Pdf theory and computation of spheroidal wavefunctions. Request pdf spheroidal wave functions in electromagnetic theory the. This is the first book to present the application of parabolic equation methods to electromagnetic wave propagation. Vaidyanathan, fellow, ieee abstractin the traditional transmitting beamforming radar system, the transmitting antennas send coherent waveforms which form a. Spheroidal wave functions in electromagnetic theory. Reference is made to more than 500 papers published since 1940. Flammer, spheroidal wave functions, 1957 are included as a special case of meixners more general functions. Intended primarily as a textbook for physics students at the advanced. The magic of the prolate spheroidal functions in various. Electromagnetic wave theory, part 2 contains the proceedings of a symposium on electromagnetic wave theory held at delft, the netherlands in september 1965. Mookseng leong spheroidal wave functions in electromagnetic theory is a fundamental reference for scientists, engineers, and graduate students practicing modern computational electromagnetics or applied. Qualitatively, the idea behind greens functions is that they provide the solution for a given differential equation corresponding to a point source. Electromagnetic wave theory 246 rle progress report number 141 denominator and numerator.
Prolate spheroidal wave function as exact solution of the. 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. Students and professionals in the fields of mathematics, physics, engineering, and economics will find this reference work invaluable. This includes also programs for coated dielectric spheroids. Theory and computation of the spheroidal wave functions. The theory of light scattering by single particles and their ensembles has important applications in various areas of science and technology, e. Niven, which lead to a helmholtz equation in spheroidal coordinates.
The electromagnetic wave disturbs the electric field at any point through which it passes. This content was uploaded by our users and we assume good faith they have the permission to share this book. The results are essential for the computational electromagnetics. The characteristic angular equation 1 for the spheroidal harmonic functions is supplemented by a regularity. Download it once and read it on your kindle device, pc, phones or tablets.
This book will enable readers to handle various emc problems, to develop their own emc computational models in applications in research and industry, and to better understand numerical methods developed and used by other researchers and engineers not only in emc, but in other areas of engineering. Volkmer department of mathematical sciences, university of wisconsinmilwaukee, milwaukee, wisconsin acknowledgements. Subsequently one can substitute an expansion of the fields in the set of spheroidal vector wave functions into the boundary condition on the particle surface for. 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. Mathematical tools for bandlimited approximation applied mathematical sciences book 187 kindle edition by osipov, andrei, rokhlin, vladimir, xiao, hong. 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. From this approximation and the inverse transformation back to the time domain, we can show that is possible to implement. Electromagnetic wave theory pdf free download epdf.
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. Application of nonorthogonal bases in the theory of light. Light scattering theories and computer codes sciencedirect. Readers can also develop their own codes according to the theory or routine described in the book to find subsequent solutions of complicated structures. Denisenko encyclopedia of life support systems eolss div jq g 11 je.
Spheroidal wave functions in electromagnetic theory request pdf. Spheroidal wave functions in electromagnetic theory nasaads. Gg the given functions on righthand sides of 11 are usually equal to zero, but appear in. The vector wave function solution of the diffraction of. Wolfram, the mathematica book wolfram mediacambridge university press, 1999. 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.
Unesco eolss sample chapters computational methods and algorithms vol. We explore a number of issues related to this problem, including the effective computation of the corresponding slepzan functions for. Plane, cylindrical, and spherical electromagnetic waves. A classic resource for working with special functions, standard trig, and exponential logarithmic definitions and extensions, it features 29. Suitable mathematica programs using spheroidal wave functions to compute scattering by spheroidal particles have been published in a book by li et al. In part i these vector functions are defined and the expansions of plane. Parabolic equation methods for electromagnetic wave. With analysis of electromagnetic fields and waves, reinhold pregla describes an important and powerful method for analyzing electromagnetic waves.
Lewei li, xiaokang kang, mookseng leong spheroidal wave functions in electromagnetic theory published. Wave theory of information by massimo franceschetti. Internal and nearsurface electromagnetic fields for an infinite cylinder illuminated by an arbitrary focused beam, j. Theory and computation of spheroidal wavefunctions. A method other than the extendedboundarycondition method ebcm to compute the t matrix for electromagnetic scattering is presented. Using prolate spheroidal wave functions chunyang chen, student member, ieee, and p. Mathieu functions and spheroidal wave functions to diffraction theory. The flagship monograph addressing the spheroidal wave function and its pertinence to computational electromagnetics spheroidal wave functions in electromagnetic theory presents in detail the. These have become the dominant tool for assessing clearair and terrain effects on radiowave propagation and are growing increasingly popular for solving scattering problems. Significant currents can create a large enough voltage at the gap to cause a spark, indicating the presence of the electromagnetic wave.
Part of the textbooks in telecommunication engineering book series tte. The analysis utilizes oblate spheroidal vector wave functions. Electromagnetic field theory is often the least popular course in the electrical engineering curriculum. Prolate spheroidal wave functions and applications. On the asymptotic expansion of the spheroidal wave functions and its eigenvalues for complex size parameter, studies appl. The flagship monograph addressing the spheroidal wave function and its pertinence to computational electromagnetics. These theorems concern the vector wave functions and with which can be obtained and used to treat various electromagnetic problems such as multiple scattering of a plane wave from prolate spheroids with arbitrary spacings and orientations of their axes of symmetry or radiation from thinwire antennas. Describes the general analysis principles for electromagnetic fields. Advanced modeling in computational electromagnetic. Spheroidal wave functions in electromagnetic theory is a fundamental reference for scientists, engineers, and graduate students practicing modern computational electromagnetics or applied physics. The field let transmitted in the region 2 book s contribution to the field of electromagnetics.
Meixner developed the theory of spheroidal wave functions with arbitrary. Spheroidal wave functions in electromagnetic theory book. If you have a user account, you will need to reset your password the next time you login. Scattering of electromagnetic waves by spheroidal particles. This prediction is effectively relevant since the pswfs are deeply studied in mathematical physics and are classically defined as a series of normalized legendre polynomials which are well known as special functions of mathematics. The rational function approximation of this impedance can be obtained by truncating the infinite products. It therefore moves the charges in the metal loop, causing a current. Understand the relationship between information theory and the physics of wave propagation with this expert guide. Monographs tying together many aspects of the theory of spheroidal wave functions were written by strutt, stratton et al.
Originally, the spheroidal wave functions were introduced by c. Spheroidal wave functions are solutions of the helmholtz equation that are found by writing the equation in spheroidal coordinates and applying the technique of separation of variables, just like the use of spherical coordinates lead to spherical harmonics. For more references on this subject using spheroidal wave function i would like to refer the interested reader to this book. Electromagnetic theory 18 56 6 greens functions greens functions are widely used in electromagnetic and other field theories. Balancing fundamental theory with engineering applications, it describes the mechanism and limits for the representation and communication of information using electromagnetic waves. Electromagnetic field theory a problemsolving approach. Introduction, scope and limitation of the report glance through the scientific literature of the last decade reveals an. 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. Numerical methods in electromagnetic scattering theory.1579 859 1339 1431 362 911 352 214 1154 1399 1471 625 546 1456 1239 970 337 223 801 748 1210 387 519 835 691 758 177 319 1173 1032 1201 1429 830 1242 1392