Universal Eigenvalue Analysis for 2D Periodic Plasmonic Nanostructures

Abstract

We developed a universal eigenvalue analysis for 2D arbitrary nanostructures com- prising dispersive and lossy materials. The complex Bloch band structures (BS) of plasmonic crystals and gratings are rigorously calculated by the ¯nite-di®erence discretization of wave equa- tion. Given a frequency of interest, the eigenvalue algorithm solves one Bloch wavenumber as the eigenvalue via ¯xing another. (1) For plasmonic crystals, the in°uence of ohmic (metallic) loss on the complex BS and eigenmodes is investigated. Regarding a TE polarization with Hz ¯eld, the ohmic loss strongly a®ects the BS and eigenmodes at plasmonic resonance frequencies. Both the fast oscillation of dispersion curve and strong ¯eld con¯nement of eigenmodes are damped due to the high ohmic loss. Regarding a TM polarization with Ez ¯eld, the introduction of ohmic loss twists the vertical dispersion curve at the bandgap and breaks the symmetry of eigenmodes. Regarding both polarizations, the high ohmic loss lowers the quality factor of eigenmodes. (2) For plasmonic gratings, 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 signi¯cantly modi¯es the original BS of the semi-in¯nite dielectric-metal structure and induces the extraordinarily large group velocity, which is di®erent from the near- zero group velocity at photonic band edge. The work is fundamentally important to the design of plasmonic nanostructures .....