Analytical non-paraxial TM polarized Gaussian beam in the source region

The non-paraxial TM polarized Gaussian beam, which approximately reduces to be a Gaussian TEM₀₀ mode at the paraxial case, is the rigorous solution of Maxwell's equations for a confocal resonator. By means of mathematical techniques, the analytical expression in the source region has been derived without any approximation and expressed as a sum of the propagating part and the evanescent part. With some certain given values of the initial Gaussian half width w ₀, the distributions of the squared modulus of the propagating part, the evanescent part, and the whole beam are depicted in the reference plane close to the source. When w ₀ is small enough, the squared modulus of the non-paraxial TM polarized Gaussian beam is composed of two lobes, which results from the contribution of the evanescent wave. This research further reveals the difference of a non-paraxial TM polarized Gaussian beam from a non-paraxial Gaussian beam.     

Axial force acting on a dielectric sphere in a focused laser beam

We present the detailed behavior of the axial force acting on a dielectric sphere exerted by the optical pressure of a focused Gaussian laser beam. Comparison is made between the numerical results and those calculated from the radiation pressure cross section. There is also a discussion as to whether the expressions for the axial force given in this paper are consistent with the previously reported experimental results. Moreover, a simple experimental method to measure the axial force on a polystyrene sphere suspended in water is demonstrated, and fairly good agreement between theoretical and experimental results was obtained.     

Transverse electric scattering by a dielectric biconvex cylinder loaded with a shallow circular trough in a ground plane

The scattering problem of transverse electric wave from a dielectric biconvex cylinder buried in a shallow circular trough of a ground plane is investigated and a rigorous series solution is also derived. Based on the region-matching method, the analysed region is decomposed into two subregions by introducing a semi-circular auxiliary boundary. The magnetic field of each subregion is expressed in terms of cylindrical wave functions with unknown expansion coefficients. After imposing the matching conditions and the boundary condition on the trough surface with the aid of Graf's addition theorem, the unknown coefficients are determined. Comparisons with published data for a dielectric circular cylinder case show very good agreement. Visible effects of depth-to-half-width ratios of a dielectric biconvex cylinder on echo width, far- field pattern and near-field distribution are illustrated in graphical form.     

Investigation in the propagation of non-paraxial TE vector Gaussian beam from vectorial structure

Based on the vectorial structure of non-paraxial electromagnetic beam and the non-paraxial vectorial moment theory of light beam propagation, the beam waists, the divergence angles and the beam propagation factors of TE and TM terms have been presented for non-paraxial TE vector Gaussian beam. The formulae obtained are further discussed at the highly non-paraxial and paraxial cases. Their respective maximum divergence angles are given at the highly non-paraxial case. When reducing to the paraxial case, the beam propagation factors of TE and TM terms are smaller than unity, which results from their special energy flux distribution. As TE and TM terms can be detached in the far field, they can be applied in the optical storage and collimation domains.     

A geodesic beam finite element for use in the-static analysis of reinforced circular cylindrical shells

The development of a geodesic beam finite element for use with a specific circular cylindrical shell finite element in the analysis of reinforced circular cylinders is described. The basic strain and curvature change equations are given and, from these, three versions of the geodesic beam element are developed. Two of the beams have nodal degress-of-freedom identical with the shell element. They differ in the treatment of the terms relating to rotation about the principal normal. The first version ignores this parameter but, under certain circumstances, the stiffness matrix contains terms which can contribute to the strain energy under arbitrary rigid body movement of the beam. This deficiency is removed by applying an aspect of Koiter's theory which is used to transform the curvature change equations. The introduction of additional rotational degress-of-freedom, at the end nodes of the beam element, produces a variation which is capable of accurately representing and transmitting in-surface bending effects to an adjoining beam element. Numerical evaluation successfully compares finite element solutions to basic problems for straight, circular and helical beams with theoretical strain energy solutions. Finally the beam is used in conjunction with a shell element to analyse an infinitely long circular cylinder, reinforced with equispaced rings, subjected to internal pressure.     

Radiation force on a nonlinear microsphere by a tightly focused Gaussian beam

We determine the characteristics of the radiation force that is exerted on a nonresonant nonlinear (Kerr-effect) rigid microsphere by a strongly focused Gaussian beam when diffraction and interference effects are significant (sphere radius a < or = illumination wavelength lambda). The average force is calculated from the surface integral of the energy-momentum tensor consisting of incident, scattered, and internal electromagnetic field vectors, which are expressed as multipole spherical-wave expansions. The refractive index of a Kerr microsphere is proportional to the internal field intensity, which is computed iteratively by the Rytov approximation (residual error of solution, 10(-30). The expansion coefficients for the field vectors are calculated from the approximated index value. Compared with that obtained in a dielectric (linear) microsphere in the same illumination conditions, we find that the force magnitude on the Kerr microsphere is larger and increases more rapidly with both a and the numerical aperture of the focusing objective. It also increases nonlinearly with the beam power unlike that of a linear sphere. The Kerr nonlinearity also leads to possible reversals of the force direction. The proposed technique is applicable to other types of weak optical nonlinearity.     

