Complex k band diagrams of 3D metamaterial/photonic crystals

TL;DR

This paper introduces a finite element method for analyzing complex k({\omega}) dispersion relations in 3D metamaterials and photonic crystals, enabling detailed study of their wave propagation and resonance phenomena.

Contribution

It generalizes a 2D eigenvalue method to 3D, facilitating analysis of dispersive materials, isofrequency surfaces, and evanescent wave decay in complex photonic structures.

Findings

Demonstrated hybridization and avoided crossings in resonances

Predicted negative index propagation modes

Showed the hyperbolic nature of the fishnet structure

Abstract

A finite element method (FEM) for solving the complex valued k({\omega}) vs. {\omega} dispersion curve of a 3D metamaterial/photonic crystal system is presented. This 3D method is a generalization of a previously reported 2D eigenvalue method. This method is particularly convenient for analyzing periodic systems containing dispersive (e.g., plasmonic) materials, for computing isofrequency surfaces in the k-space, and for calculating the decay length of the evanescent waves. Two specific examples are considered: a photonic crystal comprised of dielectric spheres and a plasmonic fishnet structure. Hybridization and avoided crossings between Mie resonances and propagating modes are numerically demonstrated. Negative index propagation of four electromagnetic modes distinguished by their symmetry is predicted for the plasmonic fishnets. By calculating the isofrequency contours, we also demonstrate that the fishnet structure is a hyperbolic medium.