Zig-zag wall lattice in a nematic liquid crystal with an in-plane switching configuration

Abstract

Liquid crystals displays with tailoring electrodes exhibit complex spatiotemporal dynamics when a large voltage is applied. We report experimental observations of the appearance of a programmable zig-zag lattice using an in-plane-switching cell filled with a nematic liquid crystal. Applying a small voltage to a wide range of frequencies, the system exhibits an Ising wall lattice. Increasing the voltage, this lattice presents a spatial instability generating an undulating wall lattice, and to higher voltages it becomes zig-zag type. Experimentally, we characterize the bifurcations and phase diagram of the wall lattice. Theoretically, we develop, from first principles, a descriptive model. This model has a good qualitative agreement with experimental observations.

Wavenumber selection via spatial parameter jump

“…Our main result is the existence of stationary half-stripe solutions to the SH equation with a parameter jump, equation (2). These half-stripe solutions tend to 0 as x → −∞ and converge to a spatially periodic solution as x → ∞.…”

“…We find that the system selects wavenumbers in a band growing linearly in the size of the parameter jump µ. Theorem 1.1. For sufficiently small µ > 0, there exists a one-parameter family of bounded, stationary solutions of the Swift-Hohenberg equation (2). The family u(x; θ) = u(x; θ + 2π) is periodic in the parameter θ.…”

“…In the remainder of this section we consider implications in two space-dimensions, considering (2) with (x, y) ∈ R 2 . First, we review the known two-dimensional instabilities of the equation with a homogeneous parameter.…”

Harnessing diffraction grating in an in-plane switching cell submitted to zigzag lattice

“…Latterly, the apparition of zigzag lattice in an IPS cell filled with nematic liquid crystal beyond a certain voltage threshold has been reported [12]. Recently, we have studied in detail, theoretically and experimentally, the zigzag instability of a wall lattice in a nematic liquid crystal with an IPS configuration [13]. We have also evidenced the importance of the liquid crystal molecule anchoring on their own dynamics when they are submitted to an external electrical forcing [14,15].…”

Asymmetric counterpropagating fronts without flow

“…One other possibility is to generate these fronts from the electrode tips. The molecular orientations and the fronts are the result of the transverse inhomonogeneous periodic electric field induced by the in-plane switching electrodes [23]. In the bulk of the sample, the molecules are oriented accordingly to the electric field.…”