Dynamic and Photonic Properties of Field-Induced Gratings in Flexoelectric LC Layers

Abstract

For LCs with a non-zero flexoelectric coefficient difference (e1–e3) and low dielectric anisotropy, electric fields exceeding certain threshold values result in transitions from the homogeneous planarly aligned state to the spatially periodic one. Field-induced grating is characterized by rotation of the LC director about the alignment axis with the wavevector of the grating oriented perpendicular to the initial alignment direction. The rotation sign is defined by both the electric field vector and the sign of the (e1–e3) difference. The wavenumber characterizing the field-induced periodicity is increased linearly with the applied voltage starting from a threshold value of about π/d, where d is the thickness of the layer. Two sets of properties of the field-induced gratings are studied in this paper using numerical simulations: (i) the dynamics of the grating appearance and relaxation; (ii) the transmittance and reflectance spectra, showing photonic stop bands in the waveguide mode. It is shown that under ideal conditions, the characteristic time of formation for a spatially limited grating is determined by the amplitude of the electric voltage and the size of the grating itself in the direction of the wave vector. For large gratings, this time can be drastically reduced via spatial modulation of the LC anchoring on one of the alignment surfaces. In the last case, the time is defined not by the grating size, but the period of the spatial modulation of the anchoring. The spectral structure of the field-induced stop bands and their use in LC photonics are also discussed.