Electromagnetic Scattering From a Metallic Prolate or Oblate Spheroid Using Asymptotic Expansions on Spheroidal Eigenvectors

Exact Eigenfrequencies in Concentric Prolate Spheroidal-Spherical Metallic Cavities

“…The first set is given by (3) TABLE I COMPARISON OF THE NORMALIZED EIGENFREQUENCIES OBTAINED FROM THE CURRENT WORK WITH [4] while the second set is obtained from (3) if is replaced with and with . The cumbersome expressions for and are given by (5)-(8) of [9]. For each different value of , the set in (3) and its accompanying one compose a matrix of infinite size of the form (4) For numerical computations, the above matrix must be truncated, and the roots of the equation represent the desired normalized eigenfrequencies.…”

“…If is the truncation order, then is of the order for . For (where is the zero matrix) since is common factor for and [9]. Thus, for and which are of the order .…”

Efficient Calculation of the Electromagnetic Scattering by Lossless or Lossy, Prolate or Oblate Dielectric Spheroids

“…It is obvious that a complete pure closed-from analytical method for this problem is absent from the literature. Recently, we have developed an efficient closed-form solution for the electromagnetic scattering by metallic spheroids [7] using asymptotic expansions on spheroidal eigenvectors, and a preliminary study on scattering by dielectric spheroids [8]. However, the accuracy of the preliminary method in [8] was not examined, the range of its applicability in terms of the eccentricity and the analytical closed-form tools for computing needs were not given.…”

“…Thus, the present work can be considered as a considerable extension of [8], where an extensive analysis on how the method works is given, and all the aforementioned issues are discussed. In general, in this study we extend the methodology from [7] to construct an efficient method for the electromagnetic scattering by dielectric spheroids. As will be shown soon, it turns out that this is not a trivial extension.…”

“…Although the method given in [7] is also applicable for dielectric spheroids, from our previous experience on scattering problems by spheroids [7], [9], it is more convenient to construct our closed-form solution by expressing the fields in terms of spherical eigenvectors and use a shape perturbation method, rather than expressing them in terms of spheroidal eigenvectors and applying asymptotic techniques. The reason for this is that, if one employs the method in [7], then he has to deal with the asymptotic properties, not only of the spheroidal wave functions, but also of the related eigenvalues, of the normalization constants, and of the cumbersome inner products relating integrals of the angular spheroidal functions. On the other hand, the shape perturbation method relies only on the asymptotic expansions of the spherical eigenvectors in terms of the standard spherical Bessel functions.…”