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arxiv: 2605.02578 · v1 · submitted 2026-05-04 · 📡 eess.SP

Closed-form Model for Radiation Pattern of Pinching Antennas

Muhammad Zubair , Vasilis K. Papanikolaou , Robert Schober This is my paper

Pith reviewed 2026-05-08 17:52 UTC · model grok-4.3

classification 📡 eess.SP
keywords pinching antennasradiation patterncoupled-mode theorydielectric slab waveguidefar-field radiationanalytical modelwireless communications
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The pith

A closed-form model derived from a two-dimensional waveguide accurately predicts the directional radiation pattern of pinching antennas.

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

The paper develops an analytical radiation-pattern model for pinching-antenna systems by first applying coupled-mode theory to a two-dimensional dielectric slab waveguide to obtain the field coupled into the antennas and then evaluating a two-dimensional radiation integral for the far-field pattern. This closed-form expression reproduces the directional characteristics observed in full-wave simulations, in contrast to the common simplification of modeling each pinching antenna as an omni-directional point source. If the model holds, system-level analyses of wireless networks can incorporate a physically grounded directional pattern instead of an isotropic assumption, and the resulting performance degradation from ignoring directionality can be quantified in representative communication scenarios.

Core claim

The authors derive a closed-form radiation pattern for pinching antennas by modeling the system as a two-dimensional dielectric slab waveguide, using coupled-mode theory to find the analytical field profile coupled into the pinching antennas, and then applying a two-dimensional radiation integral to obtain the far-field pattern; numerical validation against finite-element simulations confirms that the model accurately reproduces the directional radiation characteristics.

What carries the argument

The two-step derivation that first obtains the coupled field via coupled-mode theory on the two-dimensional waveguide and then computes the far-field via the two-dimensional radiation integral.

If this is right

  • The closed-form model can be directly substituted into existing system-level PASS analyses in place of omni-directional point-source assumptions.
  • The model reveals that pinching antennas exhibit directional radiation rather than isotropic behavior.
  • Numerical results quantify the performance loss in wireless links when the directional pattern is neglected.
  • The analytic form enables rapid evaluation of radiation effects without repeated full-wave simulations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Designs for pinching-antenna arrays could be optimized by treating each element's pattern as directional rather than assuming uniform coverage.
  • In multi-user scenarios the directional lobes might be aligned to reduce interference between nearby links.
  • Extending the model to account for mutual coupling between multiple pinching antennas placed along the waveguide would be a natural next step.

Load-bearing premise

The two-dimensional dielectric slab waveguide together with coupled-mode theory sufficiently captures the essential electromagnetic behavior of real three-dimensional pinching antennas.

What would settle it

A full-wave simulation or physical measurement of the radiation pattern for a specific pinching-antenna geometry that shows large deviation in main-lobe direction, beamwidth, or sidelobe levels from the closed-form prediction.

Figures

Figures reproduced from arXiv: 2605.02578 by Muhammad Zubair, Robert Schober, Vasilis K. Papanikolaou.

Figure 1
Figure 1. Figure 1: The main waveguide has length L, width Wm, core refractive index n1, and cladding refractive index n0. It is aligned along the x-axis and centered on y = 0, with input and output ports at M0 = (0, 0) and ML = (L, 0), respectively. Two identical dielectric PAs of length Ls and width Ws are attached symmetrically to the upper and lower surfaces of the main waveguide with their centers at Mu = (xp, yu) and Md… view at source ↗
Figure 1
Figure 1. Figure 1: System model for the 2D PASS. The guided wave is confined primarily to the core and decays exponentially in the cladding. Its transverse electric field profile is given by [9], Em (y) = ® A0 cos(βmyy), − Wm 2 ≤ y ≤ Wm 2 , A0 cos(βmy Wm 2 )e −σm(|y|− Wm 2 ) , |y| > Wm 2 , (1) Here, A0 denotes a constant normalized amplitude, and βmy = p β 2 0n 2 1 − β 2 mx and σm = p β 2 mx − β 2 0n 2 0 repre￾sent the trans… view at source ↗
Figure 2
Figure 2. Figure 2: Normalized radiation patterns for Vq = 1.5. 0 0.2 0.4 0.6 0.8 1 COMSOL Proposed Model (a) Wq = 0.408λ 0 0.2 0.4 0.6 0.8 1 COMSOL Proposed Model (b) Wq = 0.470λ view at source ↗
Figure 3
Figure 3. Figure 3: Normalized radiation patterns for different widths at a fixed PA length view at source ↗
Figure 4
Figure 4. Figure 4: Power coupling and scattering characteristics of PAs with varying lengths. view at source ↗
Figure 5
Figure 5. Figure 5: Spectral efficiency versus transmit SNR for view at source ↗
read the original abstract

In this article, we develop an analytical radiation-pattern model for pinching-antenna systems (PASS) based on a two-dimensional dielectric slab waveguide. The model is derived in two steps. First, we employ coupled-mode theory (CMT) to derive a closed-form expression for the field coupled into the pinching antennas (PAs). Second, we use this analytical field profile as a scattering source model and derive the far-field radiation pattern via a two-dimensional radiation integral. We validate the proposed model against full-wave finite-element simulations performed in COMSOL Multiphysics, showing that it accurately reproduces the directional radiation characteristics of PASS. In contrast, most existing works model PAs as omni-directional point radiators, which simplifies system-level analysis but does not accurately capture the underlying electromagnetic radiation mechanism. Because the proposed model is given in closed form, it can be easily integrated into existing system-level PASS models to replace the assumed omni-directional pattern with a physically motivated directional radiation pattern. Finally, numerical simulations quantify the performance degradation that arises when the directional behavior of PAs is neglected in a representative wireless communications scenario.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript develops a closed-form analytical radiation-pattern model for pinching-antenna systems (PASS) by representing them via a two-dimensional dielectric slab waveguide. Coupled-mode theory is first used to obtain a closed-form expression for the field coupled into the pinching antennas; this profile is then inserted as a scattering source into a two-dimensional radiation integral to yield the far-field pattern. The model is validated against COMSOL Multiphysics finite-element simulations and is shown to reproduce directional characteristics, in contrast to the omni-directional point-radiator assumption common in system-level PASS analyses. Numerical results are also presented that quantify the performance degradation incurred when the directional behavior is neglected in a representative wireless communications scenario.

