Negative Group Velocity from Quadrupole Resonance of Plasmonic Spheres

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.