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arxiv: 2601.03688 · v2 · submitted 2026-01-07 · ⚛️ physics.optics

Radiation processes in dielectric cylindrical waveguides

A.A. Saharian , L.Sh. Grigoryan , H.F. Khachatryan This is my paper

Pith reviewed 2026-05-16 17:08 UTC · model grok-4.3

classification ⚛️ physics.optics
keywords Green tensordielectric cylindrical waveguiderecurrence proceduresynchrotron-Cherenkov radiationguided modessurface polaritonic modescharged particle radiationelectromagnetic fields
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The pith

A recurrence procedure yields the electromagnetic Green tensor for a dielectric cylindrical waveguide with any number of layers and provides explicit radiation formulas for a rotating charged particle.

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

The paper establishes a recurrence procedure to evaluate the Green function of the electromagnetic field in media consisting of any number of homogeneous cylindrical layers. For the case of a single cylinder surrounded by a homogeneous medium, all components of the Green tensor are derived in the interior and exterior regions. These results are applied to the radiation emitted by a charged particle rotating around the cylinder, yielding formulas for the fields and spectral-angular densities of synchrotron-Cherenkov radiation at large distances as well as radiation on guided and surface polaritonic modes. A reader would care because such expressions allow quantitative analysis of how electromagnetic waves propagate and radiate in cylindrical structures used in photonics and telecommunications.

Core claim

The central claim is that a recurrence procedure can be used to construct the Green tensor for the electromagnetic field in a cylindrical waveguide made of an arbitrary number of homogeneous dielectric layers immersed in a homogeneous medium. Explicit expressions are given for all components of this tensor inside and outside the cylinder. Application to the radiation of a rotating charged particle produces formulas for the electromagnetic fields and the spectral-angular densities of the synchrotron-Cherenkov radiation, the guided modes, and the surface polaritonic modes.

What carries the argument

The recurrence procedure for the Green function, which iteratively solves for the field coefficients in each cylindrical layer based on boundary conditions.

If this is right

  • The spectral-angular densities of synchrotron-Cherenkov radiation are obtained explicitly for large distances from the cylinder.
  • The radiation intensities associated with guided and surface polaritonic modes are derived for the rotating particle.
  • Explicit formulas for the electromagnetic fields of all radiation processes are provided.
  • Numerical analysis compares the contributions from different radiation mechanisms.

Where Pith is reading between the lines

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

  • The Green tensor derived here could be applied to study spontaneous emission or scattering in the same waveguide geometry.
  • Extensions to quantum electrodynamics might use this classical Green function as a starting point for calculating radiation corrections.
  • The method allows investigation of how changes in layer thicknesses or permittivities affect the radiation spectra.

Load-bearing premise

The recurrence relations derived from boundary conditions at the cylindrical interfaces hold without restriction for any number of layers and any dielectric parameters.

What would settle it

Verification by substituting the derived Green tensor into the wave equation and checking continuity of tangential field components at a sample interface for a two-layer structure would test the validity of the procedure.

Figures

Figures reproduced from arXiv: 2601.03688 by A.A. Saharian, H.F. Khachatryan, L.Sh. Grigoryan.

Figure 1
Figure 1. Figure 1: The angular density of the number of the radiated qu [PITH_FULL_IMAGE:figures/full_fig_p020_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The same as in Fig. 1 for [PITH_FULL_IMAGE:figures/full_fig_p021_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The same as on the right panel of Fig. 1 for [PITH_FULL_IMAGE:figures/full_fig_p021_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The number of the radiated quanta per rotation peri [PITH_FULL_IMAGE:figures/full_fig_p027_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The surface polaritonic modes of a dielectric cyli [PITH_FULL_IMAGE:figures/full_fig_p029_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The number of the quanta, radiated per rotation per [PITH_FULL_IMAGE:figures/full_fig_p030_6.png] view at source ↗
read the original abstract

Dielectric cylindrical waveguides are widely used for confining and guiding of electromagnetic waves in relatively wide range of frequencies. They have found numerous technological and scientific applications in telecommunications, medicine, material science, photonics and quantum optics. The electromagnetic field Green function is the central object in investigations of different types of radiation processes in those structures. In this paper, we review and further develop the recurrence procedure for evaluating the electromagnetic field Green function in a medium made of any number of homogeneous cylindrical layers. The general results are specified for a cylindrical waveguide immersed in a homogeneous medium. Expressions are provided for all the components of the Green tensor in both regions inside and outside the cylinder. As an application of the results for the Green function, we consider the radiation of a charged particle rotating around a dielectric cylinder. The intensities for all types of radiation processes are discussed. They include the synchrotron-Cherenkov radiation at large distances from the cylinder and the radiation on guided and surface polaritonic modes confined inside or near the surface of the cylinder. The paper provides explicit formulas for the electromagnetic fields and the spectral-angular densities of those radiations. It also includes a numerical and comparative analysis.

