  The quasi-bound electromagnetic modes for the arrays of nanoholes perforated
in thin gold film are analyzed both numerically by the rigorous coupled wave
analysis (RCWA) method and semi-analytically by the coupled mode method. It is
shown that when the size of the nanohole occupies large portion of the unit
cell, the surface plasmon polaritons (SPPs) at both sides of the film are
combined by the higher order waveguide modes of the holes to produce multipole
surface plasmons: coupled surface plasmon modes with multipole texture on the
electric field distributions. Further, it is revealed that the multipole
texture either enhances or suppresses the couplings between SPPs depending on
their diffraction orders and also causes band inversion and reconstruction in
the coupled SPP band structure. Due to the multipole nature of the quasi-bound
modes, multiple dark modes coexist to produce variety of Fano resonance
structures on the transmission and reflection spectra.
