Observing Abnormally Large Group Velocity at the Plasmonic Band Edge via a Universal Eigenvalue Analysis

TL;DR

This paper introduces a universal eigenvalue analysis method for 2D nanostructures, revealing abnormally large group velocities at plasmonic band edges caused by radiation loss, which impacts plasmonic nanostructure design.

Contribution

A novel eigenvalue analysis algorithm for dispersive, lossy 2D nanostructures that accurately computes complex dispersion relations and reveals new physical phenomena.

Findings

Large group velocity observed at plasmonic band edge due to radiation loss.

Periodic surface modulation significantly alters dispersion relations.

The method provides fundamental insights for designing plasmonic nanostructures.

Abstract

We developed a novel universal eigenvalue analysis for 2D arbitrary nanostructures comprising dispersive and lossy materials. The complex dispersion relation (or complex Bloch band structure) of a metallic grating is rigorously calculated by the proposed algorithm with the finite-difference implementation. 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 significantly modifies the original dispersion relation of the semi-infinite dielectric-metal structure and induces the extraordinarily large group velocity, which is different from the near-zero group velocity at photonic band edge. The work is fundamentally important to the design of plasmonic nanostructures.