Arbitrary aperture synthesis with nonlocal leaky-wave metasurface antennas

Leaky-wave antennas (LWAs) offer high directivity, low profile, simple feeding, and inherent beam-scanning via dispersion, but conventional implementations provide limited degrees of freedom—primarily attenuation and propagation constants with fixed linear polarization—insufficient for modern demands in capacity, diversity, and energy efficiency. Metasurfaces composed of engineered subwavelength meta-units have expanded control over wave manipulation, enabling radiating impedance surfaces and tensorial responses for polarization control. Beyond local-response metasurfaces, nonlocal metasurfaces harness mutual coupling (e.g., via guided modes) and the physics of bound states in the continuum (BICs). Breaking symmetry in BICs yields quasi-BICs (q-BICs) that radiate with controllable features, previously leveraged in optics to sculpt wavefronts, polarization, and spectra, and recently to realize integrated photonic LWMs. This work translates the q-BIC concept to micro/millimeter waves on a PCB platform, enabling unidirectional high-directivity radiation with compact launchers and multi-port operation. The objective is to rationally design nonlocal LWMs that allow pointwise control of aperture amplitude, phase, and polarization (orientation and ellipticity), demonstrated through prototypes achieving SIMO and MIMO near-field focusing and dual-polarized far-field multi-beam shaping.

Prior LWA and metasurface antenna research includes holographic LWMs formed by modulating effective impedance to radiate guided surface waves and tensorial impedance designs for polarization control. Huygens’ metasurfaces and cascaded tensorial sheets offer simultaneous control over amplitude, phase, and polarization, while discrete dipolar meta-atom arrays trade some degrees of freedom for simpler realization. Nonlocal metasurfaces, intensively studied in optics, exploit coupling among meta-units and BIC physics: symmetry-protected BICs avoid radiation due to parity, but tailored perturbations produce q-BICs with tunable radiation. These principles enable algebraic mappings from desired wave parameters (amplitude, phase, polarization orientation and ellipticity) to geometric meta-unit parameters, reducing reliance on numerical optimization and lookup tables. Recent integrated photonic LWMs validated spatially varying perturbations for customized emission; this work extends such principles to mm-wave PCB implementations with practical launchers and unidirectional radiation.

Working principle: A perforated parallel-plate waveguide (PPWG) platform with thickness h and dielectric constant εr is patterned with a staggered array of rectangular slots supporting a quasi-TEM q-BIC that leaks under controlled symmetry-breaking. The design controls four local aperture degrees of freedom: amplitude A, phase φ, and polarization state (orientation ψ and ellipticity χ on the Poincaré sphere). Radiation magnitude control: Starting from an artificial BIC created by period-doubling along x (mode folded to Γ in the FBZ), introducing a symmetry-breaking perturbation between adjacent slots converts the a-BIC into a leaky q-BIC with finite radiative Q, which increases strongly as perturbation decreases; larger asymmetry yields stronger leakage. The resonant frequency depends weakly on perturbation for small values; larger perturbations may require slot size compensation to avoid squint. Linear polarization control: Rotating each slot pair by angle α toggles magnetic-wall symmetry, enabling continuous tuning across linear polarizations by sweeping α, thus traversing the Poincaré equator and selecting x- or y-polarized outputs and their polarity. Phase control: Independent perturbations δ1 and δ2 are applied to the lower and upper slot rows, which are 90° out of phase in the q-BIC modal profile, providing independent in-phase and quadrature control and full 360° phase coverage. A geometric parametrization (e.g., δ1=δ cos t, δ2=δ sin t, with desired phase encoded in t) yields robust phase patterns with reduced sensitivity to phase wraps. Full control: By combining (δ1,α1) and (δ2,α2) for the two rows, both linear polarization components and their in-phase/quadrature magnitudes are set, enabling deterministic mapping from desired aperture fields to geometry through simple algebraic equations with coupling coefficients obtained once via simulation. Prototypes and implementation: Three PCB-based LWMs on Rogers RO3003 (h=1.52 mm, εr=3, tanδ=0.001) are fabricated using LPKF tools. Each device comprises seven identical columns of meta-units repeated laterally to form a quasi-1D LWM, balancing performance and launcher complexity. Feeding uses a substrate-integrated waveguide (SIW) four-way power divider tapering into horn arrays; SMA flange connectors (pins trimmed to 1.52 mm) provide RF access. SIMO near-field focusing LWM: Design frequency 20.55 GHz; aperture superposes two converging circularly polarized cylindrical wavefronts centered at r1=(-2λ0,6λ0) and r2=(λ0,4λ0). Unperturbed square slot width w=1.85 mm; maximum perturbation δ=1.55 mm. Meta-unit dimensions reported as approximately 2λ0×8.25 mm and 2λ0×6.25 mm; aperture includes 16 distinct meta-units, ~9λ0 long. Assumes equal coupling to x and y polarizations (cx=cy) for synthesis. A four-way SIW launcher excites the q-BIC. MIMO near-field focusing LWM: Same nominal platform and frequency; aperture encodes one converging RCP spot and one diverging LCP virtual source for port 1; time-reversal symmetry yields exchanged CP roles and phase conjugation for port 2, enabling independent focal spots r1=(−2λ0,5λ0) and r2=(2λ0,−6λ0). Dual-polarized multi-beam LWM: Far-field antenna producing two RCP beams (θR,1=10°, θR,2=30°) and one LCP beam (θL,3 specified in design), with relative weights AR,1=AL,3=1, AR,2=1.14; realized on the same PCB platform and launcher network. Numerical simulations: Band structures via COMSOL eigenfrequency solver with Floquet periodic boundaries, PEC claddings, and scattering boundary on top; spurious modes identified and discarded. Simplified COMSOL frequency-domain models (infinite periodicity along y) validate SIMO/MIMO concepts with TEM-wave excitation at port 1 and matched termination at the opposite end. Full-prototype HFSS simulations (including seven columns, SIW networks, copper via horns, copper thickness 0.018 mm, conductivity 5.8×10^7 S/m) predict realized gain using radiation surface integrals. Measurements: Near-field planar scans (NSI-MI) with K-band open-ended waveguide probe 5 cm from the aperture; fields projected to planes to form Fresnel-zone holograms and extracted CP components. Far-field patterns measured and gains calibrated against a 15 dBi standard gain horn (Pasternack PE-9852/2F-15). During measurements, the unused port is terminated by a 50 Ω matched load.

