A spatial structure for which mirror reflection cannot be represented by rotations and translations is chiral. For photonic crystals and metamaterials, chirality implies the possibility of circular dichroism, that is, that the propagation of left-circularly polarized light may differ from that of right-circularly polarized light. Here we draw attention to chiral sheet- or surface-like geometries based on chiral triply-periodic minimal surfaces. Specifically we analyse two photonic crystal designs based on the C(Y) minimal surface, by band structure analysis and by scattering matrix calculations of the reflection coefficient, for high-dielectric contrasts.
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.