## 1 Introduction  
Demultiplexing technology is employed to convert a signal containing multiple signal streams back into the original separate and unrelated signals. Demultiplexer in the terahertz range is under active development nowadays [1; 2]. In this frequency range, lots of devices, like switches, modulators, sensors, etc., have emerged in recent years to facilitate ultra-wideband communications [3; 4; 5]. However, the rapid development of communication systems is always short of devices that can match their evolving performance requirements. Therefore, tunable materials are playing a key role in developing optic-electric devices that are flexible and easy to use. Graphene is widely used in adjustable devices owing to the diversity of its tunable parameters [6; 7; 8]. With adjustable permeability by magnetic fields, ferrite is also attractive for devices in the terahertz or optical range [9; 10; 11]. Since the liquid crystal (LC) is fluid, it is better used for volume devices, like waveguides [12], or flexible components, like wearable filters [13]. In recent years, nematic liquid crystals (NLCs) have been widely used in tunable optic-electric devices, because the optical axis of NLC molecules can be controlled by an external electric field or a magnetic field. The NLC's controllable dielectric properties, wide range of operating frequencies and multiple ways of being adjusted are attractive for design tunable devices [14; 15]. In the gigahertzband, LC has been tailored in a filter or amplifier to adjust their operating bands [16; 17]. In the optical band, LC has found its usage in switches, sensors, waveplates, etc. [18; 19; 20]. Recently, there has been growing interest in utilizing the LC for devices working in the terahertz range [21; 22; 23]. In addition to the extension of the applied frequencies using the LC, ways to adjust the LC are also diversified. Electrical control of the tilt angle of the LC is a prevailing method because it can be fully used as a tunable medium for convenience and effectiveness [24; 25]. By applying an external magnetic field, dielectric parameters of the LC can also be adjusted without any direct contact with the devices employing it [26; 27]. The temperature stability of the LC is always required to keep the devices operating effectively. The temperature sensitivity of the LC can also be used to change its properties to realize tunable devices, even though its temperature response is relatively slow [28; 29]. Among various devices that achieve tunability by using the LC, metal-insulator-metal (MIM) and insulator-metal-insulator (IMI) waveguides are preferable as the infrastructure due to their simplicity and effectiveness. This is because the metal plates forming these waveguides are well suited to applying a bias voltage to adjust the tilt angle of the LC infiltrated in the waveguide. For example, some recently devised tunable optical resonators and switches are based on the prototype of the LC-infiltrated MIM waveguides [30; 31]. As a cladding material of IMI waveguides, the LC has also found its application in surface plasmon polaritons (SPP) filters or transmission devices [32; 33]. Considering the advantages of the MIM waveguide, it is also preferred as the infrastructure of the demultiplexer presented here. In this paper, we present an LC-infiltrated tunable demultiplexer with multiple slots as output channels, which is biased by an external electric field (\(E\)). The propagating property of a MIM waveguide is closely related to dielectric parameters of the intermediate layer sandwiched by two metal layers. Thus, employing LC as the infiltrating material of the MIM waveguide can provide an efficient method of tuning the transmission characteristics of the waveguide. Meanwhile, etching slots on a metal plate of the MIM waveguide introduces multiple output channels of the device. To determine the optimistic locations of the output channels, the field distribution of Fabry-Perot (FP) resonances of the finite-length MIM waveguide is theoretically and numerically investigated.