Group theory of circular-polarization effects in chiral photonic crystals with four-fold rotation axes applied to the eight-fold intergrowth of gyroid nets

We use group or representation theory and scattering matrix calculations to derive analytical results for the band structure topology and the scattering parameters, applicable to any chiral photonic crystal with body-centered-cubic symmetry $I432$ for circularly polarized incident light. We demonstrate in particular that all bands along the cubic $[100]$ direction can be identified with the irreducible representations E_±, A, and B of the C₄ point group. E₊ and E_- modes represent the only transmission channels for plane waves with wave vector along the Δ line, and E_- and E₊ are identified as noninteracting transmission channels for right- and left-circularly polarized light, respectively. Scattering matrix calculations provide explicit relationships for the transmission and reflectance amplitudes through a finite slab which guarantee equal transmission rates for both polarizations and vanishing ellipticity below a critical frequency, yet allowing for finite rotation of the polarization plane. All results are verified numerically for the so-called 8-srs geometry, consisting of eight interwoven equal-handed dielectric gyroid networks embedded in air. The combination of vanishing losses, vanishing ellipticity, near-perfect transmission, and optical activity comparable to that of metallic metamaterials makes this geometry an attractive design for nanofabricated photonic materials.