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Finite‑aperture Bessel beams can travel only about 20 % of the radiative near field

November 3, 2026arXiv: 2610.41656v1

Finite‑aperture Bessel beams – used to improve near‑field communications – have a limited non‑diffracting range. Analytical models show that the usable propagation distance is bounded by a fraction of the Fraunhofer distance.

Plot of the normalized array gain for a circular array at 125 GHz. As the cone angle is reduced from a wide to a narrow value, the area with Gnorm > 0.5 extends farther along the propagation axis but expands laterally, with the red line indicating points where the gain is 3 dB below the maximum. (1/3)Plot of the normalized array gain for a circular array at 125 GHz. As the cone angle is reduced from a wide to a narrow value, the area with Gnorm > 0.5 extends farther along the propagation axis but expands laterally, with the red line indicating points where the gain is 3 dB below the maximum. (2/3)
Plot of the normalized array gain for a circular array at 125 GHz. As the cone angle is reduced from a wide to a narrow value, the area with Gnorm > 0.5 extends farther along the propagation axis but expands laterally, with the red line indicating points where the gain is 3 dB below the maximum. (3/3)
(a). Gains of a circular array showing the spread of the high‑gain region as the cone angle decreases. The contour of normalized array gain Gnorm = 0.5 (red) marks the 3‑dB beam depth, illustrating how the detectable non‑diffracting range grows while the beam broadens.Jolly, Aditya, Petrov, Vitaly, Fodor, Gábor, Björnson, Emil · arXiv:2610.41656v1 · (a) · CC BY 4.0

The study derives closed‑form expressions for the normalized array gain of phase‑based Bessel beams from circular and square apertures. These formulas, based on the Fresnel approximation, let designers evaluate gain across the near field.

Critical cone angles separate the beam‑parameter space into undefined, finite‑depth‑of‑field, and infinite‑depth regimes. For typical electrically large arrays, the maximum usable non‑diffracting range is about 22 % of the Fraunhofer distance for a circular aperture and about 19 % for a square aperture.

Table summarizing the maximum usable non‑diffracting ranges (Zmax) for circular and square arrays. The values are given as fractions of the Fraunhofer distance: 0.226 dFAc for circular and 0.193 dFAs for square, corresponding to roughly 22 % and 19 % of dFA respectively.
PropositionCritical Zmax
Proposition 1aRtan⁡(sin−1⁡(0.5533​λR))≈0.226​dFAc
Proposition 2Rtan⁡(sin−1⁡(0.5639​λR))≈0.222​dFAc
Proposition 3aDAP2​tan⁡(sin−1⁡(0.91606​λDAP))≈0.193​dFAs
Proposition 4DAP2​tan⁡(sin−1⁡(0.9383​λDAP))≈0.188​dFAs
TABLE II. Critical non‑diffracting ranges for circular and square apertures expressed as fractions of the Fraunhofer distance. For electrically large arrays, the maximum usable non‑diffracting range is approximately 22 % of the Fraunhofer distance for a circular array and about 19 % for a square array.Jolly, Aditya, Petrov, Vitaly, Fodor, Gábor, Björnson, Emil · arXiv:2610.41656v1 · TABLE II: · CC BY 4.0

The finding implies that only roughly one‑fifth of the radiative near field can employ finite‑depth Bessel beams before diffraction limits degrade performance.

Source paper

Limitation of Bessel Beams in Near Field Communications: A Depth of Field Perspective

Signal Processing
View on arXiv
Finite‑aperture Bessel beams can travel only about 20 % of the radiative near field | arXiv News