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.