Quasi-Closed-Form Driven Near-Field Flat-Top Beamfocusing with Concentric Circular Vertical Polarized Dipole Array For Large Intelligent Surface Applications

Jiawang Li

REVIEW 4 major objections 6 minor 13 references

Quasi-Closed-Form Driven Near-Field Flat-Top Beamfocusing with Concentric Circular Vertical Polarized Dipole Array For Large Intelligent Surface Applications

T0 review · 4 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A flat-top near-field beam can be synthesized by superposing concentric dipole rings with opposing field trends.

desk verdict A plausible fast near-field flat-top synthesis idea whose headline <1 dB ripple claim is contradicted by the paper's own FEKO result (about 4 dB), so the paper needs revision but is worth refereeing. read the letter →

arxiv 2506.07678 v1 pith:24DPDIQU submitted 2025-06-09 physics.optics eess.SP

Jiawang Li This is my paper

classification physics.opticseess.SP MSC 78A50 PACS 41.20.Jb84.40.Ba

keywords near-fieldbeamfocusingflat-topsynthesisconcentriccirculararrayverticaldipolelargeintelligentsurfacemutualcouplingBesselfunctionfieldmodelbeamforming

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tries to establish a fast, semi-closed-form recipe for shaping a near-field beam into a flat-top profile, so that power is delivered uniformly across a target region rather than concentrated at one focus. The recipe exploits a discovered contrast in the response of concentric circular rings of vertical dipoles: rings with small radius give a field that rises as the observation point moves off axis, while large-radius rings give a field that falls. Superimposing enough rings of each kind flattens the region between the two trends. The design procedure reduces what is normally a per-element amplitude and phase optimization to a search over just two global parameters, inter-element spacing and ring count, and the paper reports in-region ripple below 1 dB in the analytic model, with full-wave simulation confirming the trend.

What carries the argument

The carrying mechanism is the closed-form field expression for a ring of vertical dipoles, equation (11), whose two Bessel terms $J_0$ and $J_1$ produce radius-dependent monotonic trends along the focal axis. For $R$ small the field grows with transverse offset $\delta$; for $R$ large the Bessel term falls before its first zero and wins over the slow growth of the prefactor. The constructive rule is superposition: small-radius rings supply the rising flank, large-radius rings the falling flank, and the summed response is a flat plateau. The companion machinery is Algorithm 1, which replaces per-element optimization with a two-variable search over ring spacing $d$ in $[\lambda/4, \lambda/2]$ and ring count $R_n$, so that a design is fixed by a flatness check on the superposed field.

What would settle it

The deciding measurement is the transverse field profile at the focal plane of a realized or full-wave-simulated concentric ring array: if, after accounting for mutual coupling at every inter-element spacing in $[\lambda/4, \lambda/2]$, the in-region ripple cannot be brought back below 1 dB, the closed-form design premise collapses. The paper's own FEKO simulation is exactly such a test, and it records roughly 4 dB ripple, already at odds with the 1 dB figure.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that the transverse near-field response of a concentric circular ring array separates cleanly by radius into two opposite monotonic regimes, and that this separation gives a constructive synthesis rule. Starting from the radiated field of vertical dipoles along the array axis, the author derives a closed-form expression involving the oscillatory Bessel functions $J_0$ and $J_1$; for small ring radii the field is an increasing function of the transverse offset $\delta$, while for larger radii the Bessel term dominates and forces a decrease. Since the two trends are opposed, superposing rings of both kinds produces a region of nearly constant field intensity, a flat-top beam, with the large-radius rings also suppressing energy outside the flat region. Algorithm 1 turns this insight into a design procedure by scanning candidate spacings in $[\lambda/4, \lambda/2]$ and ring counts, assigning uniform excitation amplitudes and conjugate-matching phases, and accepting the first configuration whose in-region fluctuation falls below a tolerance. The paper validates the procedure at focal distances of $10\lambda$ and $5\lambda$, with computed execution times of 0.040 s and 0.022 s, and reports a full-wave simulation whose beam shape matches the trend although mutual coupling stretches the beam and raises in-region ripple to about 4 dB.

Load-bearing premise

The load-bearing premise is that each dipole behaves as an ideal isolated element with no mutual coupling; the paper's own full-wave simulation shows the premise fails in practice, stretching the beam and raising in-region ripple from under 1 dB to about 4 dB.