不同粗糙表面的圆柱风压分布试验研究

通过风洞试验研究了不同表面粗糙度、不同雷诺数条件下二维圆柱的压力分布和阻力特性。结果表明:通过合理地增大表面粗糙度,在相对较低的风速下有效地模拟了圆柱的超临界绕流特性,满足了工程应用对超临界雷诺数的要求。     

Validity of the cylindrical localized approximation for arbitrary shaped beams in generalized Lorenz-Mie theory for circular cylinders

Abstract

A so-called cylindrical localized approximation, allowing one to speed up the evaluation of beam shape distributions in generalized Lorenz-Mie theory for circular infinitely long cylinders, has been previously introduced and, in the case of Gaussian beams, rigorously justified. In this paper, we examine and demonstrate the validity of this approximation for arbitrary shaped beams.     

Computation of electromagnetic fields scattered by a cylindrical inhomogeneity in a homogeneous medium of infinite extent

Summary A method is presented for computing time harmonic electromagnetic fields scattered by a cilindrical inhomogeneity in a homogeneous medium of infinite extent. Geometrically, the homogeneity is a cylinder of arbitrary cross-section. Outside a circular cylinder that completely surrounds the inhomogeneity, the electromagnetic field is expanded in terms of wave functions of the circular cylinder. Inside this cylinder, the electromagnetic field equations are transformed into a system of ordinary differential equations in the radial direction. The relevant system behaves numerically unstable and is therefore transformed into a stable one through a specific transformation scheme. To elucidate the validity and the versatility of the method, numerical results are presented for fields scattered by a number of different cylindrical inhomogeneities.     

Scattering of a gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation: numerical results

We present numerical results concerning the properties of the electromagnetic field scattered by an infinite circular cylinder illuminated by a circular Gaussian beam. The cylinder is arbitrarily located and arbitrarily oriented with respect to the illuminating Gaussian beam. Numerical evaluations are provided within the framework of a rigorous electromagnetic theory, the generalized Lorenz-Mie theory, for infinite cylinders. This theory provides new insights that could not be obtained from older formulations, i.e., geometrical optics and plane-wave scattering. In particular, some emphasis is laid on the waveguiding effect and on the rainbow phenomenon whose fine structure is hardly predictable by use of geometrical optics.     

Time Domain Inverse Scattering of Buried Inhomogeneous Dielectric Cylinders

This paper presents the studies of time domain inverse scattering for a two-dimensional inhomogeneous dielectric cylinder buried in a half-space by the finite difference time domain (FDTD) method and evolutionary algorithms (EAs). For forward scattering, the FDTD method is employed to calculate the scattered E fields, while for the inverse scattering the evolutionary algorithms are utilized to determine the permittivity of the buried cylindrical scatterer with arbitrary cross section. The results obtained for different examples show that the dynamic differential evolution (DDE) algorithms outperform the non-uniform steady state genetic algorithm (NU-SSGA) variants in terms of finding best optima. The suitability and efficiency of applying these two methods for microwave imaging of 2-D inhomogeneous dielectric cylinders are examined. Moreover, when the measured scattered fields are contaminated with Gaussian noise, DDE is able to yield good reconstructed quality.     

Magnetostatic energy of paramagnetic particles in magnetic separators

A general form for the magnetostatic interaction energy of an infinitely long cylinder of arbitrary cross-section, uniformly magnetized in a direction perpendicular to its long axis, and a spherical paramagnetic particle is obtained. For cylindrical and rectangular cross-sections, expressions for this energy are given which involve simple functions only.     

On Saint-Venant’s problem for anisotropic, inhomogeneous, cylindrical Cosserat elastic shells

We investigate the static deformation of cylindrical elastic shells, using the theory of Cosserat surfaces. We consider anisotropic and inhomogeneous cylindrical shells with arbitrary (open or closed) cross-section. The constitutive coefficients are assumed to be independent of the axial coordinate. In the context of linearized theory, we determine a solution of the relaxed Saint-Venant’s problem. Finally, we apply the general results in the special cases of circular cylindrical shells and of Cosserat plates made from an orthotropic material.     

