  A theoretical study of surface plasmon polaritons (SPPs) in ultrathin lossy
metal films is presented. The dispersion relation of such films is well known
and can be solved numerically to obtain a combination of long-range (LR-) and
short-range (SR-) eigenmodes. In this contribution, a simple solution for the
SR-SPPs is derived. An approximation for the LR- eigenmodes can be found
elsewhere. To validate the approximation, a two dimensional (2D) periodic array
of small holes is studied subsequently. The spectral response of the array is
obtained by full-wave simulations and the results compared with those
calculated analytically, showing an excellent agreement for small holes.