• Demonstrated deterministic, pointwise control of aperture amplitude, phase, and polarization in mm-wave nonlocal LWMs via symmetry-broken q-BIC meta-units with a fixed periodicity.
• Radiation magnitude control: Leaky q-BIC radiative Q-factor strongly depends on perturbation strength; larger asymmetry yields stronger radiation, while the resonant frequency remains nearly constant for small perturbations.
• SIMO focusing LWM: From a single input, produced two spatially separated near-field focal spots with orthogonal circular polarizations. Measured operation frequency upshifted to 21.05 GHz due to practical nonidealities; two high-intensity regions were observed near the design focal locations. Polarization-resolved measurements showed high purity with at least 15 dB cross-polarization discrimination at focal spots across most tested frequencies; frequency tuning laterally scanned focal positions as expected for leaky-wave emission. The tapered aperture broadened the spots as designed.
• MIMO focusing LWM: Independent port excitations generated distinct RCP-focused spots at prescribed locations for port 1 and port 2 (with weak opposite-handed CP background). Polarization purity at spot centers showed cross-polar levels at most −9.3 dB (port 1) and −9.7 dB (port 2) below co-polar across measured frequencies. Measured signal-to-crosstalk ratio (half-duplex) was at least 5 dB across the scan range; simulations indicated higher SCR, attributing discrepancies to launcher reflections and truncation effects. Frequency scanning steered focal spots as designed.
• Dual-polarized multi-beam antenna: Realized two RCP beams (10° and 30°) and one LCP beam with measured realized gains and main-beam directions closely matching simulations at ~20.8 GHz. Observed −10 dB side-lobe levels for RCP beams and a −8 dB back lobe for the LCP beam (due to launcher reflection); overall low side lobes otherwise. Simulated total radiation efficiency ≈44% including dielectric and conduction loss.
• Practical platform: PCB-compatible implementation with SIW horn-array launchers; results validated by full-wave simulations and experiments.

The study addresses the need for advanced, compact, and versatile antennas by harnessing nonlocal metasurface q-BIC physics to endow leaky-wave antennas with independent control of amplitude, phase, and polarization at each aperture point. By leveraging symmetry considerations, the approach yields simple algebraic synthesis rules that bypass heavy numerical optimization and lookup tables. The demonstrations verify that a single, fixed-periodic metasurface can realize SIMO and MIMO near-field focusing and dual-polarized multi-beam far-field radiation, with frequency-enabled scanning and acceptable polarization purity and inter-channel isolation. Compared to conventional LWA designs relying on aperiodic placement and periodicity control of scatterers to set phase, the proposed method uses spatially varying geometric phase and controlled leakage within a fixed periodic lattice, providing a rational, generalizable pathway to customized aperture fields. The mm-wave PCB platform offers unidirectional radiation with high directivity and practical, compact launchers, suggesting strong relevance for 5G/6G and satellite links. The framework’s generality indicates applicability across frequency regimes and diverse physical implementations.

This work introduces a rational, symmetry-based design framework for nonlocal leaky-wave metasurface antennas that translates desired aperture amplitude, phase, and polarization into geometric perturbations of q-BIC meta-units. Prototypes validate SIMO and MIMO near-field focusing with frequency-scanned spots and dual-polarized multi-beam far-field shaping, corroborated by simulations and measurements. The approach simplifies synthesis, enhances functionality over conventional LWAs, and is compatible with scalable PCB manufacturing. Future research directions include: developing compact, broadband launchers and improved launcher–metasurface transitions; extending to fully two-dimensional apertures and fixed-frequency beam scanning using multiple inputs and phase shifters; leveraging multiple orthogonal q-BIC modes to increase channel count (e.g., doubling MIMO channels); optimizing aperture amplitude envelopes for efficiency and sidelobe suppression; and incorporating higher-order multipole modeling for accurate end-fire designs and dispersion-managed beamforming.

• Designs operate in the small-perturbation regime, reducing efficiency; higher leakage requires larger apertures or more complex meta-units (e.g., meandered slots) to increase coupling while maintaining footprint constraints.
• Trade-off between radiation efficiency and aperture efficiency: high leakage depletes guided power toward the aperture end; tailored amplitude envelopes are needed to compensate tapered excitation.
• Lateral truncation (limited number of columns) and non-ideal SIW launcher transitions introduce edge effects, reflections, and counter-propagating waves, degrading polarization purity, causing back lobes, and reducing channel isolation; improved matching and larger apertures can mitigate these issues and may enable full-duplex port isolation.
• Frequency dispersion leads to beam squint relative to prescribed scan angles; optimal operating frequency shifts were observed between simulation and experiment due to fabrication tolerances and substrate property deviations.
• The synthesis assumes primarily dipolar element factors, accurate near broadside; at large oblique angles (near end-fire), higher-order multipoles reduce formula accuracy, suggesting the need for extended models.