Abstract
A method was proposed for solving the dyadic Green’s functions (DGF) and scalar Green’s functions (SGF) of multi-layered plane media in this paper. The DGF and SGF were expressed in matrix form, where the variables of the boundary conditions (BCs) can be separated in matrix form. The obtained DGF and SGF are in explicit form and suitable for arbitrary boundary conditions, owing to the matrix form expression and the separable variables of the BCs. The Green’s functions with typical BCs were obtained, and the dispersion characteristic of the meander line slow-wave structure (ML-SWS) is analyzed based on the proposed DGF. The relative error between the theoretical results and the simulated ones with different relative permittivity is under 3%, which demonstrates that the proposed DGF is suitable for electromagnetic analysis to complicated structure including the ML-SWS.
Highlights
The dyadic Green’s functions (DGF) and scalar Green’s functions (SGF) were expressed in matrix form, where the variables of the boundary conditions (BCs) can be separated in matrix form
The obtained DGF and SGF are in explicit form and suitable for arbitrary boundary conditions, owing to the matrix form expression and the separable variables of the BCs
The relative error between the theoretical results and the simulated ones with different relative permittivity is under 3%, which demonstrates that the proposed DGF is suitable for electromagnetic analysis to complicated structure including the meander line slow-wave structure (ML-SWS)
Summary
Since the exact results of the two-layered planar dielectric model were deduced [1], more and more people have been engaged in research of the electromagnetic field for multi-layered media [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22], which has been widely utilized for the analysis of dielectric waveguides, printed circuit boards, antennas and sensors [23,24,25,26]. If the BCs has been contained in the generation function with explicit form, the corresponding Green’s function can be simple and in explicit form Methods such as the perturbative approach [16], operator theories [18,19,20], wave superposition [21] and transmission line theories [17,18,21,22] are introduced for obtaining the Green’s function and exactly analyzing the multi-layered media. The DGF and SGF were obtained in explicit form with matrixes, and corresponding equations built from BCs at the top and the bottom of the multi-layered media are independent and easy to solve, which means that the equations of the structure based on the proposed DGF may be more simple with clearer physical characteristics and that the formulae may be expressed with the computer code more friendly. The symbol ∑ will be replaced by , if the corresponding eigenvalue is continuous
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