Recursive algorithm and accurate computation of dyadic Green's functions for stratified uniaxial anisotropic media

A recursive algorithm is adopted for the computation of dyadic Green’s functions in three-dimensional stratified uniaxial anisotropic media with arbitrary number of layers. Three linear equation groups for computing the coefficients of the Som- merfeld integrals are obtained according to the continuity condition of electric and magnetic fields across the interface between different layers, which are in corre- spondence with the TM wave produced by a vertical unit electric dipole and the TE or TM wave produced by a horizontal unit electric dipole, respectively. All the linear equation groups can be solved via the recursive algorithm. The dyadic Green’s functions with source point and field point being in any layer can be conveniently obtained by merely changing the position of the elements within the source term of the linear equation groups. The problem of singularities occurring in the Sommer- feld integrals is efficiently solved by deforming the integration path in the complex plane. The expression of the dyadic Green’s functions provided by this paper is terse in form and is easy to be programmed, and it does not overflow. Theoretical analysis and numerical examples show the accuracy and effectivity of the algo-rithm.