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We use group or representation theory and scattering matrix calculations toderive analytical results for the band structure topology and the scatteringparameters, applicable to any chiral photonic crystal with body-centered cubicsymmetry I432 for circularly-polarised incident light. We demonstrate inparticular that all bands along the cubic [100] direction can be identifiedwith the irreducible representations E+/-,A and B of the C4 point group. E+ andE- modes represent the only transmission channels for plane waves with wavevector along the ? line, and can be identified as non-interacting transmissionchannels for right- (E-) and left-circularly polarised light (E+),respectively. Scattering matrix calculations provide explicit relationships forthe transmission and reflectance amplitudes through a finite slab whichguarantee equal transmission rates for both polarisations and vanishingellipticity below a critical frequency, yet allowing for finite rotation of thepolarisation plane. All results are verified numerically for the so-called8-srs geometry, consisting of eight interwoven equal-handed dielectric Gyroidnetworks embedded in air. The combination of vanishing losses, vanishingellipticity, near-perfect transmission and optical activity comparable to thatof metallic meta-materials makes this geometry an attractive design fornanofabricated photonic materials.

physical review. b, condensed matter and materials physics

Group Theory of Circular-Polarization Effects in Chiral Photonic  Crystals with Four-Fold Rotation Axes, Applied to the Eight-Fold Intergrowth  of Gyroid Nets