Dyadic Green's function for a multilayered planar medium-a dyadic eigenfunction approach

A new formulation of the dyadic Green's function for a planarly layered medium is presented, based on dyadic eigenfunctions of the Green's function operator. The general development of the dyadic Green's function is shown, resulting in a three-dimensional purely spectral representation. The spectral form is converted to a Hankel-function form using standard techniques, analogous to the sum-of-residues plus branch-cut representation often obtained from the Sommerfeld Green's function. Advantages and disadvantages of both the eigenfunction and Hankel function forms are outlined, and compared to other Green's function representations. Examples of the Green's dyadic for free space and for a grounded dielectric slab environment are provided, and the role of the continuous and discrete spectrum is discussed.