# Liquid Crystal-Tuned Planar Optics in Terahertz Range
## 2 Properties of LCs and LC-Based THz Devices  
Known for their dominant role in information displays, LCs, featuring both fluidity and anisotropy, can also be adopted for dynamic THz wave manipulations. The birefringence, \(\Delta n\), is a key parameter of the LC which determines the function of wavefront regulation. For instance, LC THz modulators work on accumulated phase modulations, which are related to the birefringence and thickness of LCs. Thick cells suffer from slow responses and poor alignments; thus, large birefringence is in high demand. The properties of 5 CB at 0.3-1.4 THz were measured 20 years ago, with a \(\Delta n\) of 0.21 [28]. E7 exhibits a birefringence range of 0.130-0.148 at 0.2-2.0 THz [29]. In 2012, the birefringence of 18-series LCs was tested, and that of 1825 reached 0.36 at 0.7-3 THz. Moreover, the absorption of these LCs was negligible in the experiments [30; 31]. In 2012, NJU-LDn-4 was synthesized, exhibited an average birefringence of 0.306 in 0.4-1.6 THz and kept the nematic phase in a large temperature range covering room temperature [32]. The nanoparticles doped E7 LC leads to a 10% increase in birefringence in 0.3-3 THz [33]. Table 1 shows the birefringence of these LC materials used in the THz band. As a typical element, the filter plays an important role in the terahertz band. The birefringence of LC is adopted for terahertz filters. [PERSON]'s group produced Lyot filters based on the combination of a magnetic field-controlled parallel-oriented LC cell exhibiting a fixed phase delay, and vertically oriented LC cells with an adjustable phase delay. Through changing the direction of the magnetic field, a modulation range of 40% at 0.388-0.564 THz was demonstrated [35]. Later, magnetically tuned Solc filters were made using two cells with vertically oriented LCs. The modulation bandwidths were 0.176-0.293 THz and 0.474-0.794 THz, respectively. The corresponding modulation ranges were 66.5% and 67.5%, separately [36]. A 60 GHz band stop filter at approximately 0.3 THz, as shown in Figure 1a,b, was realized by electrically controlling multiple LC layers [37]. A notch filter with a bandwidth of 0.35-0.7 THz was realized through electrically switching a single-layer LC cell [38]. THz filters based on LC-filled photonic crystals were theoretically investigated as well [39]. In these early works, almost all of them suffered from thick LC layers slowing down the response and increasing the absorption loss. The stacking of multiple LC cells reduces the thickness of a single cell but induces a more complicated configuration and extra interface loss. The birefringence of the LC is also adopted for phase shifters. Through electrically driven nematic LC [40; 41], shown in Figure 1c, polymer-stabilized LC [42] and hydrogen-bonded LC [43], different THz phase shifters were realized. THz LC wave plates were demonstrated in a similar way. A broadband tunable THz wave plate made of NJU-LDn-4 was reported [44]. In this element, metal wire grids and a few layers of graphene were used as conductive electrodes, illustrated in Figure 1d. Due to the large birefringence of NJU-LDn-4 in the THz band, a broadband quarter wave plate and a half wave plate were produced. By further introducing a double-layer structure, the bandwidth can be further expanded to 0.5-2.5 THz for a quarter wave plate. Compared to the transmitted THz LC wave plates, the reflective ones require only 50% LC to achieve the same modulation, which accelerates the modulation and reduces the insertion loss [45]. [PERSON]'s group used a 600 \(\upmu\)m dual-frequency LC (DFLC) to form a cell whose birefringence is frequency dependent. Via tuning the frequency from 1 kHz to 100 kHz under a constant electric field, a tunable quarter wave plate above 0.68 THz and a half wave plate above 1.33 THz were realized, as shown in Figure 1e [46]. Besides the above devices, LCs have been utilized in abundant THz applications. The THz beam was deflected by an electrically controlled LC wedge cell, as seen in Figure 2a [47].