Lasing thresholds of helical photonic structures with different positions of a single light-amplifying helix turn

Numerical simulation is used to assess the lasing threshold of helical structures of cholesteric liquid crystals (CLCs) in which only one turn amplifies light. This turn is located either in the centre of symmetric structures of various sizes or in an arbitrary place in asymmetric structures of preset size. In all cases, we find singularities in light amplification by a one-dimensional CLC structure for the most important band-edge modes (m1, m2 and m3) and plot the threshold gain coefficient k_th against the position of the amplifying turn. For the symmetric structures, the lasing threshold of the m1 mode is shown to vary linearly with the inverse of the square of the cavity length. Moreover, modes with a lower density of photonic states (DOS) in the cavity may have a lower lasing threshold. This can be accounted for by the dependence of the density of photonic states on the position of the amplifying turn and, accordingly, by the nonuniform electromagnetic field intensity distribution along the cavity for different modes. In the asymmetric structures, the same field energy distribution is responsible for a correlation between k_th and DOS curves.