Synchronised flexoelectric instability in an LC cell with periodic planar-homeotropic alignment

In a planarly aligned layer of a nematic liquid crystal (LC) the applied electric field can induce a periodic stripe pattern, which is characteristic of the well-known flexoelectric instability effect. We have studied the flexoelectric instability in LC layers with periodic planar-homeotropic alignment (PHA) at one of the layer surfaces and compared the results to the case of the homogeneously aligned layer. It is found that the PHA is more favourable for the flexoelectric spatial modulation. The flexoelectric grating is formed significantly faster in the case of short-period PHA as compared to the cell with homogeneous alignment, which is due to both PHA periodicity and flexoelectric polarisation that in the case of PHA is non-zero even in the field-off state. The impressive finding is that the flexoelectric gratings are spatially synchronised with PHA and free of fork-like defects. The Fourier analysis of the patterns shows that the wavenumber of the flexoelectric gratings is multiple of the PHA grating wavenumber, which points to the spatial resonance of the flexoelectric instability with the PHA harmonics. The improved dynamics with the synchronisation opens perspectives for new electrooptical and photonic applications of the flexoelectric gratings.