Can we trust AI-assisted technical writing in electromagnetics? characteristic mode analysis for metasurface design as a stress test

1 Introduction

Metasurfaces, consisting of engineered arrays of subwavelength elements on electrically thin surfaces, now serve as a core design paradigm for shaping electromagnetic (EM) waves. By tailoring the local boundary response, metasurfaces can implement functions such as beam steering, focusing, polarization conversion, absorption, and spatial filtering across microwave to optical regimes (Holloway et al., 2012; Achouri and Caloz, 2018; Yu et al., 2011; Achouri et al., 2015).

In antenna engineering, metasurfaces appear as radiating apertures (metasurface antennas), superstrates/lenses, matching layers, and spatially varying reflectors/transmitters. A persistent challenge in metasurface engineering is bridging three design levels that operate on different intuitions: (i) unit-cell physics (often studied under periodic boundary conditions), (ii) finite-aperture coupling and edge effects, and (iii) excitation (feeds, excitation angle, and polarization). While full-wave optimization can address these levels simultaneously, it can be computationally expensive, sensitive to initialization, and may obscure the physical reasons a design succeeds or fails.

CMA, originally developed for conducting bodies (Harrington and Mautz, 1971; Mautz and Harrington, 1971) and later refined into a practical design methodology (Cabedo-Fabres et al., 2007), provides a complementary path. Characteristic mode analysis (CMA) decomposes the induced currents (and associated fields) of a structure into a set of orthogonal modes with well-defined energetic properties. In metasurface antennas and related structures, the response is often dominated by a small subset of modes; CMA can therefore provide a principled way to identify dominant mechanisms, tune geometry to align modal resonances with the operating band, and design feeds that preferentially excites desired modes while suppressing parasitic ones (Salih et al., 2017; Liu et al., 2020).

This tutorial-style review surveys how CMA is used in contemporary metasurface design workflows. The focus is on interpretable design logic, specifically what is computed, how modes are selected and tracked, and how modal quantities are translated into actionable geometry and excitation choices, rather than reproducing every performance number reported in the literature. We emphasize methodological transparency, including solver conventions, normalization, mode tracking, and validation, and provide a minimal reporting checklist intended to improve reproducibility across CMA-guided metasurface studies. Because this manuscript was drafted with AI assistance, we additionally include an explicit citation-verification and self-consistency audit to demonstrate how automated drafting can be combined with domain-expert verification.

1.1 Scope and review methodology

Two objectives are pursued in parallel. First, the manuscript reviews how CMA is used to interpret and guide metasurface design across finite apertures, periodic surfaces, and selected reconfigurable implementations. Second, it evaluates whether AI-assisted drafting can support a technically nuanced review when paired with explicit citation verification and domain-expert editing. To keep those objectives distinct, the article should be read as a narrative review plus a methodological audit of the writing workflow, not as a paper claiming a new antenna, metasurface, or optimization result.

Consistent with that scope, we retain foundational references where they define the classical CMA framework, while adding recent literature where it broadens the design space toward volumetric, strongly coupled, or optimization-driven metastructures. We do not introduce a new numerical case study here; instead, we emphasize transparent interpretation of published results and explicit reporting boundaries for any schematic figures used in the tutorial.

This review is narrative rather than systematic. We conducted a targeted literature scan focused on peer-reviewed applications of CMA to metasurfaces and frequency-selective surfaces. Searches were performed across major publisher platforms using combinations of keywords such as “characteristic mode analysis,” “metasurface antenna,” “frequency selective surface,” “reconfigurable intelligent surface,” and “polarization conversion.” We prioritized works that (i) report modal quantities (eigenvalues λ_n and/or derived metrics), (ii) explicitly link modal behavior to a metasurface function, and (iii) include simulation and/or experimental validation. The cited examples are representative rather than exhaustive, and the tutorial emphasizes transferable design reasoning and reporting practices.

2 Metasurface and CMA fundamentals

This section summarizes the minimum background needed to connect CMA outputs to metasurface design decisions. We first recall common metasurface modeling viewpoints and then summarize the characteristic mode formulation most frequently used in antenna and metasurface practice. Throughout, we state assumptions explicitly because CMA quantities (e.g., eigenvalues and orthogonality) can change meaning when loss or periodic boundary conditions are introduced.

