Optical properties of honeycomb photonic structures

TL;DR

This study investigates the optical properties of honeycomb photonic structures, combining experimental fabrication and theoretical analysis to reveal Dirac points, band structure features, and the transition to metamaterials as dielectric properties change.

Contribution

It provides the first combined experimental and theoretical analysis of honeycomb photonic structures, including fabrication, diffraction, band structure, and Dirac phenomena.

Findings

Strong diffraction observed in experiments, allowing visual counting of elements.

Transition to metamaterial behavior as dielectric constant increases.

Identification of Dirac points and demonstration of Dirac lensing effects.

Abstract

We study, theoretically and experimentally, optical properties of different types of honeycomb photonic structures, known also as `photonic graphene'. First, we employ the two-photon polymerization method to fabricate the honeycomb structures. In experiment, we observe a strong diffraction from a finite number of elements, thus providing a unique tool to define the exact number of scattering elements in the structure by a naked eye. Then, we study theoretically the transmission spectra of both honeycomb single layer and 2D structures of parallel dielectric circular rods. When the dielectric constant of the rod materials $\varepsilon$ is increasing, we reveal that a two-dimensional photonic graphene structure transforms into a metamaterial when the lowest TE${}_{01}$ Mie gap opens up below the lowest Bragg bandgap. We also observe two Dirac points in the band structure of 2D photonic graphene at the $K$ point of the Brillouin zone and demonstrate a manifestation of the Dirac lensing for the TM polarization. The performance of the Dirac lens is that the 2D photonic graphene layer converts a wave from point source into a beam with flat phase surfaces at the Dirac frequency for the TM polarization.