  Optical properties of periodic arrays of nanoholes of a triangular shape with
experimentally realizable parameters are examined in both linear and nonlinear
regimes. Utilizing fully vectorial three-dimensional approach based on the
nonlinear hydrodynamic Drude model describing metal coupled to Maxwells
equations and Bloch equations for molecular emitters we analyze linear
transmission, reflection, and nonlinear power spectra. Rigorous numerical
calculations demonstrating second and third harmonic generation by the
triangular hole arrays are performed. It is shown that both the Coulomb
interaction of conduction electrons and the convective term contribute on equal
footing to the nonlinear response of metal. It is demonstrated that the energy
conversion efficiency in the second harmonic process is the highest when the
system is pumped at the localized surface plasmon resonance. When molecular
emitters are placed on a surface of the hole array lineshapes of the second
harmonic signal exhibits three peaks corresponding to second harmonics of the
localized surface plasmon mode and upper and lower polaritonic states.
