# Electrically Tunable Propagation Properties of the Liquid Crystal-Filled Terahertz Fiber
## 1 Introduction  
The terahertz (THz) frequency range has attracted increasing attention in recent years because of its potential applications in biology and medical-sensing [1], imaging [2], nondestructive spectroscopy [3], and communication technologies [4]. However, THz systems that rely on free-space and bulk optics to transport and manipulate the THz radiation are large and immobile, and difficult to use and integrate with infrared and optical systems. Thus, THz waveguides are extensively studied in recent years, such as metallic wires, plastic ribbons, dielectric fibers, and microstructured optical fibers (MOFs) [5; 6; 7; 8]. Moreover, tunable devices that modulate and control THz radiation are necessary in THz systems.  
In various THz waveguiding materials, it was found that polymers, e.g., polymethyl-methacrylate (PMMA), high-density polyethylene, Teflon, and Topas, have the lowest absorption loss and they are, for the most part, easy to machine [9; 10]. The Topas cyclic olefin copolymers (COCs) [11] in particular have received particular interest on account of their low material dispersion (with a constant refractive index of 1.5258) and relatively low material loss (rises at a rate of 0.36 cm\({}^{-1}\)/THz from 0.06 cm\({}^{-1}\) at 0.4 THz) in the 0.1-1.5 THz range, low water absorption (\(\sim\)1/10 of the PMMA), and chemical resistance to common solvents [12]. Polymer MOFs used for THz waveguiding [13; 14] have attracted much attention on account of the lower loss, lower processing temperature, and variety of processing methods compared with silica-based MOFs. However, their propagation properties cannot be changed any more once the MOF is fabricated.  
In this paper, a solid-core MOF working in the THz frequency was designed based on the low-loss THz polymer Topas COC. The guiding mechanism of the designed solid-core MOF was changed from total internal reflection to the photonic-bandgap (PBG) effect [15; 16] by filling the cladding air holes with high-index liquid crystal (LC) of the 5 CB type, which has higher refractive indices thanTopas (see Section 2). Electrically tunable propagation properties are obtained by taking advantage of the electrical tunability of LC. 5 CB has lower clearing temperature (\(T_{c}\) = 35.3 \({}^{\circ}\)C) and wide nematic range (\(>\)10 \({}^{\circ}\)C) around room temperature. The experimental work of [PERSON] et al. [17] found that the extinction coefficient of 5 CB is relatively small (less than 0.02) in the frequency range of 0.2-1.0 THz, so 5 CB can be utilized to construct tunable devices in THz range [18]. LC-MOF-based tunable fiber devices, such as threshold switching, tunable birefringence controllers, and tunable filters, have been reported in References [19; 20] and the references therein. The effects of LC alignment on bandgap formation and polarization dependent guiding have been theoretically investigated by [PERSON] et al. [21] and [PERSON] et al. [22], respectively. However, most work to date concentrates on LC-MOFs that works in the visible and near-infrared. In this paper, the electrically tunable propagation properties in THz frequency of the designed LC-MOF are studied theoretically by using the finite-element method (FEM).