2.1 Metasurface viewpoint

In microwave and antenna contexts, a metasurface can often be modeled as a two-dimensional sheet that enforces an effective relationship between tangential electric and magnetic fields. Depending on regime and design, this relationship may be described using an effective impedance/admittance surface or generalized sheet transition conditions (GSTCs) based on bianisotropic susceptibilities (Holloway et al., 2012)– (Achouri et al., 2015). Practical realizations include periodic or quasi-periodic arrays of patterned conductors (patches, slots, Jerusalem crosses, etc.), sometimes with vias, stacked layers, and tunable components (PIN diodes, varactors), and they may be backed by a ground plane or implemented as a transmissive stack.

2.2 CMA for conducting bodies

For a perfect electric conductor (PEC) discretized with the method of moments (MoM), the impedance matrix is written as Z = R + jX, where R and X are the real (radiation) and imaginary (reactive) parts of Z, respectively. Characteristic currents {J n} are obtained from the generalized eigenvalue problem X, J n = λ n R J n (Harrington and Mautz, 1971; Mautz and Harrington, 1971). For lossless PEC formulations, λ n are real and provide a frequency-dependent modal portrait: which current patterns can exist on the structure and whether each pattern is predominantly storing or radiating energy. The sign and magnitude of λ n indicate inductive (λ n > 0) or capacitive (λ n < 0) tendency and the distance from self-resonance (λ n = 0).

Several scalar quantities derived from characteristic modes are routinely used in metasurface design; the most common metrics and their interpretations are summarized in Table 1. A widely used measure is the modal significance M S n = 1 1 + j λ n , which ranges from 0 to 1 and peaks near unity as λ n → 0. The contribution of multiple modes across frequency is conceptually illustrated by representative modal significance curves in Figure 1. The characteristic angle α n is another derived quantity; under one common convention, α n = 180 ° − ⁡ tan − 1 ⁡ λ n, so that α n crosses 180° at resonance. Because normalizations and angle conventions vary across implementations, it is good practice to report (λ n , M S n , α n together and to state the solver, boundary conditions, and normalization choice (Cabedo-Fabres et al., 2007; Gustafsson et al., 2022b). This design logic is often implemented as an iterative workflow linking modal analysis, geometry tuning, and excitation design, as illustrated in Figure 2.

TABLE 1. Key CMA quantities used in metasurface design (definitions are solver-dependent).

Many metasurface problems involve conductive and dielectric loss, multilayers, and periodic environments, for which the classical PEC/MoM assumptions do not strictly hold. Recent work has clarified how characteristic modes can be defined more generally using transition-matrix formulations and other generalizations, and how modal tracking and losses can affect orthogonality and interpretation (Gustafsson et al., 2022a; Gustafsson et al., 2022b). These distinctions are practically important for absorptive metasurfaces, dielectric-loaded metasurface antennas, and unit-cell analyses performed with periodic boundary conditions.

3 From characteristic modes to metasurface functionality

The central design question is: how does a set of characteristic modes translate into a metasurface function such as a desired phase profile, polarization response, or aperture field distribution? A useful answer is to treat CMA as a physics prior. CMA identifies a small basis of candidate current patterns; the designer then (i) tunes which modes are accessible and strongly participating in-band and (ii) engineered excitation to control the modal weights.

3.1 Modal expansion and excitation

In many CMA implementations, the induced current (or equivalent surface current) can be approximated by a truncated modal expansion J ≈ ∑ n a n J n. The coefficients a n depend on the excitation (feed, port, or incident field) and on the solver’s normalization; under a common R-orthonormalization, a typical weighting scales as a n ∝ J n , V 1 + j λ n , where V represents the excitation in the MoM system (Harrington and Mautz, 1971; Cabedo-Fabres et al., 2007). This expression makes explicit why modes with M S n ≈ 1 are more readily excited and why feed placement/polarization determines which modes contribute.

3.2 Mode selection and tuning

Useful metasurface behavior often requires two or more modes with distinct symmetries or field types to be simultaneously accessible. Broadband radiation or wideband phase control, for example, can benefit from multiple modes with high modal significance across adjacent frequency regions. Geometric perturbations (slotting, truncation, adding vias, changing periodicity, adding resistive or reactive loading) can move modal resonances, split degenerate modes, or alter current distributions, thereby changing the achievable scattering/radiation response.

3.3 Excitation engineering

A practical advantage of CMA is the conceptual separation between what the structure can support (its modes) and what a given excitation drives (modal weights). For metasurface antennas, this separation supports systematic feed placement: a feed that overlaps strongly with the desired mode’s current distribution (and minimally with parasitic modes) tends to yield cleaner radiation and more predictable tuning behavior. For illuminated metasurfaces (reflectarrays, transmitarrays, RIS), the incident polarization and angle act as the excitation, so CMA can be used to diagnose which modes couple to a given excitation and which symmetries must be broken to enable the target response.

