Tunable two-dimensional polarization grating using a self-organized micropixelated liquid crystal structure

Abstract

Utilization of the self-organizing nature of soft materials is promising for fabricating micro- and nano-structures, which can be applied for optics. Because of the high birefringence, liquid crystals are especially suitable for optoelectronic applications such as beam steering and polarization conversion. On the other hand, most self-organized patterns in liquid crystals are one-dimensional and there are only a few examples of two dimensional systems. Here we study the light diffraction from a micro-pixelated pattern of a nematic liquid crystal which is formed by self-organization of topological defects. We demonstrate that the system works as a tunable two dimensional optical grating, which splits the incident laser beam and changes the polarization property. The intensity can be controlled by electrical voltages, which cause extinction of the zeroth-order beam. The polarization properties depend on the location of spots. The numerical calculation and the theoretical analysis not only support the experimental results but also unveil the uniqueness of the pixelated structure.

Fig. 1. (a) Schematic illustration of the sample cell and the diffraction experiments. (b) The chemical structures of the alignment layer (CYTOP) and the NLC (CCN-37).

Fig. 2. (a)–(c) The micrographic images for the grid-like texture under cross-polarized condition. Scale bar, 500 μm. The inset of (b) is a micrograph of a grid-like texture irradiated with a laser beam. (d)–(f) Diffraction patterns obtained by a laser beam irradiation. The incident beam is circularly polarized. The amplitude of the applied voltage is 25 V. (d) 12.5 Hz, (e) 18.5 Hz, (f) 23.5 Hz. (g) A schematic illustration of the director field of the grid-like texture. The square is the unit cell for the light diffraction. Here, we set the lattice constant as without loss of generality. (h) The intensity for each spot as a function of frequency. The intensity is normalized with the incident beam. The dashed line is the total power of the light transmitted through the cell. The power meter is placed right behind the cell.

Fig. 3. (a)–(c) POM images for a cell with the sample thickness of 21 μm. V₀ = 25 V. f = 11 Hz for (a), 18 Hz for (b), and 25 Hz for (c). Scale bar, 500 μm. (d) and (e) Diffraction patterns obtained by rotating the analyzer. The incident light is circularly polarized. (f) The angle dependence for the intensity of diffraction spots. Note that the experimental conditions in (f) and the other diffraction patterns ((d) and (e)) are different. (g)–(i) Diffraction patterns obtained by using a linearly polarized light.

Fig. 4. Calculated diffraction patterns for the planar alignment condition using circularly polarized input light and retardation of (a) 50 and (b) 300 nm. (c) The behavior of the intensity depending on the retardation. (d) The polarization dependence for the spot. Here the calculation is made for Δnd = 250 nm. (e) and (f) Calculated diffraction patterns under crosspolarized (e) and parallel polarized (f) conditions.

Fig. 5. (a) The angular dependence of the intensity of diffraction spots. The value of intensity is normalized with that of the incident light. The calculation is made with δ₀ = 350 nm and n = 40. (b) The intensity of I(0, 0) as a function of n and δ₀.

Fig. 6. Schematic illustration of the symmetry operation for this system.