Optical surface waves over metallo-dielectric nanostructures: Sommerfeld   integrals revisited
  The asymptotic closed-form solution to the fundamental diffraction problem of a linear horizontal Hertzian dipole radiating over the metallo-dielectric interface is provided. For observation points just above the interface, we confirm that the total surface near-field is the sum of two components: a long-range surface plasmon polariton and a short-range radiative cylindrical wave. The relative phases, amplitudes and damping functions of each component are quantitatively elucidated through simple analytic expressions for the entire range of propagation: near and asymptotic. Validation of the analytic solution is performed by comparing the predictions of a dipolar model with recently published data 
Bora Ung and Yunlong Sheng