Terahertz beamforming network with a nonuniform contour

Milad Hadei; Milad Hadei; Gholamreza Dadashzadeh; Gholamreza Dadashzadeh; Yalda Torabi; Yalda Torabi; Ali Lalbakhsh; Ali Lalbakhsh

doi:10.1364/AO.448014

Applied Optics
Vol. 61,
Issue 4,
pp. 1087-1096
(2022)
•https://doi.org/10.1364/AO.448014

Terahertz beamforming network with a nonuniform contour

Milad Hadei, Gholamreza Dadashzadeh, Yalda Torabi, and Ali Lalbakhsh

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Milad Hadei, Gholamreza Dadashzadeh, Yalda Torabi, and Ali Lalbakhsh, "Terahertz beamforming network with a nonuniform contour," Appl. Opt. 61, 1087-1096 (2022)

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Abstract

This paper presents a terahertz beamforming network based on a nonlocal lens with a 2D beam-scanning demonstration through leaky-wave antennas. The proposed design methodology is novel, to the best of our knowledge, in the aspect of using unconventional optimization parameters to significantly reduce the phase error associated with this class of beamformers. In this approach, a nonuniform contour defined by Fourier series expansion is used as a new optimization parameter to significantly decrease the phase error over a larger scan-angle than that in the previous works. The proposed system is a good candidate for industrial and security applications such as automotive radar sensors and electromagnetic THz imaging, thanks to its extensive 2D scanning range: ${-}{{68}}^\circ$ to 0° in the elevation plane and ${-}{{45}}^\circ$ to ${+}{{45}}^\circ$ in the azimuth plane over the frequency range of 140–180 GHz.

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Symbol	Value	Symbol	Value	Fourier Series Component of TX Contour	Value	Fourier Series Component of RX Contour	Value
$Θ_{1}$	$40^{\circ}$	$w_{2}$	0.005645	$a_{1}$	–0.0464	$b_{1}$	0.0344
$Θ_{2}$	${25.79998}^{\circ}$	$w_{3}$	0.001466	$a_{2}$	–0.1218	$b_{2}$	–0.0988
$r_{1}$	0.600000	$w_{4}$	0	$a_{3}$	0.0609	$b_{3}$	–0.0781
$r_{2}$	0.940322	$w_{5}$	0.001466	$a_{4}$	–0.0047	$b_{4}$	–0.0355
$R$	1.38	$w_{6}$	0.005645	$a_{5}$	–0.6310	$b_{5}$	0.1402
$w_{1}$	0.117500	$w_{7}$	0.117500	$a_{6}$	–0.0476	$b_{6}$	–0.0569

Reference	Phase Error Normalized to Focal Length ( $f_{0}$ )	Designed Methodology	Scan Angle
[32]	$1.5 * 10^{- 3}$	Introducing ray-to-beam angle ratio	–
[27]	$2.5 * 10^{- 3}$	Applying circular beam and array contours	$\pm 40^{\circ}$
[33]	$1 * 10^{- 3}$	Obtaining feed curve points assuming zero path length error at three points of the radiating array for each beam direction	–
[34]	$6.5 * 10^{- 3}$	Optimizing $α$ , $F$ , and $γ$ and moving off-axis focal points along the beam curve	$\pm 37^{\circ}$
[35]	$1.67 * 10^{- 3}$	Determining the beam’s location by applying ray optics theory	$\pm 30^{\circ}$
[36]	$3.7 * 10^{- 5}$	Optimizing the position of the input and output ports of the lens based on genetic algorithm	$\pm 28^{\circ}$
[37]	$2.68 * 10^{- 6}$	Optimizing the parallel plate for minimum phase error, based on PSO algorithm, over four geometrical parameters.	$\pm 34^{\circ}$
This paper	$3.07 * 10^{- 5}$	Optimized nonuniform contour for minimum phase error and wide scan angle based on genetic algorithm	$\pm 45^{\circ}$

Symbol	Value	Symbol	Value	Fourier Series Component of TX Contour	Value	Fourier Series Component of RX Contour	Value
$Θ_{1}$	$40^{\circ}$	$w_{2}$	0.005645	$a_{1}$	–0.0464	$b_{1}$	0.0344
$Θ_{2}$	${25.79998}^{\circ}$	$w_{3}$	0.001466	$a_{2}$	–0.1218	$b_{2}$	–0.0988
$r_{1}$	0.600000	$w_{4}$	0	$a_{3}$	0.0609	$b_{3}$	–0.0781
$r_{2}$	0.940322	$w_{5}$	0.001466	$a_{4}$	–0.0047	$b_{4}$	–0.0355
$R$	1.38	$w_{6}$	0.005645	$a_{5}$	–0.6310	$b_{5}$	0.1402
$w_{1}$	0.117500	$w_{7}$	0.117500	$a_{6}$	–0.0476	$b_{6}$	–0.0569

Reference	Phase Error Normalized to Focal Length ( $f_{0}$ )	Designed Methodology	Scan Angle
[32]	$1.5 * 10^{- 3}$	Introducing ray-to-beam angle ratio	–
[27]	$2.5 * 10^{- 3}$	Applying circular beam and array contours	$\pm 40^{\circ}$
[33]	$1 * 10^{- 3}$	Obtaining feed curve points assuming zero path length error at three points of the radiating array for each beam direction	–
[34]	$6.5 * 10^{- 3}$	Optimizing $α$ , $F$ , and $γ$ and moving off-axis focal points along the beam curve	$\pm 37^{\circ}$
[35]	$1.67 * 10^{- 3}$	Determining the beam’s location by applying ray optics theory	$\pm 30^{\circ}$
[36]	$3.7 * 10^{- 5}$	Optimizing the position of the input and output ports of the lens based on genetic algorithm	$\pm 28^{\circ}$
[37]	$2.68 * 10^{- 6}$	Optimizing the parallel plate for minimum phase error, based on PSO algorithm, over four geometrical parameters.	$\pm 34^{\circ}$
This paper	$3.07 * 10^{- 5}$	Optimized nonuniform contour for minimum phase error and wide scan angle based on genetic algorithm	$\pm 45^{\circ}$

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Applied Optics