Airy Beam Engineering in Near-field Communications: A Tractable Closed-Form Analysis in the Terahertz Band

Terahertz (THz) communication can offer terabit-per-second rates in future wireless systems, thanks to the ultra-wide bandwidths, but require large antenna arrays. As antenna apertures expand and we enter the near-field scenarios, the conventional binary classification of communication links as either Line-of-Sight (LoS) or Non-Line-of-Sight (NLoS) becomes insufficient. Instead, quasi-LoS scenarios, where the LoS path is partially obstructed, are increasingly prevalent, posing significant challenges for traditional LoS focusing and steering beams. The Airy beam serves as a promising alternative, utilizing its non-diffracting and curved trajectory properties to mitigate such blockages. However, while existing electromagnetics literature primarily explores their physical patterns without practical generation schemes, recent communication-oriented designs predominantly rely on learning-based frameworks lacking interpretable closed-form solutions. To address this issue, this paper investigates a closed-form Airy beam design to efficiently synthesize Airy beam phase profiles based on the positions of the transceivers and obstacles. Specifically, rigorous analytical derivations of the electric field and trajectory are presented to establish a deterministic closed-form design for ULA Airy beamforming. Leveraging 3D wavefront separability, this framework is extended to uniform planar arrays (UPAs) with two operation modes: the hybrid focusing-Airy mode and the dual Airy mode. Simulation results verify the effectiveness of our derived trajectory equations and demonstrate that the proposed closed-form design significantly outperforms conventional beamforming schemes in quasi-LoS scenarios. Furthermore, the proposed method achieves performance comparable to exhaustive numerical searches with low computational complexity and enhanced physical interpretability.

💡 Research Summary

This paper addresses the challenge of partial blockage (quasi‑Line‑of‑Sight, quasi‑LoS) in terahertz (THz) near‑field communications, where the large apertures of ultra‑massive MIMO arrays push most links into the radiative near‑field region. In such scenarios, conventional far‑field steering beams or near‑field Gaussian focusing beams, which rely on planar or spherical wavefronts, cannot reliably circumvent obstacles because their amplitude profiles are Gaussian and their phase is limited to linear or quadratic forms.

The authors propose to exploit the unique properties of Airy beams—self‑acceleration, non‑diffraction, and self‑healing—by imposing a cubic phase on the transmit array. They develop a fully analytical (closed‑form) design methodology that directly maps the geometric information of the transmitter, receiver, and any intervening blockage to the three key Airy‑beam parameters: curvature coefficient B, distance coefficient F, and steering angle θ.

ULA Analysis
Starting from the Fresnel diffraction integral, the paper derives the exact electric field distribution of a 1‑D Airy beam generated by a uniform linear array (ULA). The derivation yields a closed‑form expression for the beam trajectory
(x(z)=\frac{B}{2}z^{2}+θz)
and the amplitude decay governed by the Airy function. By solving for B, F, and θ such that the beam passes a prescribed waypoint (the “bending point” above the obstacle) and arrives at the receiver, the authors obtain simple algebraic formulas that require only the known coordinates of the blockage and the receiver. The resulting phase profile applied to each antenna element is
(\phi(x)=\frac{2π}{λ}\frac{B}{3}x^{3}-πλF x^{2}-k x\sinθ),
which can be programmed directly on a phased‑array controller.

Extension to UPA
Recognizing that practical THz transceivers employ uniform planar arrays (UPA), the authors leverage 3‑D wavefront separability: the 2‑D field is treated as the product of two independent 1‑D Airy beams along the x‑ and y‑axes. Two operation modes are introduced:

1. Hybrid Focusing‑Airy Mode – an Airy phase is applied along the axis that needs to bend around the obstacle, while a conventional quadratic (focusing) phase is applied along the orthogonal axis to concentrate energy at the receiver.

2. Dual Airy Mode – independent Airy phases are applied on both axes, enabling fully 2‑D curved trajectories that can navigate complex three‑dimensional blockage geometries.

For each mode, the optimal bending dimension and waypoint are derived analytically from the blockage geometry, and the corresponding closed‑form phase expressions are provided.

Performance Evaluation
Extensive simulations evaluate link budget, spectral efficiency, and beam patterns under varying blockage ratios (from 0 % to 100 %). Key findings include:

• Airy beams achieve 8–12 dB higher received power than Gaussian steering or focusing beams in typical quasi‑LoS scenarios.
• The closed‑form design matches exhaustive numerical search within 0.5 % performance loss while reducing computational complexity from exponential to constant time.
• Dual Airy mode offers the greatest flexibility for multi‑obstacle environments, whereas Hybrid mode excels when blockage is confined to a single plane.
• Even with blockage ratios exceeding 50 %, the self‑healing property of the Airy beam preserves a usable main lobe, ensuring robust connectivity.

Implications and Future Work
By providing deterministic formulas for Airy‑beam generation, the work enables real‑time beam training, adaptive beam steering, and low‑complexity hardware implementation in THz systems. The analytical framework also opens avenues for physical‑layer security (wavefront hopping) and interference mitigation. Future research directions suggested include multi‑user Airy‑beam multiplexing, closed‑loop blockage tracking, and experimental validation using metasurface‑based THz arrays.

In summary, the paper delivers a mathematically rigorous, low‑complexity solution for generating Airy beams on both linear and planar THz arrays, demonstrating superior blockage‑avoidance performance over conventional Gaussian beamforming and offering a practical pathway toward resilient THz near‑field communications.