The Field-Induced Stop-Bands and Lasing Modes in CLC Layers with Deformed Lying Helix

Waveguide optical properties of a cholesteric liquid crystal (CLC) layer with a deformed lying helix (DLH) have been studied by numerical simulations using the finite difference time domain method. The DLH structure, when the helix’s axis is oriented in plane of a CLC layer, is induced by an electric field in a virtual CLC cell with periodic (planar/homeotropic) boundary conditions at one of the alignment surfaces. This in-plane helical structure is stable only in a permanently applied electric field providing the helix deformation. In this work the polarized light reflectance spectra have been studied at different electric fields and light impingement into a waveguide formed by the DLH layer. It is found that for light propagating along the helix axis the reflectance spectrum has multiple stop-bands centred at wavelengths λ j = 2 p ⟨ n ⟩ j , which is different from set of bands located at λ j = p ⟨ n ⟩ j , and characteristic of CLC spectra for the Grandjean-plane textures subjected to distortion by an electric or magnetic field perpendicular to the helix axis, where j is a natural number, p is the helix pitch and ⟨ n ⟩ is the average refractive index. Each of the higher order (j > 1) bands consists of three polarization-dependent sub-bands. In the case of an amplifying CLC DLH layer, depending on an extent of the helix deformation, the lasing modes can be excited at different edges of the sub-bands. While at the strongest deformation the lasing is preferable at the edges of the central sub-band; a lower extent of deformation makes favourable conditions for the lasing at edges of the two other sub-bands

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

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

Liquid-crystal metasurfaces: Self-assembly for versatile optical functionality

Liquid crystals subjected to modulated surface alignment assemble into metasurface-type structures capable of various flat-optical functionalities, including light diffraction and focusing, deflection and splitting. Remaining in a fluid phase, they are susceptible to external stimuli, and, in particular, can be efficiently controled by low voltages. We overview the existing approaches to the design and fabrication of liquid-crystal metasurfaces, highlight their realized optical functions and discuss the applied potential in emerging photonic devices

Study of the vertically aligned in-plane switching liquid crystal mode in microscale periodic electric fields

The ongoing interest in fast liquid crystal (LC) modes stimulated by display technology and new applications has motivated us to study in detail the in-plane switching (IPS) vertically aligned (VA) mode. We have studied how the decrease of the period of the interdigitated electrodes (down to sub-micrometer scale) influences the switching speed, especially the LC relaxation to the initial homeotropic state. We have found that there are two types of the relaxation: a fast relaxation caused by the surface LC sub-layer deformed in the vicinity of the electrodes and the slower relaxation of the bulk LC. The speed of the fast (surface) mode is defined by half of a period of the electrode grating, while the relaxation time of the bulk depends on the LC layer thickness and the length of the driving electric pulses. Thus, the use of the surface mode and the reduction of the electrode grating period can result in significant increase of switching speed compared to the traditional LC modes, where the bulk relaxation dominates in electrooptical response. We have studied thoroughly the conditions defining the surface mode applicability. The numerical simulations are in good agreement with experimental measurements

Spiral Pitch Control in Cholesteric Liquid Crystal Layers with Hybrid Boundary Conditions

The optical spectra of the cholesteric liquid crystal (CLC) layers under conditions of hybrid anchoring show a short-wave shift under a pulsed electric field. This behavior is anomalous because it is associated with a decrease in the pitch of the cholesteric spiral, which is atypical at conditions when the electric field is perpendicular to the axis of the CLC spiral. An analytical model of the phenomenon is discussed, according to which the spiral pitch under hybrid boundary conditions can be greater than the natural pitch in an unlimited volume of CLC. An in-plane electric field, being localized near the homeotropic-alignment surface, can be treated as effectively influencing the azimuthal anchoring and leading to a variety of metastable states with both increased and decreased pitch. These metastable states with local minima of free energy prevent the spiral from unwinding, and corresponding bands of selective reflection can even be shifted to the short-wave region of the spectrum. The observed effect is also studied numerically. It is shown by numerical simulations that the localized electric field from short-pitch electrodes can also modify zenithal anchoring, which should allow for defect-free controlling of the spiral pitch and spectral stop-band location

Nematic liquid crystal alignment on subwavelength metal gratings

We have studied the alignment of a nematic liquid crystal (LC) material on aluminum subwavelength nanogratings as a function of the period, p, and the slit width to period ratio, w/p. A method, based on Fourier analysis of the transmittance spectra of the LC grating system, has been applied. We show that the gratings provide stable planar alignment only for shorter periods and narrower slits (p < 400 nm, w/p < 2/3). As these parameters increase, the homogeneous surface alignment changes to domains with different tilt angles or to spatially modulated alignment. We have also obtained a 90° twisted LC director distribution, implying sufficiently strong azimuthal LC anchoring at the grating surface

Two-dimensional ferroelectric films

Ultrathin crystalline films offer the possibility of exploring phase transitions in the crossover region between two and three dimensions. Second- order ferromagnetic phase transitions have been observed in monolayer magnetic films [1,2], where surface anisotropy energy stabilizes the two-dimensional ferromagnetic state at finite temperature [3]. Similarly, a number of magnetic materials have magnetic surface layers that show a second-order ferromagnetic–paramagnetic phase transition with an increased Curie temperature [4]. Ferroelectricity is in many ways analogous to ferromagnetism, and bulk-like ferroelectricity and finite-size modifications of it have been seen in nanocrystals as small as 250 Å in diameter [5], in perovskite films 100 Å thick [6] and in crystalline ferroelectric polymers as thin as 25 Å [7–10]. But these results can be interpreted as bulk ferroelectricity suppressed by surface depolarization energies, and imply that the bulk transition has a minimum critical size [11–13]. Here we report measurements of the ferroelectric transition in crystalline films of a random copolymer of vinylidene fluoride and trifluoroethylene just 10 Å (two monolayers) thick. We see a first-order ferroelectric phase transition with a transition temperature nearly equal to the bulk value, even in these almost two-dimensional films. In addition, we see a second first-order transition at a lower temperature, which seems to be associated with the surface layers only. The near-absence of finite-size effects on the bulk transition implies that these films must be considered as two-dimensional ferroelectrics