The same caution becomes even more important for multilayer or volumetric metamaterials. In those structures, useful behavior may arise from strong near-field coupling among electric and magnetic resonators distributed across multiple layers or throughout a three-dimensional lattice. A purely local or two-dimensional periodic modal picture may then miss global current pathways, interlayer hybridization, and edge-mediated coupling. In such cases, CMA remains valuable as a reduced-order descriptor of dominant current families, but it is often most reliable when paired with full-object analysis, supercell modeling, or other global optimization loops that preserve the finite 3D geometry and excitation environment (Dobrykh et al., 2025; Mikhailovskaya et al., 2022).

3.4 Periodic versus finite-aperture views

A recurring pitfall is assuming that a unit-cell (periodic) analysis fully predicts the behavior of a finite metasurface. Periodic CMA or Floquet-based unit-cell characterization is valuable for identifying local resonances and for designing target reflection/transmission phase responses. However, finite apertures introduce edge diffraction, non-uniform excitation, mutual coupling variations, and truncated periodicity effects that can shift modal content and bandwidth. When possible, periodic insights should therefore be validated by finite-aperture analysis (full metasurface or sufficiently large supercell) and by checking whether the same dominant modes persist under realistic excitation.

4 Applications in metasurface design

We now organize CMA applications in metasurface design into four recurring roles: (A) diagnosing dominant physics (which currents and resonances matter), (B) shaping bandwidth and patterns by multi-mode control, (C) enabling reconfigurability by understanding modal trajectories across states, and (D) reducing design iteration by providing interpretable 'feed and perturbation’ guidance.

4.1 Metasurface antennas and radiating apertures

Metasurface antennas (MTS antennas) use a patterned surface as the primary radiating aperture or as a coupled radiating layer. A common objective is to achieve wide impedance bandwidth and stable radiation characteristics in a low-profile form factor. In this class, CMA is frequently used to identify which surface-supported modes are responsible for radiation and to choose feed configurations and perturbations that excite the desired combination of modes. Table 2 summarizes how common metasurface design objectives map to the corresponding CMA cues and practical design levers.

TABLE 2. Mapping from common metasurface objectives to CMA cues and design levers (conceptual).

Representative examples include metasurface-based suppression of higher-order modes in closely spaced arrays (Salih et al., 2017) and CMA-guided suppression of unwanted modes in multiport metasurface antennas (Lin and Chen, 2018). CMA has also been used to design dual-band metasurface antennas by ensuring that two suitable modes are strongly radiating in two distinct bands (Li and Chen, 2018). At higher frequencies, CMA-guided metasurface antenna arrays have been demonstrated for Ka-band with attention to sidelobe control and aperture efficiency (Li and Chen, 2020).

CMA can also provide a compact explanation of bandwidth enhancement mechanisms that arise from coexisting resonance types. For example, an L-probe fed finite metasurface can excite both a TM leaky-wave resonance and a TE surface-wave resonance, producing broadband behavior in a low-profile design; CMA helps interpret such behavior in terms of modal coexistence and coupling (Liu et al., 2020).

4.2 Polarization conversion and wave transformation

Many metasurfaces implement polarization conversion (linear-to-linear cross-polarization, linear-to-circular, or other transformations). CMA supports this by identifying modal current symmetries and their relative phases under excitation. In an intuitive modal picture, polarization conversion occurs when two modes with suitable orthogonality and phase relationship are excited with comparable strength, producing a scattered field with a rotated or converted polarization state.

An example of CMA used as a mechanism-level explanation for polarization conversion metasurfaces is reported in Guo et al. (2023), where characteristic modes are used to interpret when cross-polarized reflected fields arise under plane-wave excitation. CMA has also guided the design of metasurface antennas that incorporate polarization conversion behavior by tuning and combining modes of the metasurface layer (Dong et al., 2022).

4.3 Periodic metasurfaces and frequency-selective surfaces

Periodic metasurfaces and frequency-selective surfaces (FSS). FSS and related periodic metasurfaces can be viewed as spatial filters whose reflection/transmission depend on frequency, angle, and polarization. In these designs, CMA can be applied in a periodic setting to reveal which resonances control the spectral response and how loading (resistors, diodes) changes those resonances.

