# Analysis and Design of Tunable THz 1-D Leaky-Wave Antennas Based on Nematic Liquid Crystals
###### Abstract  
The tunable properties of nematic liquid crystals (NLC) are here exploited in a peculiar leaky waveguide with artificial magnetic conductors as the lateral walls, a bottom metal ground plane, and a homogenized metasurface on top to obtain dynamic beamsteering at a fixed terahertz frequency. The waveguide consists of an NLC cell sandwiched between two dielectric layers. The proposed antenna system works on its transverse-magnetic leaky mode and is capable of radiating a beam that scans either by frequency or by changing the bias voltage applied across the NLC cell. The design parameters are optimized through a rigorous modal analysis of the structure, and the radiation performance is validated through full-wave simulations. The results are promising for the realization of next-generation tunable terahertz leaky-wave antennas.  
leaky-wave antennas; tunable antennas; terahertz; frequency selective surfaces; liquid crystals +
Footnote †: journal: Applied Physics Letters  
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Footnote 1: [[https://www.mdpi.com/journal/applsci](https://www.mdpi.com/journal/applsci)]([https://www.mdpi.com/journal/applsci](https://www.mdpi.com/journal/applsci))  
namely, high birefringence and moderate losses. The former is crucial to considerably affect the phase constant \(\beta\) of leaky modes in NLC-filled waveguides and, in turn, steer the beam of an antenna over an appreciable angular range. The latter is key to obtain a sufficiently low leakage rate \(\alpha\), and thereby achieve satisfactory antenna performance in terms of directivity and efficiency.  
As a result, a number of tunable passive THz devices based on NLC, such as filters, polarizers, cavities, etc., have recently appeared (see [36] and the references therein) and, more recently, even NLC-based LWAs [37; 38; 39]. The concept of tunable LWAs based on NLC at a fixed THz frequency was theoretically proposed in [38], where it was applied to a Fabry-Perot cavity-like structure to radiate a pencil beam at broadside and/or a directive conical beam achieving about a 30\({}^{\circ}\) of angular reconfigurability in elevation with efficiencies as high as 80% at around 500 GHz.  
The results in [38] were confirmed by full-wave simulations, whereas experimental results showing similar performance were obtained at lower frequencies--namely, at the W-band, with a 1-D image-line LWA [39]. More recently, preliminary results [40] demonstrated the possibility to achieve beam-steering at approximately 1 THz with a peculiar leaky waveguide filled with NLC and made of perfect electric and magnetic conductors (PEC and PMC, respectively), and a homogenized metasurface that acts as a partially reflecting sheet (PRS).  
In this work, we elaborate on the preliminary analysis of [40], providing the necessary details to properly design both the artificial magnetic conductor (AMC) and the PRS, which were previously supposed to be an ideal PMC and an ideal isotropic metasurface, respectively. Moreover, we derive a useful analytic formula to evaluate the scan rate at a fixed frequency that is then exploited to determine the optimal working points for the proposed design. An original analysis on the antenna performance clearly reveals that the angular tunability is improved by radiating close to broadside or endfire, whereas the gain monotonically increases when radiating close to endfire. However, LWAs do not usually radiate efficiently at endfire unless properly designed (see, e.g., Ref. [41; 42]); a sub-optimal operating condition is thus selected to deal with such constraints.  
The paper is organized as follows: Section 2 covers the necessary background on LWAs to understand the working principle of the original leaky waveguide proposed here. Section 3 provides design rules to optimize the antenna structure, as well as to correctly synthesize both the AMC and the PRS. Finally, in Section 4, full-wave results are reported and commented. Our conclusions are presented in Section 5.