Surface plasmons in honeycomb lattices of Ag nanoparticles exhibit Dirac-like band structures, similar to the electronic band structure of graphene [1]. Full wave simulations for an infinite honeycomb lattice of silver nano-pillars reveal hybridization of localized plasmonic modes between two neighboring pillars and the consequent formation of bonding and anti-bonding modes that are energetically degenerate at Dirac points with a relative phase of Pi. Calculations also reveal that distortion of the honeycomb lattice breaks the lattice inversion symmetry and opens a photonic bandgap, whose width is proportional to the extent of distortion. Further, electromagnetic simulations reveal the existence of Dirac-like plasmonic edge states in finite width nanoribbons of the honeycomb nanoparticle lattice. Nanoscale architecture of the honeycomb lattice may provide a new way to control directional plasmon propagation by selective excitation of surface plasmon edge states without backscattering.
Experimentally, we have utilized cathodoluminescence (CL) spectroscopy to study angular emission patterns at various wavelengths and eventually construct band structures of the silver pillars in honeycomb lattices. In a CL measurement, electron beams are incident on the sample to excite plasmonic modes in the out of plane direction, which is normally difficult to excite via optical measurement. The scattered light due to the decay of surface plasmon excitations is collected by a parabolic mirror and mapped to the momentum space, yielding a direct construction of band structures in the Brillouin zone. In our initial CL measurement, we compared angular emission patterns from a single silver pillar, silver pillar dimers and silver pillars in honeycomb lattices fabricated on a 15 nm thick free standing silicon nitride membrane. The angular emission patterns from a single silver pillar exhibits strong dipole radiation, while silver pillars in dimer have directional radiation resulting from dipole interactions. For silver pillars in honeycomb lattices, we have observed strong radiation patterns near the Brillouin zone edge, integrated over an interval of wavelength including the wavelength of the Dirac points. Efforts on CL measurements with spectral resolution down to 1nm will also be discussed.
speng@caltech.edu