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 reviews and extends a recurrence procedure to construct the electromagnetic Green tensor for a dielectric cylindrical waveguide with an arbitrary number of homogeneous layers. Explicit expressions are derived for all components of the Green tensor in the interior and exterior regions. These are then applied to compute the electromagnetic fields and spectral-angular radiation densities produced by a charged particle rotating around the cylinder, covering synchrotron-Cherenkov radiation at large distances as well as emission into guided and surface-polaritonic modes.

Significance. A validated recurrence method for the Green tensor in multi-layer cylindrical geometries would provide a practical computational framework for radiation calculations in photonic waveguides and related structures. The explicit formulas for fields and intensities could serve as a reference for both analytic limits and numerical implementations in optics and quantum optics applications.

major comments (2)
  1. [Recurrence procedure for the Green tensor] The central assertion that the recurrence procedure yields all Green-tensor components for any number of layers without additional restrictions on material parameters or frequency ranges (abstract and the section presenting the recurrence) must be accompanied by an explicit demonstration that the transfer-matrix construction remains well-defined or is properly regularized when its determinant vanishes at the dispersion relations of guided or surface modes. At those frequencies the procedure is claimed to compute radiation intensities on the modes themselves; without shown handling of the resulting singular or indeterminate forms, the formulas cannot be verified as free of post-hoc adjustments.
  2. [Radiation intensities for guided and surface modes] In the application to the rotating charge (section deriving the spectral-angular densities), the expressions for the intensities on guided and surface modes should include a concrete check that they reduce to the expected residue contributions extracted from the Green tensor poles, rather than being inserted by separate ansatz. The current presentation leaves open whether the radiation formulas are obtained directly from the recurrence or supplemented by additional steps.
minor comments (2)
  1. Notation for the cylindrical Bessel and Hankel functions in the Green-tensor components should be stated once with explicit order and argument conventions to avoid ambiguity across the interior and exterior regions.
  2. The numerical examples would benefit from a brief statement of the convergence criterion used for the recurrence when the number of layers is increased.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed review and valuable suggestions. We address each major comment below and indicate the revisions made to the manuscript.

read point-by-point responses

  1. Referee: [Recurrence procedure for the Green tensor] The central assertion that the recurrence procedure yields all Green-tensor components for any number of layers without additional restrictions on material parameters or frequency ranges (abstract and the section presenting the recurrence) must be accompanied by an explicit demonstration that the transfer-matrix construction remains well-defined or is properly regularized when its determinant vanishes at the dispersion relations of guided or surface modes. At those frequencies the procedure is claimed to compute radiation intensities on the modes themselves; without shown handling of the resulting singular or indeterminate forms, the formulas cannot be verified as free of post-hoc adjustments.

    Authors: We agree that an explicit demonstration of the regularization at the dispersion relations is important for clarity. In the revised manuscript, we have added a new subsection in the section on the recurrence procedure that analyzes the behavior when the determinant of the transfer matrix vanishes. We show that the Green tensor components develop simple poles at these frequencies, and the radiation intensities are obtained by computing the residues at these poles using the residue theorem. This approach ensures the expressions are well-defined without indeterminate forms. A specific example for a two-layer cylinder is provided to illustrate the procedure. revision: yes

  2. Referee: [Radiation intensities for guided and surface modes] In the application to the rotating charge (section deriving the spectral-angular densities), the expressions for the intensities on guided and surface modes should include a concrete check that they reduce to the expected residue contributions extracted from the Green tensor poles, rather than being inserted by separate ansatz. The current presentation leaves open whether the radiation formulas are obtained directly from the recurrence or supplemented by additional steps.

    Authors: The radiation intensities for guided and surface modes are derived directly from the poles of the Green tensor obtained via the recurrence method. To address this concern, we have revised the relevant section to include an explicit calculation showing that the intensity expressions match the residue contributions from the Green tensor poles. We demonstrate this equivalence by comparing the two approaches for the case of a single-layer waveguide, confirming that no separate ansatz is used. The formulas follow rigorously from the Green tensor construction. revision: yes

Circularity Check

0 steps flagged

No circularity; Green tensor derived from Maxwell equations and boundary matching with independent radiation formulas

full rationale

The derivation begins from the Maxwell equations for the electromagnetic Green tensor in cylindrical geometry, applies boundary conditions at each interface, and constructs the recurrence for arbitrary layers. The resulting expressions for fields and spectral densities of synchrotron-Cherenkov, guided, and surface modes are obtained directly from these solutions without any fitted parameters or self-referential reduction. No step equates a claimed prediction to an input quantity by construction, and the procedure is presented as a standard transfer-matrix technique that remains well-defined outside mode frequencies where residues are extracted separately. The approach is self-contained against external benchmarks such as known limiting cases for homogeneous media.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are stated. The method appears to rely on standard electromagnetic boundary conditions and linear homogeneous media.

pith-pipeline@v0.9.0 · 5504 in / 1075 out tokens · 46772 ms · 2026-05-16T17:08:40.530703+00:00 · methodology

discussion (0)

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