We study the dispersions of plasmonic bands that arise from the coupling of
electric quadrupole resonances in three dimensional photonic crystals (PCs)
consisting of plasmonic spheres. Through analytical derivation, we show that
two branches of quadrupole bands in simple cubic PCs with a small lattice
constant possess negative group velocities. Distinct from double negative media
in which the negative responses originates from the coupling of electric and
magnetic responses (P and M), the negative dispersion induced by quadrupole
resonance is an intrinsic property of quadrupole that does not require coupling
to another degree of freedom. In addition, there is no simple effective medium
description. In plasmonic systems composed of metallic nanoparticle clusters,
the coupled quadrupole resonance may be tuned to lower optical frequencies, and
the coupling strength between this quadrupole resonance and external
electromagnetic (EM) waves are in the same order of the magnetic dipole M.Comment: 21 pages, 4 figure