A concrete example is the characteristic mode analysis of resistor-loaded FSS using a periodic moment method with experimental verification (Zha et al., 2021). In that work, changing resistance shifts and damps modal resonances, which can be interpreted via changes in modal trajectories and reflection phase behavior. More generally, characteristic modes of periodic systems can be extracted from scattering (S-parameter) data (Schab et al., 2023), enabling mode computation from generic solvers or measurements and making CMA more accessible for periodic metasurface design.

4.4 Reconfigurable intelligent surfaces and switchable metasurfaces

Reconfigurable intelligent surfaces (RIS) and switchable metasurfaces. RIS platforms often require discrete phase states (e.g., 1-bit, 2-bit) with acceptable amplitude while maintaining manufacturability and biasing feasibility. CMA is useful here as a structured way to explain how switching elements alter the effective resonant behavior and to guide geometry modifications that increase phase separation between states. This concept of mode-dependent phase tuning across switching states is illustrated schematically in Figure 3. For scattering-maximization problems, an additional concept is resonance cascading: several nearby resonances are intentionally arranged so that electric and magnetic multipoles interfere constructively over the band of interest, increasing the effective scattering response without relying on a single narrow resonance. Recent work on superradiant scattering limits, meta-learning-assisted magneto-electric arrays, and evolutionarily designed 3D metamaterials shows that such responses can emerge from strongly coupled multilayer or volumetric meta-atoms optimized with global search methods rather than from simple planar unit-cell tuning alone (Dobrykh et al., 2025; Mikhailovskaya et al., 2022).

Mechanistically, this broadband scattering enhancement does not come from maximizing a single isolated resonance. Instead, the geometry, layer spacing, and reactive loading are adjusted so that several neighboring electric and magnetic modes become spectrally adjacent and remain excitable under the same illumination. As one mode begins to detune, another starts to contribute with a compatible phase and far-field symmetry, so the summed response stays strong over a wider band. In CMA terms, the desired condition is a cluster of nearby modes with appreciable modal significance and compatible excitation-dependent weighting coefficients, which together sustain constructive overlap rather than a single narrow peak.

For instance, Fazal and Hong (2023) presents a 2-bit reflective metasurface unit-cell design in which the symmetry and trajectories of characteristic modal currents are used to motivate slotting and via loading that improve phase coverage across switching states. Even when a final design is validated with periodic (Floquet) simulations, CMA can reduce trial-and-error by indicating which geometric regions are most influential for moving a particular mode.

4.5 Scattering control and absorption

Scattering control and absorption. Beyond antennas and beamforming apertures, CMA is valuable for metasurfaces designed for absorption or for controlling radar cross section (RCS). In absorptive periodic surfaces and rasorbers, loss is intentional; characteristic modes help clarify which current paths store energy versus dissipate it, and how resistor placement and value influence bandwidth and angular stability. The resistor-loaded FSS study in Zha et al. (2021) is one example where modal analysis supports such interpretations. For scattering enhancement, the same modal logic can be used in the opposite direction: resonance cascading deliberately places several nearby electric and magnetic resonances so that their phases combine constructively over the band of interest, thereby increasing effective backscattering or radar visibility instead of relying on a single narrow resonance. In multilayer or volumetric meta-atoms, such behavior is usually governed by strong near-field coupling and is therefore most reliably designed with full-object or globally optimized models rather than by planar unit-cell tuning alone (Dobrykh et al., 2025; Mikhailovskaya et al., 2022).

As a brief case study, the superradiant broadband magnetoelectric array in Mikhailovskaya et al. (2025) shows how optimization can discover a strongly coupled configuration whose electric and magnetic current families overlap spectrally and radiate with compatible phases, thereby sustaining enhanced scattering over a broader band than a single isolated resonance would allow. The evolutionarily designed 3D metamaterials in Dobrykh et al. (2025) provide a related volumetric example of the same principle, while (Mikhailovskaya et al., 2022) supplies the physical interpretation through the superradiant scattering limit for arrays of subwavelength scatterers. Read together, these studies make the resonance-cascading argument concrete: bandwidth is enlarged by engineering several nearby resonances to cooperate rather than by sharpening one peak.

Representative examples of how CMA has been applied across metasurface classes are summarized in Table 3.

TABLE 3. Representative examples of CMA used in metasurface design (selected; not exhaustive).

