Conformal leaky-wave antennas for wireless terahertz communications

As wireless technology looks beyond 5G, operation in the terahertz (THz) bands and the proliferation of IoT devices are anticipated. THz links require antennas with high gain, high directionality, and wide bandwidth, while IoT deployments demand antennas that can conform to nonplanar surfaces. Conventional conformal antennas at lower frequencies are often too large and cannot support ultrahigh data rates. This motivates conformal antennas operating in the THz range. The study introduces a conformal leaky-wave antenna based on an air-filled parallel-plate waveguide bent into a cylindrical geometry with an azimuthal slot aperture to radiate. The physics is governed by the interplay among three length scales: guided wavelength, cylinder radius R, and slot length L. Three distinct operating regimes arise depending on their relative values. The work develops simple models, validates them experimentally, and demonstrates data transmission with multiple high-gain beams and low bit error rates, highlighting the feasibility of conformal THz antennas for future wireless links.

Leaky-wave antennas have been extensively used at RF and THz frequencies due to their high directivity and beam scanning capabilities. At lower frequencies, conformal antennas have been important in applications such as aerospace where form factor and aerodynamics are critical, but their physical size limits IoT applicability and data rate. Prior THz leaky-wave implementations often employ dielectric-filled periodic structures that excite Floquet modes; however, common dielectrics can be lossy at THz frequencies. In air-filled parallel-plate waveguides, the fundamental mode is a fast wave (neff < 1) and always leaks; periodic slots would excite multiple leaky modes and multiple angles, so a single linear slot is preferred for single-angle radiation. Previous analyses of curved waveguides typically assumed large radii and neglected curvature-squared terms; at THz scales, small radii are practical and require retaining those terms. The study builds on these insights to analyze conformal leaky-wave antennas with air-filled waveguides and minimal dielectric loss.

Modeling: The antenna uses a curved air-filled parallel-plate waveguide (plate separation b = 1 mm, refractive index n = 1) bent to radius R, supporting a TE-like mode propagating azimuthally (y = Rθ). The Helmholtz equation in polar coordinates is reduced to a one-dimensional eigen-equation in x between the plates, with perfect electric boundary conditions at x = 0 and x = b. The resulting eigenproblem is discretized via finite differences to compute eigenvalues γ = α + jβ and eigenvectors E(x). The effective index neff and its dependence on R are extracted and fitted to neff(R) = neff(planar) + Rfit/R, with neff(planar) = sqrt(1 − (fc/f)^2), fc = c/(2b). A geometrical optics model is developed to estimate a frequency-dependent critical radius Rgeom ≈ 2b[(f/f0)^2 − 1], capturing the transition to whispering-gallery-like behavior when rays reflect primarily from the outer plate at tight curvature. Experimental waveguide characterization: Using THz time-domain spectroscopy in transmission and a cut-back technique, phases through two waveguide lengths are measured to determine neff via phase differences across 150–300 GHz for planar and curved waveguides (e.g., R = 3.5 mm). Dispersion analysis: Group velocity dispersion (GVD) is computed from neff(f) using GVD = (2/c) d neff/dω + (ω/c) d^2 neff/dω^2 and compared against the planar analytical expression GVDplanar = bπc/2[(f/fc)^2 − 1]^(−3/2). The impact on maximal bitrate Bmax (ASK) limited by dispersion is estimated using Bmax = 1/(4√(|GVD|·l)) versus propagation length l. Radiation modeling: A narrow rectangular slot along the azimuthal direction in the outer plate forms a leaky aperture. Far-field radiation is computed using the Stratton–Chu diffraction integral over the slot aperture. The field under the slot is modeled as E(θ) ∝ exp{−j(β + jα)(R + b)θ}, where α is a leakage rate chosen so most energy leaks before reaching the end of the slot (residual absorbed by a load). For narrow slots, the 3D surface integral reduces to 1D angular integrals, yielding expressions for the radiated field and revealing phase-matching cos θ = β/k0 and L-dependent sinc behavior analogous to planar antennas. Finite element method (FEM) simulations validate the semi-analytical radiation model. Antenna fabrication and measurements: Conformal leaky-wave antennas are fabricated by cutting 2-mm-wide rectangular slots in flexible copper sheets mounted on cylindrical aluminum tubes with 1-mm spacers ensuring constant plate separation. Single-slot antennas with radii R = 8 mm and R = 50.8 mm use slot length L = 10 mm. A 200 GHz source (×16 frequency-multiplier from 12.5 GHz) emits through a horn and dielectric lens, focused into a tapered input of the curved waveguide. Far-field patterns are recorded with a Schottky diode on a rotating rail. Communications experiments: A multi-beam conformal antenna is made with two 2-mm-wide, 20-mm-long slots separated azimuthally by 60°, laterally offset by 2 mm, enabling sequential leakage. A 12.5 GHz tone is OOK-modulated by a pulse pattern generator at 1.12 Gbps with PRBS length 2^27 − 1. Reception uses a zero-bias Schottky diode, low-pass filtering (0.1–6 GHz), and measurement of power, real-time BER, and eye diagrams.

