Eigenfunctional representation of dyadic Green's functions in multilayered gyrotropic chiral media

Abstract

Studying electromagnetic waves in complex media has been an important research topic due to its useful applications and scientific significance of its physical performance. Dyadic Green's functions (DGFs), as a mathematical kernel or a dielectric medium response, have long been a valuable tool in solving both source-free and source-incorporated electromagnetic boundary value problems for electromagnetic scattering, radiation and propagation phenomena. A complete eigenfunctional expansion of the dyadic Green's functions for an unbounded and a planar, arbitrary multilayered gyrotropic chiral media is formulated in terms of the vector wavefunctions. After a general representation of Green's dyadics is obtained, the scattering coefficients of Green's dyadics are determined from the boundary conditions at each interface and are expressed in a greatly compact form of recurrence matrices. In the formulation of Green's dyadics and their scattering coefficients, three cases are considered, i.e. the current source is immersed in (1) the first, (2) the intermediate, and (3) the last regions, respectively. Although the dyadic Green's functions for an unbounded gyroelectric medium has been reported in the literature, we here present not only unbounded but also multilayered DGFs for the gyrotropic chiral media. The explicit representation of the DGFs after reduction to the gyroelectric or isotropic case agrees well with those existing corresponding results.

Green’s Functions of Multi-Layered Plane Media with Arbitrary Boundary Conditions and Its Application on the Analysis of the Meander Line Slow-Wave Structure

“…The Green's functions, including dyadic Green's functions (DGF) and scalar Green's functions (SGF), are powerful tools in electromagnetic theory [2][3][4], because the relationship between the field and excitation sources can be easily described by them. As a result, many years of effort have been devoted to obtaining Green's functions for inhomogeneous media [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] There are many approximation and numerical methods that have been utilized for calculating the DGF and SGF, such as the finite sum superposition method [3], the total least squares method [4], the fast full-mode method [5], the numerical modified steepest descent path method [5] and the numerically stable analysis method [6]. In addition, the pure theoretical derivations of Green's functions for the stratified media, without numerical approximation and error, were also pursued for a long time [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]…”

“…As a result, many years of effort have been devoted to obtaining Green's functions for inhomogeneous media [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] There are many approximation and numerical methods that have been utilized for calculating the DGF and SGF, such as the finite sum superposition method [3], the total least squares method [4], the fast full-mode method [5], the numerical modified steepest descent path method [5] and the numerically stable analysis method [6]. In addition, the pure theoretical derivations of Green's functions for the stratified media, without numerical approximation and error, were also pursued for a long time [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] The form of the dyadic Green's function has been presented based on the methods of generation function expansions [7][8][9][10]…”

Electromagnetic reflection and transmission from a planar isotropic chiral-uniaxial chiral interface with optical axis normal to interface

“…The synthesized materials can be designed to have their permittivity and permeability artificially of negative or positive values. Studies relevant to these materials focused on isotropic chiral media have been carried out by several authors [5][6][7][8][9][10][11][12]. However, from researches in chiral and in uniaxial chiral materials, it has been found that materials with complex properties can find more possible applications in the microwave and optical regions [13].…”

Analysis of electromagnetic field transmitted by a quadratic inhomogeneous slab composed of chiral medium

“…For example, a chiral slab with negative refractive index has been shown to act as a perfect lens having subwavelength for circularly polarized waves [2,3]. Many other applications of the chiral metamaterials include but not limited to waveguides, antennas, polarization rotators, and cloaking surfaces [4][5][6][7][8][9][10].…”