Software for computing the spheroidal wave functions. The separated angular equations are called the spinweighted spheroidal wave equations. The scientific discoveries and technological innovations produced by bell system research and engineering were critical not only to the evolution of global telecommunications but, more widely, they had a considerable impact on the technological base of the global economy and, indeed, on our daily lives. There are two kinds of eigenvalues in the differential and corresponding integral equations, and the relation between them is given explicitly. On the asymptotic expansion of the spheroidal wave function. The use of direct, numerically exact computer solvers of the macroscopic maxwell equations to study electromagnetic scattering by volumes of discrete random medium drm has been a hot topic over the past decade see, e. In 1973, teukolsky first obtained separable equations of scalar, electromagnetic and gravitational fields perturbation to the kerr blackhole4. Rigorous solutions are presented of the problems of diffraction of plane electromagnetic waves by an infinitely thin, perfectly conducting, circular disk and by a circular aperture in a plane conducting screen.
Prolate spheroidal wave function as exact solution of the. The magic of the prolate spheroidal functions in various. The electromagnetic field is expressed in terms of spherical eigenvectors only, while the equation of the spheroidal boundary is given in spherical coordinates. A set of tables of spheroidal wave functions designed to simplify the computation of acoustic and electromagnetic scattering from spheroids. On the asymptotic expansion of the spheroidal wave. The symposium provided a forum for discussing electromagnetic wave theory and tackled a wide range of topics, from propagation in nonlinear media to electromagnetic wave propagation and.
Electromagnetic scattering by spheroidal volumes of discrete. Monographs tying together many aspects of the theory of spheroidal wave functions were written by strutt, 10 stratton et al. In this paper, we develop an analytic theory for describing the photoacoustic wave generation from a spheroidal droplet and derive the first complete analytic solution. Spheroidal wave functions in electromagnetic theory lewei li, xiaokang kang, and mookseng. A new integral equation for the spheroidal equations in. It is wellknown that the spinweighted spheroidal functions are indispensable in many physical processes, such as gravitational wave detection, quantum eld theory in curved spacetime, black hole stability problems, nuclear modeling, spheroidal cavity problems, spheroidal electromagnetic di raction, scatter. The dyadic greens function for an unbounded medium is expanded in terms of the spheroidal vector wave functions and the singularity at. Ciric department of electrical and computer engineering university of manitoba winnipeg, manitoba canada r3t sv 6 i. Spheroidal wave functions in electromagnetic theory wiley.
Asymptotics of prolate spheroidal wave functions t. Electromagnetic resonant behavior of a confocal spheroidal cavity system in the microwave region a thin spheroidal antenna in empty space is known 1 to show resonance effects when its wavelength is approximately a whole number of halfwavelengths. Niven, which lead to a helmholtz equation in spheroidal coordinates. An introduction discusses the mathematical properties of the functions and describes some of their applications. Pier online electromagnetic scattering by a metallic. This paper introduces the oblate spheroidal quaternionic wave functions osqwfs, which extend the oblate spheroidal wave functions introduced in the late 1950s by c. This chapter is based in part on abramowitz and stegun 1964, chapter 21 by a. Hu c 1986 prolate spheroidal wave functions of large frequency parameters c kf and their applications in electromagnetic theory ieee trans.
Volkmer department of mathematical sciences, university of wisconsinmilwaukee, milwaukee, wisconsin. Internal and nearsurface electromagnetic fields for a spheroidal. As the verification, besides carrying out the asymptotic analyses which recover the. The analysis utilizes oblate spheroidal vector wave functions. It is therefore reasonable to be interested in expressing the solution of the schrodinger equation in terms of prolate spheroidal wave functions. Electromagnetic sea ttering by spheroidal particles loan r. Spheroidal wave functions in electromagnetic theory. Spheroidal wave functions are useful to describe acous tic and electromagnetic waves radiated by sources with spheroidal shapes, and to describe the scattering. The flagship monograph addressing the spheroidal wave function and its pertinence to computational electromagnetics spheroidal wave functions in electromagnetic theory presents in detail the theory of spheroidal wave functions, its applications to the analysis of electromagnetic fields in various spheroidal structures, and provides comprehensive programming codes for those computations. Using prolate spheroidal wave functions chunyang chen, student member, ieee, and p. Originally, the spheroidal wave functions were introduced by c. A stepbystep procedure of computation is then outlined together with an indication of precision achieved and method of checking. Spheroidal wave functions become elementary if gammanpi2. The method of lines is a very accurate and powerful way to analyze electromagnetic waves, enabling a full wave solution without the computational burden of pure finite element or finite difference methods.
Computational geometric and boundary value properties of. Jan 26, 2017 the whole new humongous field of electromagnetic theory came into existence when the great scientist james clerk maxwell found out the correlation between electric and magnetic fields by presenting a set of already existing equation with the intro. Dunster san diego state university san diego, ca 92182 usa abstract. Light concentration in the nearfield of dielectric. Sampling theory approach to prolate spheroidal wavefunctions. The scientific discoveries and technological innovations produced by bell system research and engineering were critical not only to the evolution of global telecommunications but, more widely, they had a considerable impact on the technological base of the global economy and, indeed, on our daily. The vector wave function solution of the diffraction of. Separation of variables of the wave equation in spheroidal coordinates results in a differential equation that is satis. The establishment of rotationaltranslational addition theorems for spheroidal scalar wave functions 1,2 requires the use of rotational and translational addition theorems for spherical scalar wave functions, as previously provided by friedman and russek 3, stein 4, and cruzan 5. D where d is a spherical volume of radius a centered about the origin.
