The Method Of Transfer Matrix Solving Green's Function In Anisotropic Plane Layered Medium

The calculation of the dyadic Green‘s function in planar layered media has important application value in many electromagnetic engineering problems.The purpose of this thesis is to find a simple,fast and high precision algorithm for the solution of Green‘s function in an anisotropic planar multilayered medium.Firstly,the analytic expression of Green‘s function in cylindrical coordinate system is deduced based on the dyadic Green‘s function of no coordinate form in isotropic medium,and the spatial variation characteristics of Green‘s function of current point and magnetic point element are inspected in detail.The expression of the spatial spectrum of the electromagnetic field of magnetic point element in homogeneous anisotropic medium under cylindrical coordinate system is derived by the Sommerfeld identity equation.Secondly,The transfer matrix method is built up to solve the Green‘s function problems in an anisotropic planar multilayered medium,combined with an equivalent boundary condition method for dealing with point source is proposed,which replaces the Sommerfeld identity equation and the current element and the magnetic element is equivalent to a special boundary condition of the current and surface current distribution on the plane where the source is located,which simplifies the way of dealing with the point source and forms layer boundary unified processing mechanism.The extended Hankel transform is used to derive the state vector of the transverse field and spatial spectrum representation of the state equation,which effectively reduces the computational complexity of the integral function of the Green‘s function from the spatial spectral domain to the spatial domain.The transmission matrix is used to replace the propagation matrix,which simplifies the derivation and calculation of the reflection and transmission coefficients and their recursive formulas in the layered medium.Finally,on the basis of the above ways,the Green‘s function calculation program of anisotropic planar multilayered medium is developed in C ++ language.The feasibility and efficiency of the way are verified by the comparison of the Green‘s function in uniform isotropic medium.In addition,it is theoretically proved the expression of the spatial spectral domain of the electromagnetic field of magnetic point element in the uniform anisotropic medium obtained by this article is exactly the same as the expression of the spatial spectrum of the electromagnetic field of magnetic point element derived by the Sommerfeld identity equation.At the end,the simulation diagram of the Green's function in the planar multilayered medium and the simulation diagram of the Green's function in the homogeneous medium are given.