Diffraction gratings formed spontaneously by a two-dimensional undulation of the pseudo-layer structure of a twist-bend nematic phase

Structure and optical transmission properties of spontaneously formed diffraction gratings by bent-core liquid crystalline materials that exhibit a twist-bend nematic (N-TB) phase transition, when confined in thin planar cells are reported. We begin with experimentally measuring the polarisation properties of diffraction peaks up to the second-order and observe a generalised behaviour of polarisation of the first-order peaks. Moreover, we show that the study of the second-order diffraction peaks combined with the proposed preliminary model can be an effective tool to predict the spatial variation of the optic axis. Then, we build a continuum model that describes the formation of gratings as a result of competition between surface conditions and bulk strain due to the shrinking of pseudo-layers and determine the threshold conditions on the onset of a 2D pseudo-layer structure of the N-TB phase. We use the beam propagation method and transfer matrix method to calculate the transmissivity of diffracted light by using the spatial variation of the optic axis determined from the modelled structure. It is established that the beam propagation method is superior to the transfer matrix method.