Editorial extensions

If this is right

The same two-parameter recipe produces flat-top beams at different focal distances, $10\lambda$ and $5\lambda$ in the examples, with flat-top widths of roughly $\pm 2\lambda$ and $\pm 1.2\lambda$ respectively.
Design time drops to tens of milliseconds, 0.040 s and 0.022 s in the two cases, because per-element amplitude and phase tuning is replaced by a scan over spacing and ring count with uniform excitation.
Amplitude fine-tuning of ring excitations suppresses sidelobes on top of the flat region, so the flatness criterion and sidelobe control are handled separately.
The analytic and full-wave beam shapes stay consistent, so the closed-form model can serve as a fast starting point for near-field beam synthesis even where mutual coupling later needs compensation.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The paper's own full-wave result implies the sub-1 dB flatness claim is not yet achievable in a physical array; a natural next step the author leaves implicit is to fold a coupling or embedded-pattern correction into the closed-form model and re-run the two-variable search.
The radius-versus-slope dichotomy is a qualitative property of the aperture field, so the same superposition argument might transfer to other centrally symmetric apertures or to shaping the longitudinal field profile rather than only the transverse one.
A testable extension is to treat the ripple floor under coupling as a function of inter-ring spacing: denser rings with smaller radial gaps should weaken edge-coupling distortion and restore flatness closer to the analytic 1 dB target.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The core idea is sound enough to take seriously: combine concentric circular rings whose near-field transverse responses increase with radius for small rings and decrease for large rings, then search over spacing and ring count to flatten the beam. That is a neat twist on classic ring-array/Bessel synthesis, and the algorithm is appropriately cheap (tens of milliseconds). The paper reports a useful two-variable search instead of per-element optimization, so it is a genuine contribution to LIS beam-shaping.

What it does well: the physical intuition in Fig. 3 is clear, the closed-form approximations (Eqs. 10-13) are at least plausible, and the paper does not hide the full-wave result. It explicitly states that in FEKO mutual coupling stretches the beam and reduces the in-region flatness to about 4 dB. That honesty counts.

The soft spots are real, though. The abstract and conclusion say full-wave simulations validate the <1 dB flat-top claim, but the FEKO figure shows roughly 4 dB ripple. That is not a minor numerical deviation; it changes what 'flat-top' means in practice. The derivation uses unquantified approximations (continuous ring, Taylor expansion of the phase) and no error bounds, so the closed form is more quasi-closed-form than closed-form. There is also no comparison to existing near-field synthesis methods (convex optimization, BCS, spectral factorization), no code/data, and no mutual-coupling compensation. Without a benchmark, the claimed advantage over per-element approaches is asserted rather than demonstrated. The reference list is reasonable and not padded; self-citation is not the problem here.

None of this kills the basic idea. The ring-superposition mechanism is plausible, and the FEKO discrepancy points to a specific, fixable omission - element pattern distortion. But the paper as written overstates what is validated. A revision that (a) aligns the claims with the 4 dB result, (b) quantifies the approximation error, and (c) adds a comparison or at least a convergence study would make this a useful letter.

Who is this for? People working on near-field wireless power transfer or LIS beamforming who need a quick flat-top design. It deserves a serious referee: the idea is novel enough and the execution transparent enough, but it needs major revision before acceptance.

Referee Report

4 major / 6 minor

Summary. This letter proposes a semi-closed-form synthesis method for near-field flat-top beams using concentric circular rings of vertically polarized dipoles. The method exploits the observation that small-radius rings produce a field that increases with transverse offset while large-radius rings produce a field that decreases, so that superposition can flatten the axial intensity. An algorithm searches over element spacing and ring count to satisfy a ripple tolerance, and ring excitations are then fine-tuned to suppress sidelobes. The authors report full-wave FEKO simulations intended to validate the approach.

Significance. If the claimed <1 dB in-region ripple were achieved in the full-wave setting, the method would offer a computationally cheap, low-complexity design for near-field uniform power coverage in LIS applications, reducing a per-element optimization to a two-parameter search. The underlying superposition idea is simple and potentially useful, and the algorithm runs in tens of milliseconds. However, the paper's own FEKO results show about 4 dB ripple under mutual coupling, so the headline flatness is not actually demonstrated in a realistic array. The closed-form derivation also has unquantified approximation steps that weaken the claimed theoretical basis.

major comments (4)

