Fast generation of spherical Bessel functions with complex arguments

A simple recurrence technique for fast generation of spherical Bessel functions of order n and real or complex arguments is presented. The technique is accurate and very efficient, especially when the order of the function is less than the magnitude of the argument.     

The numerical computation of Bessel functions of the first andsecond kind for integer orders and complex arguments

A rigorous algorithm for computing integer order Bessel functions of the first and second kind with complex arguments is discussed. The algorithm makes use of backward recurrence for computing Bessel functions of the first kind where applicable, and of Hankel's asymptotic expansion for large arguments. The argument is limited only by the ability of the computer to handle large numbers. Orders up to a few thousand have been computed to 13-digit accuracy     

New approximations to J0 and J1 Besselfunctions

New approximate solutions to the 0th- and 1st order Bessel functions of the first kind are derived. The formulations are based upon using a new integral with no previously known solution. The new integral in the limiting case is identical to the 0th-order Bessel function integral. It is solved in closed form, and the solution is expressed as a simple even order polynomial with integer coefficients. The polynomial coefficients are all of integer value. The 1st-order Bessel function approximation can then be found through a simple derivative. Comparisons are made between the exact solution, classic solutions, and the new approximation. The new approximation proves to be much more accurate than the classic small argument approximation. It is also sufficiently accurate to bridge the gap between the classic large and small argument approximations and has potential applications in allowing one to analytically evaluate integrals containing Bessel functions     

A procedure for determining the largest computable order of Besselfunctions of the second kind and Hankel functions

Routines for the computation of Bessel functions of the second kind, Y_n(z), and Hankel functions H_n^{(1/)(z) and H}sub n//sup (2/)(z), may exhibit numerical overflow problems for large order n and small complex or real arguments z. An upper limit for the largest calculable order of these functions for a given argument, is derived     

整数阶复宗量圆柱函数的数值计算

提出了一种复宗量圆柱函数数值计算的新方法。该方法通过研究各类圆柱函数模值随其阶数ｎ的变化关系，提出了首先解决复宗量第二类修正Ｂｅｓｓｅｌ函数Ｋｎ（ｚ）的数值计算，然后应用Ｊｎ（ｚ）、Ｋｎ（ｚ）与其它圆柱函数的关系，解决Ｙｎ（Ｚ）、（ｚ）的数值计算方法。在计算机允许的数值范围内，该方法对圆柱函数的阶数及宗量范围均没有限制，而且计算精度高、编程简单。     

Computation for the gain of ridge loaded ring-plane traveling wave tube

The ridge loaded ring-plane traveling wave tube can provide high output power in a relatively broader bandwidth. The dispersion relation for the interaction between the electron beam and the symmetrical mode propagating in this slow wave circuit is obtained, by means of the Variational method. The method to calculate the arbitrary order Bessel function with complex argument is discussed. The three dimensional trajectory graph of the Bessel function with complex argument is plotted. The instantaneous operating bandwidth can be estimated in terms of the relation between of the gain and frequency.     

任意实数阶复宗量第一类和第二类Bessel函数的精确计算

本文介绍了精确计算任意实数阶复宗量第一类和第二类Ｂｅｓｓｅｌ函数Ｊｕ（ｚ）和Ｙｕ（ｚ）的递推算法；给出了计算函数值时要用到的数学公式和典型数值计算结果，并对如何验证程序的正确性和分析计算结果的精度以及编程技巧作了较详细的讨论。     

Impulse response of a lossy magnetoplasma half-space

An exact solution for the transient reflected wave from a lossy magnetoplasma half-space is derived for the case of a vertically incident impulsive plane wave. The solution is expressed as an infnite series of modified Bessel functions of the first kind with complex argument. For small values of the collision and magnetic parameters, the exact solution is approximated in terms of a single integer-order Bessel function.     

Propagation of space-charge waves in diodes and drift spaces

It has generally been found that propagation of space-charge waves may be described 1) in space-charge-limited gaps by Gauss' hypergeometric functions, 2) in gaps with no space charge but with an accelerating homogeneous field by Bessel functions with real argument; and 3) in spaces free of dc fields by simple trigonometric functions. The equations derived become simpler through the selection of the dc velocity u, rather than the time t, as the independent variable.     

基于编码电磁超表面的Bessel波束设计

编码电磁超表面构成信息超材料研究领域的一个分支. 文中提出了基于编码电磁超表面的Bessel波束产生设计方法，为Bessel波束的产生与调控提供了新的解决方案；同时对基于电磁超表面的Bessel波束产生与设计的基本方法进行了梳理总结. 首先通过反射型编码电磁超表面分别设计了不同类型的Bessel波束，包括单波束零阶Bessel波束、双波束零阶Bessel波束、单波束高阶Bessel波束以及双波束高阶Bessel波束；然后对于每一种类型的Bessel波束分别对应给出了有关的设计理论和方法，并通过全波电磁仿真的方法进行了相应的仿真验证；最后，鉴于信息超材料技术的发展，基于编码电磁超表面的Bessel波束设计可以进一步地应用于信息超材料有关的系统设计，如近场无线信息/能量传输、近场雷达探测与成像，这也为信息超材料提供了一种可供选择的应用场景.     

