Negative group velocity from quadrupole resonance of plasmonic spheres

Abstract

We study the dispersion relations of plasmonic bands that arise from the coupling of electric-quadrupole resonances in three-dimensional plasmonic lattices consisting of metallic nanospheres. Through analytical derivation, we show that two branches of quadrupole bands in simple-cubic lattices with a small lattice constant possess negative group velocities. Distinct from double negative $(\ensuremath{\epsilon},\text{ }\ensuremath{\mu}<0)$ media in which the negative dispersion originates from the coupling of electric and magnetic responses ($\mathbf{P}$ and $\mathbf{M}$), 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, the quadrupole dispersions are intrinsically anisotropic, which defies a simple isotropic effective-medium description without spatial dispersion even though the lattice constant is small compared with the wavelength. In plasmonic systems composed of metallic nanoparticle clusters, the coupled quadrupole resonance may be tuned to lower optical frequency and the coupling strength between this quadrupole resonance and external electromagnetic (EM) waves could be in the same order of magnitude as the magnetic dipole $\mathbf{M}$.