Search results for "Bessel function"
showing 10 items of 61 documents
Ultrafast laser-induced micro-explosion: material modification tool
2016
Femtosecond Bessel pulses with a needle-like intensity distribution were focused inside sapphire crystal to create voids and the shock-wave affected volume which is by more than two orders of magnitude larger as compared with that made by the Gaussian pulse.
MUTUAL INDUCTANCE FOR AN EXPLICITLY FINITE NUMBER OF TURNS
2011
Non coaxial mutual inductance calculations, based on a Bessel function formulation, are presented for coils modelled by an explicitly flnite number of circular turns. The mutual inductance of two such turns can be expressed as an integral of a product of three Bessel functions and an exponential factor, and it is shown that the exponential factors can be analytically summed as a simple geometric progression, or other related sums. This allows the mutual inductance of two thin solenoids to be expressed as an integral of a single analytical expression. Sample numerical results are given for some representative cases and the approach to the limit where the turns are considered to be smeared ou…
Indefinite integrals of special functions from inhomogeneous differential equations
2018
A method is presented for deriving integrals of special functions which obey inhomogeneous second-order linear differential equations. Inhomogeneous equations are readily derived for functions sati...
Form defect influence on the shrinkage fit characteristics
1998
Abstract Today, manufacturing products must meet more and more severe specifications. The different parts composing the product often necessitate high dimensional precision, which increases the difficulties for a large series production. Then it it necessary to optimize dimensioning of the different components in an economic context. In the case of small dimensional fits, there is an influence of the micro-geometry (form of defect, roughness) and time of the process on the geometrical characteristics of the assembly. At the time of conception, it is necessary to obtain a good specification that relates the product functionalities with the best cost. The objective study of this is to simulat…
A code to calculate (high order) Bessel functions based on the continued fractions method
1993
Abstract We have developed a fast code to calculate Bessel functions of integer and fractional order based on the continued fractions method. This algorithm is specially useful in the case of Bessel functions of high order because it does not require any recalculation using normalization relations.
Energy flow canalization of evanescent cylindrical-vector beams
2013
We analyzed ultra-confined vector beams with radial and azimuthal polarizations which are critically self-governed inside plasmonic metamaterials. We succeeded in the separation of polarization singularities in the fields at the nanoscale. The examined metamaterials are suitable for long-range transport of subwavelength Bessel beams without discernible blurring. These results open the door to develop integrated devices for applications such as the manipulation of polarization and angular momentum of surface-plasmon excitations.
Highly localized accelerating beams using nano-scale metallic gratings
2015
Spatially accelerating beams are non-diffracting beams whose intensity is localized along curvilinear trajectories, also incomplete circular trajectories, before diffraction broadening governs their propagation. In this paper we report on numerical simulations showing the conversion of a high-numerical-aperture focused beam into a nonparaxial shape-preserving accelerating beam having a beam-width near the diffraction limit. Beam shaping is induced near the focal region by a diffractive optical element that consists of a non-planar subwavelength grating enabling a Bessel signature. This research was funded by the Spanish Ministry of Economy and Competitiveness under the project TEC2011-29120…
Nonparaxial shape-preserving Airy beams with Bessel signature
2014
Spatially accelerating beams that are solutions to Maxwell equations may propagate along incomplete circular trajectories. Taking these truncated Bessel fields to the paraxial limit, some authors have sustained that it has recovered the known Airy beams (AiBs). Based on the angular spectrum representation of optical fields, we demonstrated that the paraxial approximation rigorously leads to off-axis focused beams instead of finite-energy AiBs. The latter will arise under the umbrella of a nonparaxial approach following elliptical trajectories in place of parabolas. The analytical expression of such a shape-preserving wave field under Gaussian apodization is disclosed by using third-order no…
Diffraction-free beams with elliptic Bessel envelope in periodic media
2007
We report on discrete, nondiffracting, paraxial beams with a Bessel spatial envelope in 1D periodic structures of dielectric media. Anisotropy of the envelope profile is demonstrated to behave in the same manner as extraordinary waves in uniaxial crystals.
Generation of accelerating beams using nano-scale metallic circular gratings
2014
Spatially accelerating beams that are solutions to the Maxwell equations may propagate along incomplete circular trajectories, after which diffraction broadening takes over and the beams spread out. In this paper we report on numerical simulations that show the conversion of a high-numerical-aperture focused beam into a nonparaxial shape-preserving accelerating beam having a beam-width near the diffraction limit. Beam shaping is induced by a diffractive optical element that consists of a non-planar sub-wavelength grating enabling a Bessel signature.