Significance. If the central claim holds, the work supplies a practical, closed-form directional radiation pattern that can replace simplified omni-directional models inside existing system-level PASS analyses. This would improve the physical fidelity of link-budget and beamforming calculations without sacrificing computational tractability. The explicit quantification of performance loss when directionality is ignored supplies concrete motivation for adopting the more accurate model.

major comments (2)
  1. [Abstract / Validation] Abstract and validation section: the claim that the model 'accurately reproduces the directional radiation characteristics' rests on COMSOL finite-element comparisons, yet no quantitative error metrics (e.g., normalized mean-square error, pattern correlation coefficient, or maximum sidelobe deviation) or parameter-sweep results are reported. Without these, the accuracy statement cannot be independently assessed.
  2. [Model derivation] Model derivation (two-dimensional slab + CMT reduction): the central modeling step replaces a three-dimensional pinching antenna with a two-dimensional dielectric-slab waveguide. No error bounds, sensitivity analysis with respect to pinching depth, dielectric contrast, or finite length in the third dimension, nor explicit 3D-to-2D validation are provided. This dimensionality reduction is load-bearing for the claim that the closed-form pattern represents real PASS devices.
minor comments (2)
  1. The abstract would be strengthened by the inclusion of at least one quantitative validation figure of merit.
  2. Ensure that every equation in the CMT and radiation-integral derivations is numbered and explicitly referenced in the surrounding text.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the constructive and detailed review of our manuscript. We address each major comment below and indicate the revisions made to strengthen the presentation.

read point-by-point responses

  1. Referee: [Abstract / Validation] Abstract and validation section: the claim that the model 'accurately reproduces the directional radiation characteristics' rests on COMSOL finite-element comparisons, yet no quantitative error metrics (e.g., normalized mean-square error, pattern correlation coefficient, or maximum sidelobe deviation) or parameter-sweep results are reported. Without these, the accuracy statement cannot be independently assessed.

    Authors: We agree that quantitative metrics would allow readers to independently assess the accuracy. In the revised manuscript we have added the normalized mean-square error and pattern correlation coefficient between the closed-form model and the COMSOL results for all presented cases. We have also included a parameter sweep over pinching depth to illustrate robustness. The abstract has been updated to reference these quantitative comparisons. revision: yes

  2. Referee: [Model derivation] Model derivation (two-dimensional slab + CMT reduction): the central modeling step replaces a three-dimensional pinching antenna with a two-dimensional dielectric-slab waveguide. No error bounds, sensitivity analysis with respect to pinching depth, dielectric contrast, or finite length in the third dimension, nor explicit 3D-to-2D validation are provided. This dimensionality reduction is load-bearing for the claim that the closed-form pattern represents real PASS devices.

    Authors: The two-dimensional reduction is justified by the elongated geometry of the pinching antennas, for which radiation in the principal plane can be approximated by a 2D slab model. In the revised manuscript we have added a sensitivity analysis with respect to pinching depth and dielectric contrast together with approximate error bounds obtained from the coupled-mode assumptions. An explicit 3D-to-2D validation for finite third-dimension lengths is not provided, as it would require a separate computational study; the 2D model is shown to match the corresponding 2D full-wave simulations and supplies a practical closed-form directional pattern for system-level use. revision: partial

standing simulated objections not resolved
  • Explicit 3D-to-2D validation and comprehensive error bounds for the dimensionality reduction across finite third-dimension lengths.

Circularity Check

0 steps flagged

No significant circularity; derivation relies on standard CMT and radiation integral

full rationale

The paper constructs its closed-form radiation pattern in two explicit steps: (1) application of coupled-mode theory on a 2-D dielectric slab waveguide to obtain an analytical expression for the field coupled into the pinching antennas, and (2) substitution of that field profile into the standard 2-D radiation integral to produce the far-field pattern. Both steps invoke established electromagnetic methods whose validity is independent of the final PASS-specific result. The abstract reports validation against separate full-wave finite-element simulations, which functions as an external benchmark rather than a self-referential confirmation. No fitted parameters, self-definitional equations, load-bearing self-citations, or uniqueness theorems imported from prior author work are indicated. Consequently the claimed analytical model does not reduce to its inputs by construction and receives a circularity score of 0.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The model rests on standard electromagnetic theory without introducing new free parameters or invented entities in the abstract description.

axioms (2)
  • domain assumption Coupled-mode theory accurately describes the field coupling into pinching antennas placed on a dielectric slab waveguide
    Invoked as the first step to obtain the analytical field profile inside the PAs.
  • standard math The far-field pattern can be obtained from a two-dimensional radiation integral treating the coupled field as a scattering source
    Standard technique in electromagnetics used for the second derivation step.

pith-pipeline@v0.9.0 · 5495 in / 1297 out tokens · 58043 ms · 2026-05-08T17:52:54.409837+00:00 · methodology

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Reference graph

Works this paper leans on

15 extracted references · 15 canonical work pages

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