EBCM for Electromagnetic Modeling of Gyrotropic BoRs

We employ the extended boundary condition method (EBCM) that we properly extend so as to describe gyroelectric and gyromagnetic (i.e., gyrotropic) anisotropy and report on the electromagnetic (EM) complex resonances of magnetooptic (i.e., gyroelectric) bodies of revolution (BoRs), as well as on the complex magnetic plasmon resonances (MPRs) of ferrite (i.e., gyromagnetic) BoRs. The proposed extension is based on an alternative scheme for the expansion of the EM field inside a gyrotropic medium, namely, a discrete eigenfunction (DE) expansion in terms of spherical vector wave functions (SVWFs). This approach provides the transition matrix (namely, T-matrix) that allows not only for the direct computation of the scattered field from the incident one, but also for the determination of the complex resonances of open (i.e., situated in free space) gyrotropic BoR resonators. The EBCM is validated on two levels: first, by calculating the EM scattering from various BoRs, including anisotropic spheroids, cylinders, and rods, and comparing with HFSS commercial software; second, by computing the complex eigenfrequency spectrum of gyroelectric spheroidal resonators and comparing with a recently developed rigorous technique for the EM modeling of anisotropic spheroids.

I. Introduction

The complex resonances of open electromagnetic (EM) structures are of particular interest since such resonators are widely used as antenna or millimeter-wave elements [1], microwave ferrite filters [2], or for optical applications utilizing the whispering gallery mode technology [3]. Although spherical particles, especially isotropic ones, comprise a special class of open resonators where mode degeneracy takes place, in nonspherical particles, the degeneracy of Mie modes is removed, and the interplay of shape and material anisotropy may allow for enhanced and controllable magneto-optical effects, such as Hall photon currents [4]. However, the modeling of nonspherical geometries calls for a method that can overcome the limitation of the spherical shape. In this context, the extended boundary condition method (EBCM) may be readily employed. Since its introduction by Waterman [5], the EBCM—also known as the null-field method—has been proven to be a powerful tool for the analysis of EM scattering by arbitrarily shaped objects. In particular, EBCM has been widely used to cast the scattering problem in matrix form and calculate the so-called T-matrix [6]. The method has been employed for the description of EM scattering by a variety of geometries, such as axisymmetric bodies [7], ellipsoids [8], composite objects [9], for internal field computation [10], or for the calculation of complex eigenfrequencies of isotropic resonators [11], [12]. In addition, several schemes have been proposed to overcome its limitations for the treatment of highly aspherical and electrically large objects [13], [14]. While aforementioned works deal with objects composed of isotropic materials, extensions of the EBCM have been proposed for uniaxial [15] and biaxial [16] materials, arbitrary permittivity tensors [17], and various complex anisotropic media [18]–[20]. However, to the best of our knowledge, a systematic application of EBCM to the modeling of gyrotropic bodies has not been reported in the literature.