Unified Implementation and Cross-Validation of the Integral Equation-Based Formulations for the Characteristic Modes of Dielectric Bodies

Abstract

Theory of characteristic modes (TCM) can provide physical insight into the radiation mechanism of arbitrarily-shaped electromagnetic objects. However, how to compute the characteristic modes (CMs) of different structures is still an open problem. Even for the calculation of CMs of an isolated dielectric body, there are eleven integral equation (IE)-based formulations which result in different modal solutions. Such kind of non-uniqueness of solutions makes CMs community confused. One of the objectives of this paper is to outline the differences among all existing IE-based formulations for the CMs of dielectric bodies. The existing formulations are briefly reviewed and carefully compared. We present a procedure to implement the different formulations in a unified manner. Then, we make a complete comparison of the numerical results of existing methods for a dielectric cylinder, which also serves as cross-validation for these approaches. We hope that this paper will help researchers understand the calculation of CMs of dielectric bodies and explore the computation methods of CMs for more complex objects.

Unified Theory of Characteristic Modes: Part II -- Tracking, Losses, and FEM Evaluation

“…The modal significance |t n | and phase φ n evaluated from (1) and s n = 1 + 2t n are depicted in Fig. 2 showing five distinct peaks corresponding to TE 01 , HEM 11 , HEM 12 , TM 01 , and HEM 21 modes, in agreement with the results in [28], [29]. The corresponding surface currents calculated from…”

“…The benchmark example from [27]- [29] consisting of a cylindrical dielectric resonator with height 4.6 mm, radius 5.25 mm, and relative permittivity ε r = 38 is used to illustrate the potential of the proposed methodology on a challenging and well-studied case. The PMCHWT [30]- [32] formulation is used to obtain the impedance matrix.…”

Prediction of Experimental Electromagnetic Coupling to a UAV Model Using Characteristic Mode Analysis

“…CMA is a full-wave electromagnetic technique that decomposes the total surface current coupled to a scatterer into a set of fundamental modes, called eigen-currents, and calculates the relative importance of each mode at any frequency [36]. The modes can be calculated using the following eigenvalue equation [13]:…”

Variant Characteristic Mode Equations Using Different Power Operators for Material Bodies

“…But VOLUME XX, 2021 regrettably, both the measures in [8] and [9] were found to generate extra modes that were inconsistent with analytical solutions [10]. Recently, a unified manner [11] to implement the approaches in [7]- [10] was introduced, but no spurious modes were found for a specific example by using the schemes in [9]- [10]. In addition, instead of using the PMCHWT equations to construct the GEE, the external EFIE or MFIE were employed to play the role, while the internal equations were used to express the dependent relation of the electric and magnetic currents [12], which was reported able to suppress spurious modes for lossless cases, but lossy cases were not tested.…”

“…To summarize, eliminating one of the electric or magnetic current is highly recommended but not sufficient to get rid of the spurious or extra modes. And the approaches presented in [7]- [9] and [11]- [13] are just for lossless materials and further tests for lossy cases are needed.…”