[III, text following Fig. 8] The paper's own FEKO simulation result shows that mutual coupling stretches the beam and reduces in-region flatness to approximately 4 dB, whereas the design target and the abstract/conclusion state that full-wave simulations validate the proposed method. A flatness of 4 dB is not a flat-top beam in the sense claimed (target <1 dB), and the sentence 'Full-wave simulations validate the effectiveness of the proposed approach' (Conclusion) is therefore contradicted by the paper's own data. At best, the full-wave result shows a qualitative trend, not a validated flat-top beam. This is a load-bearing discrepancy between the central claim and the evidence.
[II, Eqs. (10)-(13)] The transition from the discrete sum (9) to the continuous integral (10) and the closed form (11) rests on two unquantified approximations: a Taylor expansion of the phase term and a replacement of the discrete ring by a continuous current distribution. For the examples, outer rings with 12 elements have inter-element spacings exceeding 2λ, so the continuous approximation is not obviously valid. In addition, the J1 term in Eq. (11) has a sign inconsistent with the standard identity ∫_0^{2π} cosθ e^{-ia cosθ} dθ = -2πi J1(a); substituting the −2δR cosθ term in Eq. (10) gives +4πiδR J1, not −4πiδR J1 as written. Since Eq. (11) is presented as the theoretical basis for the 'monotonic increase/decrease' design rule, the sign error and missing error bounds should be corrected or the derivation should be replaced by a more careful asymptotic analysis.
[II-A and Algorithm 1] The manuscript begins with the assumption of half-wavelength element spacing, but then states that each ring carries 12 elements rather than being uniformly spaced at half-wavelength intervals. For the z0=10λ example, ring radii from 0.5λ to 4.5λ with 12 elements give spacings from about 0.26λ to about 2.35λ; the outer rings thus violate the paper's own caution (Section II, text around Fig. 4) that spacings beyond about 2λ degrade the pattern. The algorithm's assignment N_m = N_1 for all rings causes this nonuniform angular sampling, and the claim that the normalized gain remains consistent across rings is not justified. This is a design inconsistency that plausibly contributes to the FEKO mismatch.
[III, Figs. 5-8] Flatness is only evaluated along a single transverse cut (δ along x or y), but the flat-top beam is intended to cover a two-dimensional region. No 2D field maps or area-based ripple statistics are reported, so the method's suitability for LIS coverage over an area is not established, even in the ideal model. The FEKO results likewise show only one cut; the statement that the beam is 'stretched along the flat-top direction' without an orthogonal cut suggests the 2D pattern may not retain a flat-top shape.

minor comments (6)

[Introduction] The first line of the Introduction contains a typo: 'T HIS With the rapid development'.
[II, Eq. (9) and Eq. (7)] Equation references are inconsistent: after Eq. (9), the text says 'equation (5) can be rewritten' but it should refer to Eq. (9); later, 'the normalized gain defined in (7)' likely refers to Eq. (9) or (11).
[II, Eqs. (4)-(5) and (11)] The absolute-value notation is used with two different meanings: in Eqs. (4)-(5) it denotes an absolute value of a coordinate difference, while in Eq. (11) it denotes the magnitude of a complex expression. Clarify the notation.
[III, Figs. 5-6] The figure captions for Figs. 5 and 6 appear inconsistent with the text: the text describes the first case as z0=10λ and the second as z0=5λ, but the captions mix the ring counts and distances. Please standardize.
[II-A and III] The paper does not explain why 12 elements per ring is chosen for the examples, nor how the 'normalized gain' consistency across rings is defined.
[Index Terms] The Index Terms include 'monotonically', which is not a topical keyword; consider replacing it with 'near-field beamforming' or 'mutual coupling'.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: the closed-form field model is self-contained, the synthesis search is an explicit design fit, and the FEKO check is an independent external validation that disagrees with the ideal model.

full rationale

The paper's claimed derivation chain is self-contained rather than circular. The core analytic result, Eqs. (9)-(11), is obtained from the dipole field expression by symmetry reduction, Taylor expansion of the phase, and replacement of the discrete ring sum by a continuous angular integral; the desired flat-top pattern never appears as an input to these equations. The monotonic increase/decrease for small/large ring radii (Eq. (12) vs. Eq. (13)) is a mathematical consequence of the Bessel-function expression, not an assumption imported from the target. Algorithm 1 performs an explicit design search over element spacing and ring count with a flatness tolerance rho; reporting a <1 dB ripple for the chosen configuration is reporting the constraint that the search enforced, which is normal synthesis rather than a hidden prediction. The FEKO full-wave simulation is an external numerical check independent of the closed-form model, and the paper honestly states that mutual coupling degrades the in-region flatness to about 4 dB (text following Fig. 8). This disagreement is a robustness/correctness limitation, not circularity; on the contrary, it shows the closed-form model is falsifiable. Self-citations [1], [2], and [4] are background antenna-design references and are not load-bearing for the flat-top synthesis claim. No uniqueness theorem or prior-work ansatz is invoked. Hence no circular step is present.