• Mode behavior in curved waveguides: Only TE1-like modes propagate in the 150–300 GHz single-mode band (b = 1 mm). Curvature distorts the mode at higher frequencies and small R, shifting energy toward the outer plate and approaching whispering-gallery-like behavior for tight bends.
• Effective index versus curvature: neff(R) fits neff(planar) + Rfit/R, with Rfit increasing with frequency; a critical radius near 10·Rfit separates planar-like and curved regimes. A geometric optics estimate Rgeom ≈ 2b[(f/f0)^2 − 1] captures the trend of the transition.
• Experimental validation: Measured neff for R = 3.5 mm agrees well with the semi-analytical model, and planar measurements agree with the analytical planar expression.
• Dispersion impact: GVD is more affected at lower frequencies and smaller R. Examples: at 200 GHz, GVD changes from −49 ps·THz⁻1·cm⁻1 (planar) to −60 ps·THz⁻1·cm⁻1 (R = 2 mm). At 280 GHz, it changes from −9.5 ps·THz⁻1·cm⁻1 (planar) to about 9 ps·THz⁻1·cm⁻1 (R = 2 mm). Corresponding maximal bitrate reductions over 1 cm are about 11% at 200 GHz and 3.6% at 280 GHz.
• Radiation patterns and directivity: Even for moderate curvature (e.g., R = 25 mm) where neff is near planar, the radiation pattern broadens significantly because the guided wavevector rotates along the arc over the aperture length L. Directivity approaches the planar case as R increases. Measured patterns for R = 8 mm and R = 50.8 mm match semi-analytical and FEM predictions; FEM directivities are approximately 14 dB and 18 dB, respectively.
• Angular dispersion: Peak radiation angle satisfies cos θ = β/k0, leading to frequency-dependent beam angles (rainbow-like pattern). For planar parallel plates, sin θ = c/(2bf), implying angular dispersion considerations for wideband transmission and high-gain narrow beams.
• Multi-beam demonstration: A conformal antenna with two slots separated by 60° generates two directional beams of similar amplitude with total angular coverage exceeding 90°. With 1 Gbit/s OOK, measured bit error rates are < 1e−5 for both beams, and eye diagrams show clear openings with minimal distortion, indicating minimal inter-symbol interference even for the second slot’s beam.

The study addresses the need for compact, conformal THz antennas capable of high-gain, directional radiation over wide bandwidths. By modeling and experimentally validating curved air-filled parallel-plate waveguides, it identifies distinct propagation regimes from planar-like to whispering-gallery-like as curvature tightens, and quantifies how curvature influences dispersion and radiation. A key insight is that even when guided-mode properties remain near-planar (large R), the far-field pattern can degrade in directivity if the guided wavevector rotates significantly across the slot length; thus, aperture length relative to radius (L/2R) becomes a critical design parameter. The results guide design trade-offs among curvature, aperture length, plate separation, and leakage rate to maintain directivity and bandwidth. The communications experiments demonstrate practical viability: multi-beam operation with wide angular coverage and low BER at Gbit/s rates, with dispersion-induced inter-symbol interference being modest in the demonstrated configurations. Design strategies such as varying plate separation to compensate angle changes and tapered-slot leakage engineering are suggested to mitigate curvature-induced directivity loss, while recognizing constraints like multimode avoidance and uniform leakage.

The work demonstrates conformal leaky-wave antennas at THz frequencies using curved air-filled parallel-plate waveguides with slot apertures. A semi-analytical eigenmode model captures curvature effects on the TE1-like mode, revealing planar-like to whispering-gallery-like regimes and a frequency-dependent critical radius. Curvature increases the magnitude of dispersion more at lower frequencies and tight bends, modestly reducing maximal bitrates over centimeter-scale lengths. Far-field directivity is strongly influenced by the rotation of the guided wavevector across the aperture arc, even for relatively large radii. A proof-of-concept two-slot conformal antenna produces two high-gain beams separated by 60°, achieving BER < 1e−5 at 1 Gbit/s and coverage exceeding 90°. These findings elucidate the physics of curved THz waveguides and support the development of compact, conformal, high-performance THz antennas for future wireless systems and IoT. Future research could explore advanced leakage-rate tapering, curvature-compensation via spatially varying plate separation or metasurfaces, mitigation of angular dispersion for ultra-wideband links, and integration with THz front-ends for fully packaged conformal modules.

• Increased dispersion at small radii (tight curvature), especially at lower frequencies, reduces maximal achievable bitrate over a given length.
• Angular dispersion (frequency-dependent beam angle) can cause angular spreading for wideband signals, particularly problematic with high-gain narrow beams.
• Compensation by varying plate separation b is limited by the onset of multimode propagation; careful design is required to remain single-mode.
• Uniform power leakage along the slot requires engineered leakage-rate tapering; the semi-analytical model uses a constant leakage parameter α as an approximation.
• The geometric optics model provides only a qualitative trend and is a low-order approximation; exact agreement with eigenmode fits is not expected.
• Experimental demonstrations are at specific frequencies (around 200 GHz), slot dimensions, and radii; broader validation across bands and geometries is not shown.
• Free-space coupling via horn and lens was used; fully integrated feeding strategies were not implemented in this work.