups generated by Bessel processes
1996
We construct a quantum extension of the Markov semigroup of the classical Bessel process of orderv≥1 to the noncommutative von Neumann algebra s(L2(0, +∞)) of bounded operators onL2(0, +∞).
Products of Bessel functions and associated polynomials
2013
The symbolic method is used to get explicit formulae for the products or powers of Bessel functions and for the relevant integrals.
Coordinate space calculation of two- and three-loop sunrise-type diagrams, elliptic functions and truncated Bessel integral identities
2019
We integrate three-loop sunrise-type vacuum diagrams in $D_0=4$ dimensions with four different masses using configuration space techniques. The finite parts of our results are in numerical agreement with corresponding three-loop calculations in momentum space. Using some of the closed form results of the momentum space calculation we arrive at new integral identities involving truncated integrals of products of Bessel functions. For the non-degenerate finite two-loop sunrise-type vacuum diagram in $D_0=2$ dimensions we make use of the known closed form $p$-space result to express the moment of a product of three Bessel functions in terms of a sum of Claussen polylogarithms. Using results fo…
Dimensional interpolation and the Selberg integral
2019
Abstract We show that a version of dimensional interpolation for the Riemann–Roch–Hirzebruch formalism in the case of a grassmannian leads to an expression for the Euler characteristic of line bundles in terms of a Selberg integral. We propose a way to interpolate higher Bessel equations, their wedge powers, and monodromies thereof to non–integer orders, and link the result with the dimensional interpolation of the RRH formalism in the spirit of the gamma conjectures.
Orientational analysis of planar fibre systems observed as a Poisson shot-noise process
2007
Summary We consider two-dimensional fibrous materials observed as a digital greyscale image. The problem addressed is to estimate the orientation distribution of unobservable thin fibres from a greyscale image modelled by a planar Poisson shot-noise process. The classical stereological approach is not straightforward, because the point intensities of thin fibres along sampling lines may not be observable. For such cases, Karkkainen et al. (2001) suggested the use of scaled variograms determined from grey values along sampling lines in several directions. Their method is based on the assumption that the proportion between the scaled variograms and point intensities in all directions of sampl…