  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.
