Scattering of an arbitrary order acoustical Bessel beam by a rigid off-axis spheroid

2018 ◽  
Vol 143 (6) ◽  
pp. 3676-3687 ◽  
Author(s):  
Wei Li ◽  
Mingsheng Wang
Keyword(s):  
Arbitrary Order ◽  
Bessel Beam

Generation of an arbitrary order Bessel beam in FDTD for time domain calculation

2019 ◽  
Author(s):  
Zhefeng Wu ◽  
Jiajie Wang ◽  
Paul Briard ◽  
Yiping Han ◽  
Antao Chen ◽  
...  
Keyword(s):  
Time Domain ◽  
Arbitrary Order ◽  
Bessel Beam

scholarly journals Photonic nanojet generated by a spheroidal particle illuminated by a vector Bessel beam

2021 ◽  
pp. 100106
Author(s):  
Yongjie Jia ◽  
Renxian Li ◽  
Wenze Zhuang ◽  
Jiarui Liang
Keyword(s):  
Bessel Beam ◽  
Spheroidal Particle ◽  
Photonic Nanojet

scholarly journals The determinant of one-dimensional polyharmonic operators of arbitrary order

2020 ◽  
Vol 279 (12) ◽  
pp. 108783
Author(s):  
Pedro Freitas ◽  
Jiří Lipovský
Keyword(s):  
Arbitrary Order ◽  
One Dimensional

scholarly journals Arbitrary-order intrinsic virtual element method for elliptic equations on surfaces

CALCOLO ◽  
2021 ◽  
Vol 58 (3) ◽  
Author(s):  
Elena Bachini ◽  
Gianmarco Manzini ◽  
Mario Putti
Keyword(s):  
Arbitrary Order ◽  
Surface Geometry ◽  
Virtual Element Method ◽  
Anisotropic Character ◽  
Local Reference System ◽  
Local Reference ◽  
Local Parametrization ◽  
Manufactured Solution ◽  
Virtual Element ◽  
Element Method

AbstractWe develop a geometrically intrinsic formulation of the arbitrary-order Virtual Element Method (VEM) on polygonal cells for the numerical solution of elliptic surface partial differential equations (PDEs). The PDE is first written in covariant form using an appropriate local reference system. The knowledge of the local parametrization allows us to consider the two-dimensional VEM scheme, without any explicit approximation of the surface geometry. The theoretical properties of the classical VEM are extended to our framework by taking into consideration the highly anisotropic character of the final discretization. These properties are extensively tested on triangular and polygonal meshes using a manufactured solution. The limitations of the scheme are verified as functions of the regularity of the surface and its approximation.

scholarly journals Polyanalytic boundary value problems for planar domains with harmonic Green function

2021 ◽  
Vol 11 (3) ◽  
Author(s):  
Heinrich Begehr ◽  
Bibinur Shupeyeva
Keyword(s):  
Green Function ◽  
Boundary Value Problems ◽  
Arbitrary Order ◽  
Boundary Value ◽  
Planar Domains ◽  
Schwarz Problem ◽  
Bianalytic Functions ◽  
Neumann Type ◽  
The Neumann Problem ◽  
Well Posed

AbstractThere are three basic boundary value problems for the inhomogeneous polyanalytic equation in planar domains, the well-posed iterated Schwarz problem, and further two over-determined iterated problems of Dirichlet and Neumann type. These problems are investigated in planar domains having a harmonic Green function. For the Schwarz problem, treated earlier [Ü. Aksoy, H. Begehr, A.O. Çelebi, AV Bitsadze’s observation on bianalytic functions and the Schwarz problem. Complex Var Elliptic Equ 64(8): 1257–1274 (2019)], just a modification is mentioned. While the Dirichlet problem is completely discussed for arbitrary order, the Neumann problem is just handled for order up to three. But a generalization to arbitrary order is likely.

scholarly journals “Perfect” Terahertz Vortex Beams Formed Using Diffractive Axicons and Prospects for Excitation of Vortex Surface Plasmon Polaritons

2021 ◽  
Vol 11 (2) ◽  
pp. 717
Author(s):  
Boris Knyazev ◽  
Valery Cherkassky ◽  
Oleg Kameshkov
Keyword(s):  
Surface Plasmon ◽  
Surface Plasmon Polaritons ◽  
Bessel Beam ◽  
Diffraction Theory ◽  
Terahertz Range ◽  
High Resistivity ◽  
Visible Range ◽  
Optical Elements ◽  
Scalar Diffraction ◽  
Plasmon Polaritons

Transformation of a Bessel beam by a lens results in the formation of a “perfect” vortex beam (PVB) in the focal plane of the lens. The PVB has a single-ring cross-section and carries an orbital angular momentum (OAM) equal to the OAM of the “parent” beam. PVBs have numerous applications based on the assumption of their ideal ring-type structure. For instance, we proposed using terahertz PVBs to excite vortex surface plasmon polaritons propagating along cylindrical conductors and the creation of plasmon multiplex communication lines in the future (Comput. Opt. 2019, 43, 992). Recently, we demonstrated the formation of PVBs in the terahertz range using a Bessel beam produced using a spiral binary silicon axicon (Phys. Rev. A 2017, 96, 023846). It was shown that, in that case, the PVB was not annular, but was split into nested spiral segments, which was obviously a consequence of the method of Bessel beam generation. The search for methods of producing perfect beams with characteristics approaching theoretically possible ones is a topical task. Since for the terahertz range, there are no devices like spatial modulators of light in the visible range, the main method for controlling the mode composition of beams is the use of diffractive optical elements. In this work, we investigated the characteristics of perfect beams, the parent beams being quasi-Bessel beams created by three types of diffractive phase axicons made of high-resistivity silicon: binary, kinoform, and “holographic”. The amplitude-phase distributions of the field in real perfect beams were calculated numerically in the approximation of the scalar diffraction theory. An analytical expression was obtained for the case of the binary axicon. It was shown that a distribution closest to an ideal vortex was obtained using a holographic axicon. The resulting distributions were compared with experimental and theoretical distributions of the evanescent field of a plasmon near the gold–zinc sulfide–air surface at different thicknesses of the dielectric layer, and recommendations for experiments were given.

scholarly journals Horndeski genesis: consistency of classical theory

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Yulia Ageeva ◽  
Pavel Petrov ◽  
Valery Rubakov
Keyword(s):  
Strong Coupling ◽  
Dimensional Analysis ◽  
Classical Theory ◽  
Arbitrary Order ◽  
Specific Model ◽  
Power Counting ◽  
Coupling Energy ◽  
Classical Description ◽  
Higher Order Terms ◽  
The Universe

Abstract Genesis within the Horndeski theory is one of possible scenarios for the start of the Universe. In this model, the absence of instabilities is obtained at the expense of the property that coefficients, serving as effective Planck masses, vanish in the asymptotics t → −∞, which signalizes the danger of strong coupling and inconsistency of the classical treatment. We investigate this problem in a specific model and extend the analysis of cubic action for perturbations (arXiv:2003.01202) to arbitrary order. Our study is based on power counting and dimensional analysis of the higher order terms. We derive the latter, find characteristic strong coupling energy scales and obtain the conditions for the validity of the classical description. Curiously, we find that the strongest condition is the same as that obtained in already examined cubic case.

Sign in / Sign up

Export Citation Format

Share Document