With this formulation we have a connection to the well known transmission line theory and resulting in an easy understanding. This paper discusses the calculation of prolate spheroidal wave functions for integral mode numbers and real spheroidal parameter. The formulation of the problem is realised by expanding the incident as well as the scattered electromagnetic fields in terms of appropriate spheroidal vector wave functions and imposing the appropriate boundary. On the asymptotic expansion of the spheroidal wave function and. The flagship monograph addressing the spheroidal wave function and its pertinence to computational electromagnetics. Request pdf spheroidal wave functions in electromagnetic theory the flagship monograph addressing the spheroidal wave function and its pertinence to. Formulas useful for the numerical calculation of prolate radial function of the first and second type, together with their first derivatives, are derived and explained. Calculation of spheroidal wave functions sciencedirect. The spheroidal wave functions, which are the solutions to the helmholtz. Spheroidal wave functions in electromagnetic theory presents in detail the theory of spheroidal wave functions, its applications to the analysis of electromagnetic fields in various spheroidal structures, and provides comprehensive programming codes for those computations.
Spheroidal wave functions flammer pdf spheroidal wave functions of flammer c. Spheroidal wave electromagnetic theory wiley online library. The applicability ranges of the relations obtained are discussed. A new integral equation for the spheroidal equations in case. We show that the theory of the osqwfs is determined by the moisilteodorescu type operator with quaternionic variable coefficients. Some relations between the spheroidal and spherical wave. Mar 11, 2016 new relations are found between the spheroidal and spherical wave functions, as well as between the spheroidal functions related to different spheroidal coordinate systems. The general theory and background on spheroidal wave functions is contained in the. Monographs tying together many aspects of the theory of spheroidal wave functions were written by strutt, stratton et al. Simulating photoacoustic waves produced by individual biological particles with spheroidal wave functions. Spheroidal wave functions in electromagnetic theory request pdf. Calculation of radial prolate spheroidal wave functions of the second kind. Planewave spectrum point of view of diffraction and its equivalence to the rayleighsommerfeld diffraction theory both for scalar and vector fields, including smythe diffraction integrals, apertures in conducting screens, bethebouwkamp theory of diffraction by small holes, and the babinet principle for scalar and vector electromagnetic fields.
Osa analytic theory of photoacoustic wave generation from a. Internal and nearsurface electromagnetic fields for a spheroidal particle with arbitrary illumination. Electromagnetic wave theory pdf free download epdf. It is a generalization of the mathieu differential equation. Uniform asymptotic approximations are obtained for the prolate spheroidal functions ps n mx.
Spheroidal wave functions in electromagnetic theory by le. Volkmer department of mathematical sciences, university of wisconsinmilwaukee, milwaukee, wisconsin acknowledgements. In part i these vector functions are defined and the expansions of plane. Prolate spheroidal wave functions from pde point of view pswfs as eigenfunctions of a di erential and an integral operator some properties of the pswfs 1 t c is a selfadjoint compact operator. In mathematics, the spheroidal wave equation is given by. The spheroidal coordinate system is one of the systems in which the homogeneous scalar wave equation.
The tables were computed to fiveplace accuracy on the whirlwind digital computer, and automatically tabulated. Pdf theory and computation of spheroidal wavefunctions. The scattering of a plane electromagnetic wave by a perfectly conducting prolate or oblate spheroid is considered analytically by a shape perturbation method. The dyadic greens functions for defining the electromagnetic em fields for the inner and outer regions of a dielectric spheroid are formulated in this paper. Spheroidal wave functions in electromagnetic theory wiley, new york, 2002. The method of lines is a very accurate and powerful way to analyze electromagnetic waves, enabling a fullwave solution without the computational burden of pure finite element or finite difference methods. Theory and computation of the spheroidal wave functions arxiv. Numerical test calculations have demonstrated a high. Simulating photoacoustic waves produced by individual.
Theory and computation of spheroidal wave functions. We explore a number of issues related to this problem, including the effective computation of the corresponding slepzan functions for. The singular functions for the problem of recovering a time limited function from its fourier transform in a certain band of frequencies are given, in the simplest case, by the prolate spheroidal wave functions. Ground state eigenfunction of spheroidal wave functions. Theory and computation of the spheroidal wave functions. The wave equation in spheroidal coordinates and its solutions.
Electromagnetic wave theory, part 2 contains the proceedings of a symposium on electromagnetic wave theory held at delft, the netherlands in september 1965. Spheroidal wave functions in electromagnetic theory is a fundamental reference for scientists, engineers, and graduate students practicing modern computational electromagnetics or applied physics. Cartesian derivatives of the scalar spheroidal wave functions are derived, leading. Including tables of separation constants and coefficients the mit press stratton, julius a. Spheroidal wave functions in electromagnetic theory by lewei. The systems must have a common origin of coordinates and a common symmetry axis of coordinate surfaces. Our derivation is based on solving the photoacoustic helmholtz equation in spheroidal coordinates with the separationofvariables method. The functions have applications in electromagnetism, acoustics, quantum mechanics and finite fourier analysis. The objective is the use of large values of mode number and spheroidal parameter. Prolate spheroidal wave functions and their properties computation of the pswfs by flammers method uniform estimates of the pswfs and their derivatives applications of the pswfs prolate spheroidal wave functions from pde point of view pswfs as eigenfunctions of a di erential and an integral operator some properties of the pswfs. Spheroidal wave functions in electromagnetic theory lewei li, xiaokang kang, mookseng leong on. Prolate spheroidal wave functions and applications. An exact solution to the problem of scattering of electromagnetic waves from a perfect electromagnetic conducting spheroid is presented, using the method of separation of variables.
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