# A Wide-Angle Scanning Sub-Terahertz Leaky-Wave Antenna Based on a Multilayer Dielectric Image Waveguide

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## Abstract

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## 1. Introduction

## 2. Antenna Array and Design Method

#### 2.1. Radiating Element

_{r}, backed by a copper ground plane as presented in Figure 1a. The relative permittivity (ε

_{r}), width (2a), and thickness (b) of the substrate are the key design parameters of the DIL. The substrate material used in the antenna structure should have a high permittivity (~10 or above in practice) to achieve a high field confinement around the unshielded dielectric and a compact antenna with a large scanning angle. Additionally, to realize a high-gain and high-efficiency antenna, the considered substrate should have low dielectric losses in the sub-THz regimes. Accordingly, in this work, an alumina substrate of 0.254 mm thickness with a dielectric constant of 9.7 and a loss tangent of 0.0005 was considered for the DIL [27]. After choosing the substrate, the width (2a) and thickness (b) of the DIL was designed. The DIL thickness is the most crucial parameter to control the operating frequency range. However, the DIL width has less influence on the working frequency band and strongly affects the second DIL mode cutoff frequency. The widest practical bandwidth is achieved with a nearly equal height and half-width (a unity aspect ratio b = a), using the following formula [45]

_{0}is the free space wavelength at the operational frequency. The estimated value of a is equal to the substrate thickness b which equals 0.15 mm using (1) at the center frequency of 172 GHz. Therefore, the initial value of the DIL width was chosen as 2a = 0.3 mm. Since the commercially available alumina substrate does not have the thickness b = 0.15 mm, the closest available thickness b = 0.25 mm was considered in our design.

#### 2.2. Operation Mechanism and Leaky-Wave Generation

_{m}< k

_{0}were excited. The propagation constant of the mth order space harmonic is defined by [18]

_{0}and β

_{m}are the propagation constants for the fundamental and mth order space harmonics, correspondingly and m covers all integer ranges. As the fundamental space harmonic for open dielectric waveguides is usually a slow-wave, the negative spatial harmonics (m = −1, −2, −3, etc.) can only be leaky and radiative. It should be noted that not all leaky modes are physically important, and more than one leaky mode may be excited at the same time. An explanation of how each leaky mode contributes to the antenna radiation performance follows from the dispersion plot in Figure 2. This dispersion diagram of a unit-cell including the propagation (β

_{m}) and attenuation constant (α) graphs was obtained using the following equations [18]

_{−1}| < k

_{0}), at 157.5 GHz. When the frequency reaches 172 GHz, the leaky-wave antenna scans to the broadside without encountering an open-stop-band (OSB) problem, which corresponds to a β

_{−1}= 0. The OSB, as a known problem of many LWAs, is mainly caused by the coupling between the forward- and the backward-travelling of the n = −1 leak wave harmonic [46]. In the OSB, the reflection coefficient was increased and the gain drops considerably which avoided continuous beam scanning. In the proposed design, by printing two circular metal discs a quarter wavelength apart, OSB is suppressed. This will be explained in detail later in this section.

_{−2}| < k

_{0}) and β

_{−1}p = π. The coupling between the forward-traveling n = −1 and the backward-traveling n = −2, generally encounters the LWAs with another stop band. This can be observed as a sudden increase in the reflection coefficient which restricts the scanning range in the forward direction as well, appearing as a grating lobe around the backward end fire [4]. To suppress this stop band, the radiation from the n = −2 space harmonic should be avoided or weakened. One commonly used technique is to prevent the n = −2 space harmonic from entering the radiation region (i.e., (|β

_{−2}| > k

_{0})). This method has been previously mentioned in the literature [22,24,27]. Another approach is to make the attenuation constant of the n = −2 space harmonic as small as possible (near zero). We used the latter technique for designing the proposed antenna using the optimization algorithms in HFSS. The dispersion diagram clearly showed that the stop band corresponding to the n = −2 space harmonic had been successfully suppressed as the propagation constant increased almost linearly and smoothly with the frequency around 190 GHz and the attenuation constant remained relatively stable. As the frequency approached 205 GHz, the reflection coefficient and attenuation constant increased again due to the stop band relating to β

_{−1}p = 2π. The other higher spatial harmonics (i.e., n = −3, n = −4 and so on) did not enter the radiation region in the operating frequency range. These bounded modes (slow waves) will attenuate exponentially in the transverse direction and can only propagate along the structure. Consequently, the given frequency range is dominated by a single leaky mode (n = −1) scanning in the backward and the forward directions.

