Optical responses of planar composites consisting of monolayer graphene sheets and axially helicoidal (bi)anisotropic films

Optical responses of planar composites made of monolayer graphene sheets and axially helicoidal (bi)anisotropic films (HBFs) are studied using our developed algorithm based on spectral-domain exponential matrix (SDEM) technique. Such HBF-based structures possessing z-axis inhomogeneity, in particular, include locally uniaxial chiral nematic and biaxially smectic liquid crystals (CNLC and CSLC) with double or a few layered graphene sheets inserted. In our mathematical treatment, they are artificially divided into many very thin sub-layers, where each one can be described by a set of z-coordinate independent constitutive tensors. The effects of wavelength and angle of the incident light, chemical potential of monolayer graphene, period of the z-axis inhomogeneity and angle of rise of the composites on their reflectance and transmittance are investigated numerically for different constitutive features and geometries. It is shown that the first- and second-order Bragg reflection or transmission zones at optical bands do exist in the presence of double or a few layered dispersive graphene sheets with slight loss but more freedom introduced.