Fano resonance in a cholesteric liquid crystal with dye

In this paper, we consider the optical properties of cholesteric liquid crystals (CLCs) with a dye. We investigate the reflection, transmission, and absorption spectra peculiarities. We show that in the presence of dye molecules, in certain conditions, the photonic band gap (PBG) splits into two, three, etc., PBGs. A simple geometric method for determination of the Bragg frequencies and the widths of forbidden bands is proposed. It is shown that we can change the Bragg frequencies and the widths of forbidden bands by changing the parameters of dye molecules. We investigate the light localization peculiarities in the CLC layer in the presence of dye molecules. The peculiarities of the spectra of the photonic density of states and the spectra of light energy density in the CLC layer are also investigated. We show that in the presence of two types of resonances the observation of Fano resonance is possible. The peculiarities of Fano resonance in the CLC with dyes are investigated. We show that this system can be used for achieving a narrow bandwidth spectral response in transmission or reflection.