轴棱锥聚焦涡旋光束获得高阶贝塞尔光束

采用轴棱锥聚焦涡旋光束,获得了高阶贝塞尔(Bessel)光束.首先,从理论模拟了涡旋光束经过轴棱锥聚焦后所获得的聚焦光强分布,结果表明,涡旋光束经过轴棱锥聚焦后可获得高阶贝塞尔光束.并且所获得的高阶贝塞尔光束的阶数与涡旋光束的拓扑电荷数相司.进而,从实验获得高阶贝塞尔光束,并且采用不同锥角的轴棱锥对涡旋光束进行聚焦,研...     

Incomplete Hankel and modified Bessel functions: a class of special functions for electromagnetics

A novel class of special functions for electromagnetics is presented. Formed by the incomplete Hankel and modified Bessel functions, this class allows solving electromagnetics problems concerning truncated cylindrical structures. The differential and recurrence equations of these functions feature additional terms with respect to the classical theory of the Hankel and Bessel functions. The general properties, the most important analytical characteristics, and the large argument asymptotic approximations of the incomplete functions are derived using the steepest descent path (SDP) technique, showing that each special function splits into two terms. The first one has a discontinuous character and is linked to the saddle-point(s) contribution(s), while the second one, arising from the integral end-point contribution(s), compensates exactly the said discontinuity. In the solution of electromagnetic problems, the first term describes the geometrical optics (GO) field, the diffracted field being described by the second one. The general theory is employed to find the closed form analytical solution of the field radiated from a uniform line current source. Using the properties of the incomplete Hankel functions, it is demonstrated that this source excites cylindrical fields having optical character. Finally, the shape of the spatial regions where the GO solution cannot be applied is determined and discussed in details.     

Rapid evaluation of integer-order Bessel functions using an FFTalgorithm

A rapid, accurate, and stable method for computing integer-order Bessel functions is presented. In contrast to the iterative procedures normally used in the numerical evaluation of Bessel functions, this approach requires little more than a commonly available fast Fourier transform algorithm, and yet, for a given argument, can provide many J_ns in a single pass     

航空时间域电磁法回线源有限差分初始场计算

针对时间域回线源航空电磁有限差分法初始场中双重贝塞尔函数的数值计算,通过分析回线积分法、宗量近似法和贝塞尔函数展开法的特点,提出将贝塞尔函数展开与小宗量近似相结合的混合法,并用共求解全部空间的初始电磁场,不仅计算速度快,而且精度高,满足有限差分对计算时间和计算精度的要求,为计算全空间复杂地质异常体电磁响应奠定了基础。     

Further note on fast generation of spherical Bessel functions with complex arguments

The author discusses two extensions to previous work which may speed up, and render more accurate, the evaluation of the Bessel function. These extensions are real recursion for complex argument and the suppression of overflows.     

The neumann series: A tool for the analysis of some microstrip structures

The aim of this paper is to present a general methodology for studying printed electromagnetic structures. Canonical microstrip structures can be described by means of a system of coupled integral equations, which can be easily transformed into a system of algebraic equations by using the Neumann series, namely a series of Bessel functions. Careful numerical analysis shows that, in order to obtain a reasonable accuracy of the fields and/or potential, small matrices are necessary. Static and dynamic cases are discussed.     

分数阶无衍射光束的实验研究

实验研究了轴棱锥聚焦分数阶涡旋光束获得分数阶贝塞尔光束。研究结果表明：当分数阶涡旋光束通过轴棱锥聚焦后,获得的分数阶贝塞尔光束其横截面上的光强分布具有高阶无衍射贝塞尔光束的特点;在轴棱锥后的最大准直距离内,光斑的形状基本保持不变,即呈现出很好的无衍射传输特性;另外还研究了轴棱锥角度改变对分数阶贝塞尔光束的影响,实验结果表明,轴棱锥的角度越大时,横截面光强图中的中心空心越小。     

有耗电磁场问题中复宗量整数阶圆柱函数的计算

本文介绍了复宗量整数阶圆柱函数数值计算的递推算法。在计算机允许的数值范围内对圆柱函数的阶数及宗量范围均没有限制。试算结果经加法定理和Wronskian关系式的验算表明准确度很高。     

A refractive index chart for a scattering sphere

The Mie solution for the scattered electromagnetic fields from a sphere is briefly summarized. A refractive index chart is introduced which makes it possible to evaluate the modal coefficient for lossy materials without evaluating Bessel functions of complex argument. This refractive index chart is used for this purpose and also to find spheres made of different material that have the same scattering pattern and also to find the condition for resonance in small spheres. It is also useful in establishing a solution for the inverse problem for small spheres, e.g., evaluating the constitutive parameters from the scattered fields.