Investigation of the Leaky-Wave Characteristics of a Cylindrical Dielectric Rod Using the Coefficient Matrix of the System of Characteristic Equations and Davidenko’s Method

Abstract

An open dielectric waveguide includes both guided propagating modes within the waveguide and radiating and evanescent modes that propagate transversely outside the waveguide. In this study, the leaky-wave characteristics of a cylindrical dielectric rod are investigated using the coefficient matrix of the system of characteristic equations and Davidenko’s method. Using the coefficient matrix of the system of characteristic equations simplified the derivative(s) required to use Davidenko’s method. The results obtained for a 10-mm radius structure with a relative dielectric constant of 4 showed that a second antenna mode region existed for higher-order hybrid HE modes and lower-order transverse magnetic (TM) modes. However, it did not exist for transverse electric (TE) modes. Additionally, the hybrid HE modes had larger leaky-wave spectrum and antenna mode regions than both the TE and TM modes. This demonstrates that for antenna applications, hybrid HE modes supply a wider frequency spectrum.

Guiding and Leakage Dispersion Characteristic of TM01Mode in a Circular Dielectric Rod

“…In previous studies, TM and TE leaky-wave modes for a circular dielectric rod were obtained from Davidenko's method based on the closed function expression of the structure [24][25][26], and HEM leaky-wave modes were obtained from Davidenko's method based on the coefficients matrix of the system of characteristic equations [27,28].Davidenko's method, requiring derivation of the dispersion equation with respect to the propagation constant, is insensitive to select initial guess and an efficient algorithm to find complex roots of multiple dimension systems of nonlinear algebraic equations. e approximation based on the coefficient matrix of the system of characteristic equations in references [27,28] simplifies the derivation of the characteristic equation with respect to c, required by Davidenko's method. Hereby, Davidenko's method can be used for the structures belonging to complex characteristic equations with numerous variables depending on the propagation constant.…”

“…While only TE and TM modes could be obtained by using auxiliary mathematical software for derivations in previous studies, HEM modes of the circular dielectric rod were obtained from completely analytical expressions for the first time in the literature. Detailed analytical expressions for the approach based on Davidenko's method and the coefficient matrix of the system of characteristic equations are presented in references [27,28].…”

“…e dispersion equation in the form of F(ω; c) � 0 is transformed into a system of two coupled first-order ODE's by Davidenko's method as below. e standard procedures and expressions for Davidenko's method are given in reference studies [24,[26][27][28][29].…”

“…). e numerical solutions can be calculated when the presented equations above substitute in the equations given in [27,28] with. e leakage dispersion characteristics of TM, TE, and HEM modes of the circular dielectric rod with a � 10 mm and ε r � 4 were presented in [27].…”

“…e numerical solutions can be calculated when the presented equations above substitute in the equations given in [27,28] with. e leakage dispersion characteristics of TM, TE, and HEM modes of the circular dielectric rod with a � 10 mm and ε r � 4 were presented in [27]. e aim of the study is to show the correspondence between analytic results and the simulations executed on CST microwave studio software.…”