Research On Series Expansion Method Of The Dyadic Green’s Function For Cylindrical Layered Media Based On Perfectly Matched Layers

The effective calculation method of the dyadic Green’s function of layered media (plane layered media, cylindrical layered media, and spherical layered media) is the foundation of the full-wave electromagnetic simulation of layered medium structures by means of the method of moments. The numerical method of the dyadic Green’s function of plane layered media is deeply studied first of all, and a lot of methods have been developed, typically including the Discrete Complex Image Method (DCIM). Recent years, the series expansion method based on the perfectly matched layer has been proposed, and this method replaces the original dyadic Green’s function of plane layered media with the Green’s function of the corresponding plate waveguide structure with the PML. The Green’s function of the plate waveguide structure can be expressed as series expansion of mode functions without any numerical integration, but the efficient algorithms for accurately locating all mode poles are needed. Like plane layered medium structures, cylindrical layered medium structures are also an important type of struc-tures. Compared with the Green’s function of the plane layered media, the Green’s function of the cylindrical layered media is more complex. The center of this thesis is to establish series expansion method for Green’s function of the cylindrical layered media. Firstly, based on the existing theory, the mathematical expressions for every coordinate components of the Green’s function of the cylindrical layered media is derived. Secondly, a recursive algorithm is proposed to achieve separation of numerator and denominator of the spectral domain Green’s function, resulting in the dispersion equation for determining all mode poles. Thirdly, mathematical ho-motopy method is applied to accurately locate all modes of the spectral domain Green’s function of the cylindrical layered media with the PML. Lastly, the spatial Green’s function of the cylin-drical layered media with the PML is expressed as an infinite series expansion using the residue theorem of complex functions. The main contributions of this paper are as follows:1. The dispersion equation based on which one can locate all mode poles with high nu-merical stability is derived. Deforming reflection and transmission coefficient matrices recursively based on the recursive form of the spectral Green’s function results in a new form of the dispersion equation, which is particularly suitable for accurately locating all Berenger mode poles through the homotopy method. Two forms of series expansion for-mulae are given, which are used in two cases, respectively:One is the case when both the field point and source point are in the same layer, the other is the case when the field point and source point are in different layers. Besides, it is proved that when the field point and source point are in different layers, all of mode poles of the spectral Green’s function are of second order.2. The implementation of locating mode poles of the spectral Green’s function using the homotopy method is proposed, including two steps:1) Locating all mode poles of the spectral Green’s function of the cylindrical layered structure with lossless media:The poles on the axis are found by using the di-chotomy, and the estimation formula for isolating poles is established theoretically. The poles (complex mode poles) off the axis are sketchily located by using the quadratic polynomial estimation. Then the complex modes are accurately located by the Newton-Raphson iteration.2) Locating all mode poles of the spectral Green’s function of the cylindrical layered structure with the PML:The poles obtained by the first step being used as starting points, the required poles are found by the homotopy method. Here, an algorithm for accelerating the location of Berenger mode poles is also proposed.3. By comparing the series expansion method with the direct integration method, two kinds of error sources are recognised:the model error and the truncation error. Besides, the effect of both the PML parameters and the number of mode poles used in the series expansion on the error curve is numerically analyzed.