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The interaction of surface plasmon polariton (SPPs) on a periodic array of metal holes is investigated in theory and experiment. Extraordinary transmission through a silver film perforated with square and rectangular shaped hole arrays in a square lattice was demonstrated. When the squared hole size is close to a half lattice constant all, the split of the degenerate (plusmn1,0) Ag/Si and (0,plusmn1) Ag/Si modes into two peaks becomes apparent. Surface plasmon polaritons dispersion relations demonstrate the photonic bandgap opens up when the size of the squared hole exceeds a half lattice constant all. Additionally, the SP dispersion relations of the square hole array with different aspect ratios of holes were measured that demonstrate that the localized surface plasmons (LSPs) were created by the coupling of surface plasmons between the edges of the rectangular holes.