Dispersion and attenuation of the eigenwaves for light propagation in heiicoidal liquid crystals

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Abstract
The dispersion curves and attenuation factors of the Bloch eigenwaves in heiicoidal liquid crystals (chiral smectic C and cholesterics) are calculated using the 4 × 4 characteristic matrix method. Four possible types of eigenmodes are seen to exist in the medium. The reflection peaks, which correspond to odd parts of the full pitch, are total reflection peaks, while those corresponding to even parts of the full pitch are composed of three branches at high incidence angles, where the outer branches are selective reflection and the central one is a total reflection peak. Selective reflection regions occur only at the edges of the Brillouin zones, while total reflections can occur anywhere inside the zones. The former are interpreted according to the coupled mode theory as resonant Bragg reflections, with the latter as exchange Bragg reflections. When the tilt direction exceeds the propagation direction, the central branch of the even sequence of peaks starts to be due to resonant Bragg reflections. The first order peak for cholesterics becomes strongly structured at large incidence angles.