Eigenfunctional Representation of Dyadic Green's Functions in Cylindrically Multilayered Gyroelectric Chiral Media

Abstract

Abstract-This paper presents an eigenfunction expansion of the electric-type dyadic Green's functions for both a unbounded gyroelectric chiral medium and a cylindrically-multilayered gyroelectric chiral medium in terms of the cylindrical vector wave functions. The unbounded and scattering Green dyadics are formulated based on the principle of scattering superposition for the electromagnetic waves, namely, the direct wave and scattered waves. First, the unbounded dyadic Green's functions are correctly derived and some mistakes occurring in the literature are pointed out. Secondly, the scattering dyadic Green's functions are formulated and their coefficients are obtained from the boundary conditions at each interface. These coefficients are expressed in a compact form of recurrence matrices; coupling between TE and TM modes are considered and various wave modes are decomposed one from another. Finally, three cases, where the impressed current source are located in the first, the intermediate, and the last regions respectively, are taken into account in the mathematical manipulation of the coefficient recurrence matrices for the dyadic Green's functions.

Modified Spherical Wave Functions With Anisotropy Ratio: Application to the Analysis of Scattering by Multilayered Anisotropic Shells

“…For planarly multilayered media, DGFs have been derived [11]- [13]. For cylindrical multilayered media, DGFs were constructed for chiral media [14]. However, due to the complexity of the parameter tensors, plane wave expansion along with the Fourier transform and the theory of TE and TM decomposition are widely employed in the analysis of anisotropic media [15].…”

Cylindrical Vector Wave Function Representation of Green's Dyadic in Gyrotropic Bianisotropic Media

“…where the vector expansion coefficients a n (h, λ), b n (h, λ) and c n (h, λ) are obtained by substituting (11) and (7) into (6), which the dyadic Green's function must satisfy. Noting the common properties of the vector wave functions [1]…”

“…These complex media include chiral [5]; Faraday chiral [6]; uniaxial chiral [7] and [8]; gyroelectric chiral [9][10][11]; uniaxial bianisotropic [12] and [13]; transversely bianisotropic uniaxial [14]; biisotropic [15]; and gyrotropic bianisotropic [16] and [17] materials. A generalization of these materials mentioned so far would be the gyrotropic bianisotropic media which have all the constitutive dyadics expressed in coaxially gyrotropic carrying a total of twelve independent scalars/pseudoscalars not necessarily constrained by losslessness, reciprocity [2], or uniformity conditions.…”

Analysis of Radiation From a Cylindrical-Rectanguar Microstrip Patch Antenna Loaded With a Supersrate and an Air Gap, Using the Electric Surface Current Model

“…In [1,2], the cavity model has been used to analyze cylindrical-rectangular patch antennas, printed on a dielectric substrate, while in [3,4] the method of moments (MoM) has been used for analyzing them. Similar antennas printed on a chiral substrate have been analyzed in [5] using the MoM and the dyadic Green's functions derived for the problem with reference to [6,7]. The MoM has been used in [8,9] also, but for analyzing a cylindrical-rectangular patch antenna loaded with a lossless dielectric superstrate.…”