Controlling the dynamic behavior of piezoceramic cylinders by cross-section geometry

This paper focuses on the possibilities of controlling the dispersion spectra and wave characteristics of cylindrical waveguides by changing their geometry and electro-elastic properties. We consider cylinders with classical circular and hollow cross-sections, and waveguides that have sector cut of arbitrary angular measure in the cross-section. Numerical results are presented for the cylinders of all studied types with different boundary conditions. It is shown that the required wave characteristics can be obtained by a variation of the cross-section geometry of the waveguides.     

A fully nonlinear implicit model for wave interactions with submerged structures in forced or free motion

The purpose of this work is to develop advanced numerical tools for modeling two-way fully nonlinear interactions of ocean surface waves (irregular waves in the general situation) with submerged structures undergoing large amplitude motion, that could represent Wave Energy Converters (WECs). In our modeling approach, an existing two-dimensional Numerical Wave Tank (NWT), based on potential flow theory, is extended to include a submerged horizontal cylinder of arbitrary cross-section. The mathematical problem and related numerical solution are first introduced. Then, conservation of volume and conservation of energy are checked, respectively, in the case of a circular cylinder in a prescribed large amplitude motion and in the case of a circular cylinder in a free motion. Interactions between waves and a submerged circular cylinder computed by the model are then compared to mathematical solutions for two situations: a cylinder in prescribed motion and a freely moving cylinder.     

Computation of the External Magnetic Field, Near-Field or Far-Field, From a Circular Cylindrical Magnetic Source Using Toroidal Functions

A method is developed for computing the magnetic field from a circular or noncircular cylindrical magnetic source. A Fourier series expansion is introduced which yields an alternative to the more familiar spherical harmonic solution, Elliptic integral solution, or Bessel function solution. This alternate formulation coupled with a method called charge simulation allows one to compute the external magnetic field from an arbitrary magnetic source in terms of a toroidal expansion which is valid on any finite hypothetical external observation cylinder. In other words, the magnetic scalar potential or the magnetic field intensity is computed on a exterior cylinder which encloses the magnetic source. Also, one can compute an equivalent multipole distribution of the real magnetic source valid for points close to the circular cylindrical boundary where the more familiar spherical multipole distribution is not valid. This method can also be used to accurately compute the far field where a finite-element formulation is known to be inaccurate     

沿水平向运动的水中截断圆柱体辐射波浪问题的解析解答

根据线性势波理论,分析了水中截断圆柱体作水平简谐运动时结构周围的辐射波浪。利用分离变量法,分别得到了含有未知常数的三个流体子域速度势的简谐表达形式,并采用一个较为简单的匹配方法使其在流体子域的共同边界上满足压力和法向速度的连续条件。于是求解得到了速度势,进而可得到由等效附加质量和附加阻尼表示的柱体侧面上的动水力。不仅能考虑自由表面波对动水压力的影响,也适用于位于任意水深处的截断圆柱体。实例分析表明,该方法具有较高的计算精度;同时对于截断圆柱体,采用Morison方程中的动水附加惯性力项会高估柱体侧面上的动水力。     

Computation of Stokes Flow due to the Motion or Presence of a Particle in a Tube

The computation of Stokes flow due to the motion or presence of a rigid particle in a fluid-filled tube with arbitrary geometry is discussed with emphasis on the induced upstream to downstream pressure change. It is proposed that expressing the pressure change as an integral over the particle surface involving (a) the a priori unknown traction, and (b) the velocity of the pure-fluid pressure-driven flow, simplifies the numerical implementation and ameliorates the effect of domain truncation. Numerical computations are performed based on the integral formulation in conjunction with a boundary-element method for a particle translating and rotating inside a cylindrical tube with a circular cross-section. The numerical results are consistent with previous asymptotic solutions for small particles, and complement available numerical solutions for particular types of motion     

任意轴对称荷载作用下的圆杆分析

锚杆与周围介质相互作用问题涉及圆杆在轴对称荷载作用下的应力应变分析，本文提出一种付里叶方法来分析圆杆在任意轴对称荷载作用下的位移场和应力场，而且考虑了付里叶级数中任意两项的耦合。为了验证这一方法的正确性，本文还导出圆杆在均匀轴对称荷载作用下的理论解。分析成果表明所提方法对于任意轴对称荷载作用下的圆杆问题具有相当好的精度，分析时必须考虑付里叶级数中任意两项的耦合作用。     

A MoM solution for TM scattering by dielectric cylinders above an infinite flat surface

A simple solution method is presented for transverse magnetic plane wave scattering by a dielectric cylinder of arbitrary cross-section in front of an infinite flat dielectric surface. The interface between two semi-infinite, dissimilar half-spaces is considered by a perturbed equivalent magnetic current. Coupled integral equations are obtained from a special form of surface equivalence principles and are solved numerically by the Method of Moments. The scattered tangential electric field at interface is displayed and far-zone fields are compared to the results available in the literature.