Exact Eigenfrequencies in Concentric Prolate Spheroidal-Spherical Metallic Cavities

Abstract

In this letter the eigenfrequencies in prolate spheroidal-spherical and spherical-spheroidal cavities are calculated. The metallic boundaries of the cavities are perfect conductors. The matrix equations are constructed using expansions connecting the spherical and the spheroidal eigenvectors. Then, by truncating the resulting matrices, the exact eigenfrequencies are obtained as the converged roots of determinantal equations. This method allows to study elongated spheroidal cavities that existing methods fail to handle. The method is validated by comparison with published results from the literature. Original results for spheroids having large eccentricities are given for various values of the parameters.

Robust Calculation of the Modes in Parabolic Cylinder Metallic Waveguides by Means of a Root-Finding Method for Bivariate Functions

“…This algorithm essentially uses Chebychev polynomials as interpolants of the functions that make up the bivariate system in ( 20)- (23), with proper coefficients P ij , Q ij for the approximation [25]. Thus, these four bivariate systems would be defined accordingly in our problem as: (25) where each pair p, q is replaced, after being properly scaled, by the pair of functions in (20) for even TM modes, in (21) for odd TM modes, in (22) for even TE modes, and in (23) for odd TE modes. The Chebychev polynomials T j (x) take the following usual form:…”

“…In this context, the emerging root-finding algorithms play a major role. The problem of the determination of roots of characteristic functions is a classic problem present in a large number of works in applied electromagnetics, with very recent advances in diverse areas such as wave propagation [17], multilayer structures [18]- [20] or metallic cavities and waveguides [21]- [24]. In the area of applied mathematics, a recent work has been proposed for computing the solutions of a non-linear system of two bivariate equations [25], applied initially as the first systematic root-finding approach for the parabolic cylinder waveguide in [26].…”

Analytical expressions of the Q ‐factor for the complete resonant mode spectrum of the equilateral triangular waveguide cavity

“…In this context, it is crucial to have analytic or quasi-analytic reference models to check the numerical CAD computations as it happens in diverse fields of applied electromagnetism [12,13]. In this Letter, this goal is fully achieved by providing simple and closed-form expressions for the unloaded Q-factor in the equilateral triangular cavity, whose computation is extremely fast and direct.…”