# Electronic Beam Steering Metamaterial Antenna with Dual-Tuned Mode of Liquid Crystal Material
## 2 Dual-Tuned Mode of Liquid Crystal Material  
The schematic diagram of an LC dual-tuned mode structure is shown in Figure 1. It consists of two parts: the main structure part and the support structure. The main structure part is an LC dual-tuned structure, which includes three substrate layers (Substrates A, B and C) and double LC layers (LC1 and LC2). A metal layer is deposited on the upper and lower surface of the middle substrate, Substrate B. The lower surface of Substrate A and the upper surface of Substrate C are coated with a metal layer. Two LC layers are sandwiched between the middle substrate, Substrate B, and the upper and the lower substrates, Substrates A and C. Substrates A and C are provided with small holes for filling LC material, and these holes can be sealed with glue after filling. Each metal layer on the dielectric substrate can be loaded with bias voltage separately. Furthermore, in order to fix the substrates, the non-dielectric support and the base are adopted as fixing devices on both of the laterals and the bottom. Small notches are machined on the inner sides of the support part to fix the substrates and ensure the thickness of the LC layers.  
Nematic LCs are anisotropic materials composed of rod-like molecules, and they usually presents two permittivities along different directions: the parallel dielectric constant, \(\epsilon_{rf/}=3.22\) (in the direction of the LC molecules' axes); the vertical dielectric constant, \(\epsilon_{r\perp}=2.43\) (in the directions orthogonal to the LC molecules' axes); and the loss tangent, \(tan\delta=0.006\), which is derived from the material TUD-649 produced by Merck Corpora  
Figure 1: Schematic diagram of the LC dual-tuned mode structure.  
tion [29]. When LC material is in its natural state, the LC molecules are in a confused state, and the permittivity of LC is \(\varepsilon_{r}=2.83\), as shown in Figure 1.  
In the practical work of the LC, the dielectric constant along the \(z\)-axis direction mainly affects the dual-tuned mechanism; thus, the dielectric constant of the anisotropic LC material is expressed by the dielectric constant along the \(z\)-axis direction. When the LC layer is aligned along the \(x\)-axis (\(V_{\text{DC}}=0\) V), LC molecules are parallel to the \(x\)-axis without the bias voltage, and the permittivity of the LC is \(\varepsilon_{r\perp}=2.43\), as depicted in Figure 2a. Upon the condition that the LC layer is loaded with bias voltage along the \(z\)-axis, the LC molecules tend to deflect from the direction of \(x\)-axis to \(z\)-axis as the bias voltage increases. At present, the dielectric constant is between the vertical dielectric constant and the parallel dielectric constant, \(\varepsilon_{r\perp}<\varepsilon_{r}<\varepsilon_{r\parallel}\). When the bias voltage reaches the saturation value of the LC molecules (\(V_{\text{DC}}=V_{max}\)), the LC molecules are perpendicular to the direction of the \(x\)-axis and parallel to the direction of the \(z\)-axis, as sketched in Figure 2d. In this case, the permittivity of the LC is \(\varepsilon_{r\parallel}=3.22\). Upon the condition that the bias voltage is loaded on two LC layers, each LC layer presents two different states, as illustrated in Figure 2b,c. Thus, the dual-tuned mode makes the LC layer form four completely different extreme states. Meanwhile, it achieves continuing linear tuning between the four extreme states by modulating the magnitude of the bias voltage. Therefore, when the dual-tuned mode of the LC is adopted on metamaterial antennas, it provides a more diverse, more flexible beam-steering pattern and a wider beam-steering range of the metamaterial antenna.