# Analysis and Design of Tunable THz 1-D Leaky-Wave Antennas Based on Nematic Liquid Crystals

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## Abstract

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## 1. Introduction

## 2. Theoretical Analysis

#### 2.1. Closed Waveguide

#### 2.2. Open Leaky Waveguide

#### 2.3. Tunable Leaky Waveguide Filled with NLC

#### 2.4. Tunable Leaky Waveguide Partially Filled with NLC

## 3. Optimization and Design

#### 3.1. Optimization of the Ideal Structure

#### 3.2. Design of the AMC Walls

#### 3.3. Design of the PRS

#### 3.4. Liquid-Crystal Switching

## 4. Results

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**From left to right, an air-filled PEC/PMC waveguide, which evolves first in an open leaky waveguide where the PEC top plate is replaced by a PRS, is then entirely filled with an NLC to allow for dynamic beamsteering and, finally, is only partially filled with an NLC material to compensate for losses.

**Figure 2.**(

**a**) A schematic 3-D view of a 1-D unidirectional LWA based on PRS and NLC, (

**b**) its cross section along the $yz$-plane, and (

**c**) the related transverse equivalent network. The biasing scheme is shown only in (

**b**).

**Figure 3.**(

**a**,

**b**) Dispersion curves $\hat{\beta}$ (solid lines) and $\hat{\alpha}$ (dashed lines) vs. f for NLC states continuously varying from the ‘off’ (blue) to ‘on’ state (red). The results in (

**a**,

**b**) are for the lossy and lossless cases, respectively. Dotted vertical colored lines highlight the frequency at which the antenna performance shown in (

**c**,

**d**) are evaluated. (

**c**) The beam angle ${\theta}_{0}$ (in solid lines) and half-power beamwidth $\Delta \theta $ (in dashed lines), and (

**d**) gain G as the optical axis $\delta $ tilts from the horizontal z-axis $\delta ={0}^{\circ}$ to the vertical x-axis ($\delta ={90}^{\circ}$) for the frequencies shown in (

**a**).

**Figure 4.**(

**a**) Phase of the reflection coefficient vs. f (solid black line) of the patch unit cell for realizing the PMC. The vertical dotted line highlights that the phase of the reflection coefficient is zero at the desired frequency of 1.049 THz. (

**b**) Sheet reactance vs. f (solid black line) of the transverse slot for realizing the PRS. The parameters are in the text.

**Figure 5.**(

**a**) Radiation efficiency ${\eta}_{\mathrm{rad}}$, and (

**b**) gain (in dB) vs. NLC tilt angle $\delta $ for $f=1.049$ THz. The CST results are shown as black circles, and the numerical results are shown as solid black lines. (

**c**) Normalized radiation patterns at $f=1.049$ THz for four different LC states—namely, $\delta ={0}^{\circ},\phantom{\rule{0.166667em}{0ex}}{30}^{\circ},\phantom{\rule{0.166667em}{0ex}}{60}^{\circ},$ and ${90}^{\circ}$ in black, light blue, green, and yellow, respectively. The CST results are shown as colored circles, and the analytical results are shown as solid colored lines. The inset of (

**c**) shows the normalized 3-D radiation pattern for the last NLC state for which the beam peak points at approximately ${45}^{\circ}$ (as expected from Figure 3c). The intensity of the normalized 3-D radiation pattern goes from −20 dB (green) to 0 dB (red).

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**MDPI and ACS Style**

Fuscaldo, W.; Zografopoulos, D.C.; Imperato, F.; Burghignoli, P.; Beccherelli, R.; Galli, A.
Analysis and Design of Tunable THz 1-D Leaky-Wave Antennas Based on Nematic Liquid Crystals. *Appl. Sci.* **2022**, *12*, 11770.
https://doi.org/10.3390/app122211770

**AMA Style**

Fuscaldo W, Zografopoulos DC, Imperato F, Burghignoli P, Beccherelli R, Galli A.
Analysis and Design of Tunable THz 1-D Leaky-Wave Antennas Based on Nematic Liquid Crystals. *Applied Sciences*. 2022; 12(22):11770.
https://doi.org/10.3390/app122211770

**Chicago/Turabian Style**

Fuscaldo, Walter, Dimitrios C. Zografopoulos, Francesca Imperato, Paolo Burghignoli, Romeo Beccherelli, and Alessandro Galli.
2022. "Analysis and Design of Tunable THz 1-D Leaky-Wave Antennas Based on Nematic Liquid Crystals" *Applied Sciences* 12, no. 22: 11770.
https://doi.org/10.3390/app122211770