Dual diffraction bands of heliconical liquid crystal gratings

Gratings composed of cholesteric liquid crystals as an important optical element for emerging applications such as augmented and virtual reality and are renowned for their characteristic single reflective diffraction band. Heliconical liquid crystal is a newly discovered state where the constituent molecules self-organize into helical structures with a non-90\ifmmode^\circ\else\textdegree\fi{} polar angle between the director and the helical axis. Here, we present a numerical study on the reflective diffraction of gratings made of heliconical liquid crystals. Remarkably, numerical results demonstrate that there exist two diffraction bands at the same diffraction angle, with one peak wavelength being twice the other. We show that the short-wavelength diffraction originates from the Pancharatnam-Berry phase acquired by the reflected light while the long-wavelength diffraction stems from the reflection of the slanted volume grating, and that the wavelengths of these two diffraction bands can be attributed to the first and second band gaps of the slanted volume grating as a one-dimensional photonic crystal. We further show that the polarization of the reflected diffraction light is circular, exhibiting the same handedness as the liquid crystal for the short-wavelength band, whereas it is perfectly linearly polarized along the grating direction for the long-wavelength band.