Assumptions & free parameters 3 free parameters · 3 assumptions · 0 invented entities

The central claim rests on design choices, spacing, ring count, and minimum radius, that are selected to meet the flatness target, plus approximations in the closed-form Bessel derivation and the neglect of mutual coupling. No free physical constants are fitted; the fitting happens in the parameter search that defines the array.

free parameters (3)

Element spacing and inter-ring spacing d = lambda/4 in both examples (candidate range lambda/4 to lambda/2)
Algorithm 1 searches d in [lambda/4, lambda/2] and accepts the first d that gives ripple <= rho; the flat-top width and ripple thus depend on a parameter fitted to the target pattern.
Number of rings R_n = 9 for z0=10 lambda and 6 for z0=5 lambda
Selected by Algorithm 1's loop over R_n to meet the flatness tolerance; it controls the achievable flat-top region and is fitted to the desired in-region ripple.
Minimum ring radius R_min = Implied as 0.5 lambda from Fig. 3, but the text also says radii 0.1 m to 0.9 m
The initial radius sets the ring radii sequence R = R_min + d*(0:R_n-1); the paper does not derive it and gives conflicting value sets in text versus figure.

assumptions (3)

domain assumption Ideal isolated dipole element patterns and no mutual coupling in the closed-form model
Equations (1) to (6) use the free-space Hertzian dipole field and neglect coupling; Section III reports that mutual coupling in FEKO stretches the beam and reduces flatness to about 4 dB, so this assumption is load-bearing and empirically violated.
ad hoc to paper The discrete ring sum can be replaced by a continuous integral and a Bessel closed form after Taylor expansion
Equation (10) to Eq. (11) replaces the sum with an integral and ignores denominator variation; the monotonicity argument in Eqs. (12) and (13) relies on this approximation with no error bound.
ad hoc to paper All rings can use the same element count N_m = N_1 while maintaining acceptable array behavior
Algorithm 1 sets N_m = N_1 for every ring, which makes outer-ring arc spacing grow with radius; the paper does not analyze grating-lobe consequences beyond Fig. 4.

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Cite this review

Pith. "Pith review of Quasi-Closed-Form Driven Near-Field Flat-Top Beamfocusing with Concentric Circular Vertical Polarized Dipole Array For Large Intelligent Surface Applications." pith.science (2026). https://pith.science/paper/24DPDIQU

@misc{pith2026250607678,
  author       = {Pith},
  title        = {Pith review of: Quasi-Closed-Form Driven Near-Field Flat-Top Beamfocusing with Concentric Circular Vertical Polarized Dipole Array For Large Intelligent Surface Applications},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/24DPDIQU}},
  note         = {Machine review of arXiv:2506.07678}
}

read the original abstract

This letter presents a near-field flat-top beam synthesis method based on a semi-closed-form approach. First, the feasibility of achieving a flat-top beam in the near field is examined using a closed-form analysis. A circular concentric ring array structure is adopted, and it is observed that circular rings with different radii exhibit distinct gain characteristics along the focal region on the z-axis. Specifically, smaller radii lead to a monotonic increase in electric field strength near the focus, whereas larger radii result in a monotonic decrease. Based on this behavior, parameters such as the number of rings and the initial radius are determined through field superposition. Subsequently, an optimization algorithm is employed to fine-tune the excitation amplitudes of the individual rings in order to suppress sidelobes. The effectiveness of the proposed method is validated through full-wave electromagnetic simulations.

Figures

Figures reproduced from arXiv: 2506.07678 by the authors.

**Figure 2.** Configuration of the proposed circular array. [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 4.** Beam focusing results under the conjugate matching method with a [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗

Figures from the paper (3 more)

**Figure 5.** Figure 5: Flat-top beam patterns synthesized by two algorithms. (a) 9 rings with [PITH_FULL_IMAGE:figures/full_fig_p003_5.png]

**Figure 6.** Figure 6: Flat-top beam patterns synthesized by two algorithms. (a) 9 rings with [PITH_FULL_IMAGE:figures/full_fig_p004_6.png]

**Figure 7.** Figure 7: Normalized simulated beams (-10 to 0 dB): (a) numerical simulation; [PITH_FULL_IMAGE:figures/full_fig_p004_7.png]

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Reference graph

Works this paper leans on

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

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K. Chen, J. Xu, Q. Lin, Y . Zhu, and W. Hong, “Single-layer wideband tilted beam phased array antenna for millimeter-wave vehicle communications,”IEEE Trans. V eh. Technol., vol. 73, no. 3, pp. 3536–3550, Mar. 2024

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Substrate integrated waveguide (SIW) leaky-wave antenna with transverse slots,

J. Liu, D. R. Jackson, and Y . Long, “Substrate integrated waveguide (SIW) leaky-wave antenna with transverse slots,”IEEE Trans. Antennas Propag., vol. 60, no. 1, pp. 20–29, Jan. 2012

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Garnica, R. A. Chinga and J. Lin, ”Wireless power transmission: from far-field to near field,”Proceedings of the IEEE., vol. 101, no. 6, pp. 1321-1331, June 2013

work page 2013

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On the near-field shaping and focusing capability of a radial line slot array,

M. Ettorreet al., “On the near-field shaping and focusing capability of a radial line slot array,”IEEE Trans. Antennas Propag., vol. 62, no. 4, pp. 1991–1999, Apr. 2014

work page 1991