# Helix-Free Ferroelectric Liquid Crystals: Electro Optics and Possible Applications
## 5 Theoretical Model of the Ferroelectric Liquid Crystal Deformation and Director Reorientation
### Modulation of Light Scattering  
The deformation of a single-domain structure of the FLC caused by a pulse of the electric field can be accompanied under certain conditions by a short \"flash\" of light scattering. Such scattering was observed for the first time in 1984 and was called \"transient\" [4], but it was considered parasitic and was not studied in detail. Intense transient scattering in the helix-free FLC was first studied in [30], where it was also proposed to be used in high-speed modulators of a three-dimensional display with a volumetric screen (volumetric display). Transient light scattering in new helix-free FLCs, including bistable scattering, was studied in detail in [5; 16]. This scattering occurs on the boundaries of spontaneously ordered regions which are formed in the process of the appearance of waves of a stationary profile, i.e., solitons. Scattering occurs after changing the electric field sign and disappears when the motion of solitons reorients the director in all smectic layers--that is, a new homogeneous structure of the FLC layer is no longer formed. A change in the electric field direction induces transient domain formation again, and the process is repeated. The frequency dependence of the optical response time for light scattering is similar to that described in Section 4. The transition to the Maxwellian mechanism of energy dissipation is accompanied by a strong frequency dependence of the response time \(\tau_{0.1\text{--}0.9}\) similar to that shown in Figure 4. Some increase in the time \(\tau_{0.1\text{--}0.9}\) is due to the simultaneous presence of two dissipative coefficients \(\gamma_{\varphi}\) and \(\gamma_{\psi}\). After the transition to the soliton mode, the time \(\tau_{0.1\text{--}0.9}\) is determined by the velocity of soliton wave motion, so the frequency dependence of the response time is practically absent. During operation in a light-scattering mode, the polarizers are not required, and this increases the light transmission of the electro-optical cell by up to 80%. Basically, it is limited by the transparency of conductive coatings on glass substrates. If the pulse duration is less than the minimum time required for a complete disappearance of the transition domains, the light transmission of the cell decreases. The maximum efficiency of light scattering corresponds to the regular structure of the scattering centers in the form of circular domains that are fairly uniformly distributed throughout the volume of the FLC layer. A decrease in the cell thickness shifts the maximum corresponding to a regular scattering structure toward shorter pulse durations, but the contrast ratio also decreases. For a certain experimentally chosen relationship between the amplitude and duration of the alternating impulses of the control voltage, and also between the elastic deformation energy of smectic layers and the FLC spontaneous polarization, the process of light scattering on the dynamic domain structure at the transition to the Maxwellian energy dissipation becomes bistable with a maximum light transmission above 80% and a contrast ratio of about 200:1 (Figure 13). Both optical states (with or without scattering) could be turned off for a few tens of microseconds and be memorized for a few tens of seconds, or until a pulse of opposite polarity was applied. The maximum light-scattering modulation frequency was about 5 kHz [16]. A change in the duty cycle between the control voltage pulses (the duration is maintained) leads to a change in the ratio between the lifetimes of both optical states. When an alternating pulse duration is reversed (the duty cycle is maintained), and the duration of a pulse switching on the scattering becomes equal to the duration of a pulse switching off the scattering (and vice versa), the ratio of the lifetimes of states with the maximum light transmission and with the maximum light scattering is reversed. There is a limit on the minimum duration of voltage pulses which turn on and turn off the scattering process.