Momentum-dependent group velocity of surface plasmon polaritons in two-dimensional metallic nanohole array

We determine the momentum-dependent group velocities of ( ± 1,0) and (0, ± 1) Bloch-like surface plasmon polaritons (SPPs) in two-dimensional Au nanohole array by measuring their propagation lengths and decay lifetimes at different SPP propagation length via angle- and polarization-resolved reflectivity spectroscopy and real- and Fourier-space microscopy. We find the decay length and lifetime, as well as group velocity, are highly dependent on the propagation direction. In particular, close to the Γ-M direction where two SPPs begin to interfere, the group velocity decreases due to the increase of the standing wave character. More importantly, the two SPPs are strongly interacted with each other at the Γ-M direction, resulting in forming the dark and bright modes. We find the group velocity of the dark mode is higher that of the bright mode despite its higher quality factor, or longer decay lifetime. We attribute such difference to the distinct field symmetries of dark and bright modes, yielding different effective indices. While bright mode has fields mostly concentrated at the flat metal region to produce higher effective index and therefore lower velocity, the fields of the dark mode are located near the air hole, resulting in higher velocity.