Group Theory of Chiral Photonic Crystals with 4-fold Symmetry: Band Structure and S-Parameters of Eight-Fold Intergrown Gyroid Nets

TL;DR

This paper introduces a group theoretical approach to analyze the band structure and S-parameters of chiral photonic crystals with 4-fold symmetry, revealing their strong circular polarization sensitivity and optical activity.

Contribution

It develops a scattering matrix method for photonic crystals with I432 symmetry, specifically analyzing the 8-srs structure formed by intergrowth of eight srs nets, highlighting its unique chiral optical properties.

Findings

Identifies non-interacting transmission channels for circular polarizations.

Shows identical reflection rates for both polarizations across frequencies.

Demonstrates large optical activity comparable to metallic metamaterials.

Abstract

The Single Gyroid, or srs, nanostructure has attracted interest as a circular-polarisation sensitive photonic material. We develop a group theoretical and scattering matrix method, applicable to any photonic crystal with symmetry I432, to demonstrate the remarkable chiral-optical properties of a generalised structure called 8-srs, obtained by intergrowth of eight equal-handed srs nets. Exploiting the presence of four-fold rotations, Bloch modes corresponding to the irreducible representations E- and E+ are identified as the sole and non-interacting transmission channels for right- and left-circularly polarised light, respectively. For plane waves incident on a finite slab of the 8-srs, the reflection rates for both circular polarisations are identical for all frequencies and transmission rates are identical up to a critical frequency below which scattering in the far field is restricted to zero grating order. Simulations show the optical activity of the lossless dielectric 8-srs to be large, comparable to metallic metamaterials, demonstrating its potential as a nanofabricated photonic material.