_{−1}= 0, the phase difference between unit-cells (Δφ) became 2π. This implies that the reflected waves from each circular disc become equally in phase at the broadside direction and hence, the maximum power is reflected towards the source. Therefore, the wave is rapidly attenuated as it propagated along the structure and the attenuation constant α becomes high, leading to the open-stop-band (OSB) phenomena [47].

_{0}calculated by [48]

_{−1}of the n = −1 space harmonic can be obtained by the propagation constant of the fundamental mode β

_{0}and the periodicity p of the unit-cells using the Equation (2). Consequently, the main beam direction of the proposed antenna is defined by the phase constant β

_{0}of the fundamental harmonics and the periodicity p as.

#### 2.3. Feeding Network

## 3. Simulation Results and Discussion

_{0}, where λ

_{0}is the free-space wavelength at the broadside frequency (172 GHz). The simulated scattering parameters of the antenna including reflection loss (S

_{11}) and insertion loss (S

_{21}) for two types of unit-cells with one circular disc and two overlapped circular discs with a center-to-center spacing of λg/4 are described in Figure 3a,b, respectively. It is seen from Figure 3a that the unit-cell with a single metal disc presents a high reflection loss over the frequency range of 173–181 GHz, causing no radiation and creating an OSB problem. However, the unit-cell with two overlapped discs gives a very low reflection loss, less than –18 dB at 172 GHz leading to radiation of the broadside (See Figure 3b). From this figure, it can be inferred that from 157.5 GHz to 206 GHz, the return loss S

_{11}was less than 10 dB, and the antenna was completely matched. It exhibits a relatively wide impedance bandwidth of 28.19%. Moreover, the simulated insertion loss S

_{21}was less than −8 dB.

_{LL}) of 13.2 dB was obtained.

## 4. Fabrication and Measurement Challenges

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Layout of the proposed LWA. (

**a**) Cross-sectional view of the array and (

**b**) a top view of the structure along with the feeding network; 2a = 0.3, p = 0.8, t

_{y}= 0.7, S = 0.12, g = 0.1, r = 0.1 mm, b = 0.254, h

_{2}= 0.254, h

_{1}= 0.127, (Unit: mm).

**Figure 2.**Dispersion curve of the optimized unit-cell with dimensions indicated in Figure 1.

**Figure 3.**Frequency variation of S-parameters of the proposed antenna for two type of unit-cells; (

**a**) one circular disc, (

**b**) two overlapped circular discs with a center-to-center spacing of λg/4.

**Figure 5.**Simulated co- and cross-polar E-plane and H-plane radiation patterns at the broadside frequency of 172 GHz.

Frequency Range (GHz) | Scanning Range (Degree) | Peak Gain (dBi) | Broadside Radiation | Size | Efficiency (%) | |
---|---|---|---|---|---|---|

[25] | 75–85 | −10°–8° | 12.7 | Yes | 11.1 λ_{0} | Not mentioned |

[50] | 55 to 67 | Forward only 4°–18° | 6 | No | 12 λ_{0} | 79 |

[51] | 230–245 | −25°–25° | 29 | Yes | 8 λ_{0} | 55 |

[1] | 220–300 | Backward only −75°–−30° | 28.5 | No | 10 λ_{0} | 75.8 |

[27] | 86–106 | −31°–10° | 11 | Yes | 6 λ_{0} | 58 |

[26] | 58–67 | Forward only 7°–38° | 11.7 | No | 2.6 λ_{0} | 85 |

This work | 157.5–206 | −23°–38° | 15 | Yes | 6.9 λ_{0} | 60 |

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**MDPI and ACS Style**

Torabi, Y.; Dadashzadeh, G.; Hadeie, M.; Oraizi, H.; Lalbakhsh, A.
A Wide-Angle Scanning Sub-Terahertz Leaky-Wave Antenna Based on a Multilayer Dielectric Image Waveguide. *Electronics* **2021**, *10*, 2172.
https://doi.org/10.3390/electronics10172172

**AMA Style**

Torabi Y, Dadashzadeh G, Hadeie M, Oraizi H, Lalbakhsh A.
A Wide-Angle Scanning Sub-Terahertz Leaky-Wave Antenna Based on a Multilayer Dielectric Image Waveguide. *Electronics*. 2021; 10(17):2172.
https://doi.org/10.3390/electronics10172172

**Chicago/Turabian Style**

Torabi, Yalda, Gholamreza Dadashzadeh, Milad Hadeie, Homayoon Oraizi, and Ali Lalbakhsh.
2021. "A Wide-Angle Scanning Sub-Terahertz Leaky-Wave Antenna Based on a Multilayer Dielectric Image Waveguide" *Electronics* 10, no. 17: 2172.
https://doi.org/10.3390/electronics10172172