Multiplet structure of the defect modes in 1D helical photonic crystals with twist defects

Abstract

We theoretically analyse the defect modes generated by equispaced twist defects in 1D helical (cholesteric-like) structures within their frequency gap which is such that only the first two of the four eigenwaves 1±, 2± are exponentially attenuated. n0 identical defects generate n0 different defect modes, each one represented by a linear combination of the four eigenwaves. The components 1+ and 1− are by far the dominant ones and they are localized near the defect planes. We give exact analytic expressions for the elements of the transfer and scattering matrices of the defect planes, for the functions defining the defect mode when n0 = 1, and for the defect frequencies when n0 = 1, 2, 3. In the particular case n0 = 2 and twist angle θ = π/2, the difference between the two defect wavelengths λd2, λd1 depends exponentially on the distance z1 between the defect planes, going to zero for z1 → ∞ and becoming as large as the entire frequency gap for z1 → 0.