  This report concerns with the theoretical studies of SPP Bloch waves in
arrays of cylindrical holes. Most analytical solutions are simplified,
approximate and fitted, thus leading to wrong design parameters. A rigorous
analytical solution that can accurately predict the desired dimensions
associated with hole arrays is complex to derive. Finite element analysis
(FEA), on the other hand, offers extensive capabilities for modelling and
simulating the response of periodic structures such as that of an infinite
array of holes. In this chapter, a square array of cylindrical holes is
modelled numerically. A simple analytical model is presented (not for design
purposes) only to identify the origin of the alleged (1,1) and (0,2) modes and
the results are compared to the numerical ones. Changes in the transmission
spectrum vs the refractive index of the surrounding dielectric when illuminated
with a linearly polarized light at normal incidence is studied. Circumstances
in which an obliquely incident light changes to the SPP momentum are also
identified.
