  We developed a novel universal eigenvalue analysis for 2D arbitrary
nanostructures comprising dispersive and lossy materials. The complex
dispersion relation (or complex Bloch band structure) of a metallic grating is
rigorously calculated by the proposed algorithm with the finite-difference
implementation. The abnormally large group velocity is observed at a plasmonic
band edge with a large attenuation constant. Interestingly, we found the
abnormal group velocity is caused by the leaky (radiation) loss not by metallic
absorption (Ohmic) loss. The periodically modulated surface of the grating
significantly modifies the original dispersion relation of the semi-infinite
dielectric-metal structure and induces the extraordinarily large group
velocity, which is different from the near-zero group velocity at photonic band
edge. The work is fundamentally important to the design of plasmonic
nanostructures.
