# Helix-Free Ferroelectric Liquid Crystals: Electro Optics and Possible Applications
## 1 Introduction
Figure 1: The helix ferroelectric liquid crystal (FLC)-based electro-optical cell with planar orientation of a layer (**a**) and mutual location of the spontaneous polarization vector \(\mathbf{P_{S}}\), a smectic layer, and FLC director \(\mathbf{n}\) (**b**). \(I_{\mathbf{0}}\) and \(I\) are the intensities of the incident light and the light passing through an FLC cell, correspondingly. 1—glass substrates with conductive covers 2; 3—smectic layers; 4—generator of bipolar pulses; 5 and 6—polarizers; \(p_{0}\)—helix pitch; \(\Theta_{0}\)—angle of molecule tilt in smectic layers. In the research carried out at the Lebedev Physical Institute (LPI), it was shown that the nature of the FLC director reorientation in an electric field depends essentially on the coefficient responsible for the energy dissipation in an FLC layer: the rotational or shear viscosity [9]. If the alternating electric field of the frequency \(f\) acts on the FLC, and the period of its variation is large (\(\tau_{m}\)\(\cdot\)\(f\)\(<<\) 1) in comparison with the Maxwellian relaxation time \(\tau_{m}\)[10], then the FLC behaves as a liquid with the viscosity \(\gamma_{\varphi}\). On the contrary, at sufficiently high frequencies (\(\tau_{m}\)\(f\)\(>>\) 1), the FLC behaves as an amorphous solid, and the dissipative coefficient is the shear viscosity (denoted \(\gamma_{\varphi}\)). The predominance of shear viscosity leads to a change in the character of the motion of the helix FLC director in weak electric fields: the reorientation occurs due to the motion of 180\({}^{\circ}\)-domain walls [9; 11; 12]. Such a reorientation process made it possible to obtain a modulation frequency of light radiation of the order of 3 kHz with an electric field strength of about 1 V/\(\upmu\)m. The time of the electro-optical response was 50 \(\div\) 70 \(\upmu\)s. As a disadvantage, some distortion of the spectral composition of the modulated radiation and the residual light scattering caused by the presence of a helix was noted. The character of the electric field action is practically the same for known helix-free FLCs. In them, the azimuth angle \(\varphi\) of the director's orientation in the volume of a layer is a value that is practically constant in all smectic layers; i.e., there is a so-called spatially homogeneous structure. The magnitude of the spontaneous polarization is much higher than 50 nC/cm\({}^{2}\). The dissipative coefficient is the rotational viscosity \(\gamma_{\varphi}\), and the director reorientation time, as for the helix FLC, does not depend on the frequency of the electric field change [8]. A new type of helix-free FLC specially developed at the LPI has a different character of interaction with the electric field. This material is a spatially inhomogeneous structure with periodic deformation of smectic layers (with a pitch from 1.5 to 5 \(\upmu\)m) in the absence of an electric field and a relatively small value of spontaneous polarization (less than 50 nC/cm\({}^{2}\)). In such an FLC, the director reorientation in the alternating electric field is due to the motion of structurally stable localized waves of a stationary profile--dynamic solitons that arise upon the transition to the Maxwellian mechanism of energy dissipation--and the electro-optical response depends essentially on the frequency of the electric field change [13; 14; 15; 16]. Note that a director reorientation through solitons was proposed for the first time in [17]. The new materials provided unique parameters of radiation modulation unattainable for LC analogs. For example, in a transparent mode, in an electric field of the order of 1 V/\(\upmu\)m (at a control voltage of \(\pm\)1.5 V), experimental samples of electro-optical cells with the novel helix-free FLC show a modulation characteristic with the fastest optical response (about 25 microseconds) and the highest modulation frequency (up to 7 kHz), including hysteresis-free characteristics with a continuous gray scale up to 6 kHz.