5 Practical considerations

5.1 Practical considerations and common pitfalls

CMA results are only as useful as their interpretation and their numerical reliability. The issues below occur frequently in metasurface publications and can materially change design conclusions if not reported transparently:

• Mode tracking and degeneracy: Many metasurface geometries exhibit closely spaced or degenerate modes. Across frequency, eigenvalue crossings and mode swapping can occur; without robust tracking, plots of M S n or α n may inadvertently stitch together different physical modes. Authors should describe how modes were tracked (e.g., correlation of currents/fields between frequency samples) and should comment on any degeneracy or symmetry-driven mode pairing. The unified theory and tracking discussions in Gustafsson et al. (2022a), Gustafsson et al. (2022b) are relevant when CMA is used as a design loop rather than as a one-off diagnostic.
• Periodic versus finite structures: Unit-cell CMA (periodic) can be misleading when finite-aperture coupling, edge diffraction, or feed non-uniformity dominate performance. If unit-cell CMA is used to justify a finite-aperture design, the manuscript should state the boundary conditions (Floquet phase shifts, incidence angle), clarify the link to the finite structure, and provide at least one finite-aperture validation (simulation or measurement).
• Loss modeling and interpretation: In lossy structures, classic orthogonality properties of characteristic modes can break down and eigenvalues may become complex, altering the meaning of M S n and α n (Gustafsson et al., 2022a; Gustafsson et al., 2022b). Authors should state what loss mechanisms are included (conductor loss, dielectric loss tangent, lumped element loss) and explain how modal quantities were computed and interpreted under loss. This is not a failure of CMA; it is a reminder that the assumptions behind a metric must match the physics of the metasurface (e.g., absorbers versus radiators) (Gustafsson et al., 2022b).
• Reporting for reproducibility and validation: Commercial tools differ in normalization, characteristic-angle conventions, and in the default definition of “modal significance.” To support reproducibility, authors should report: the solver and formulation (MoM, FEM, integral equation type), boundary conditions (open, periodic/Floquet), frequency sampling, number of modes retained, mesh settings, normalization conventions, and the definition of each reported modal metric (λ n , M S n , α n). Validation should include at least one cross-check that modal interpretations match observable quantities, e.g., that predicted dominant modes correlate with port patterns, far-field behavior, or S-parameter features in a full-wave model or measurement.
• Scope boundaries and evidence level: When a manuscript combines a technical review with a methodological discussion about AI-assisted writing, the scope should be stated explicitly so readers can distinguish between tutorial synthesis and original research claims. For the present article, the synthetic figures are intended only as conceptual visualizations of modal behavior. They should not be interpreted as substitutes for full-wave simulation, measurement, or benchmarked case studies, which remain necessary when claiming a new metasurface performance result.

6 Conclusion

CMA has become a practical tool for metasurface design because it offers an interpretable basis of current/field mechanisms that complement unit-cell parameter retrieval and brute-force optimization. When used with careful mode tracking, explicit reporting of solver conventions, and validation against full-wave results, CMA can help designers understand bandwidth limits, identify parasitic mechanisms, and engineer excitation to realize metasurface functions such as radiation control and polarization conversion. Ongoing progress in generalized CMA formulations and in extracting characteristic modes from scattering data broadens the range of metasurface problems where modal thinking can provide actionable design guidance (Gustafsson et al., 2022a; Gustafsson et al., 2022b; Schab et al., 2023). Future work is likely to expand robust CMA formulations for lossy, dispersive, and strongly coupled periodic structures, and to establish community benchmarking and reporting practices that make CMA-guided metasurface designs more reproducible across solvers and laboratories. Looking forward, one promising direction is to combine CMA-based physical interpretability with global optimization tools such as genetic algorithms, covariance-matrix adaptation evolution strategies, and related learning-assisted search methods, especially for multilayer or volumetric scatterers where constructive interference among several resonances can be designed rather than guessed (Dobrykh et al., 2025; Mikhailovskaya et al., 2022).

As concrete examples, (Dobrykh et al., 2025) uses a covariance-matrix adaptation evolution strategy (CMA-ES) to design 3D metamaterials for broadband scattering maximization, whereas (Mikhailovskaya et al., 2025) presents a meta-learning-empowered evolutionary optimization of superradiant magnetoelectric arrays; interpreted together with the superradiant scattering limit in Mikhailovskaya et al. (2022), these examples show how global search can intentionally align several nearby electric and magnetic resonances so that their modal contributions remain constructively phased over a broader operating band. This explicit linkage clarifies the statement above about genetic/evolutionary and learning-assisted optimization methods, and why they are especially valuable for multilayer or volumetric scatterers whose current pathways are strongly coupled and difficult to tune by intuition alone.

7 AI-generated review stress test: what to trust

Can we trust AI-assisted drafting in engineering reviews? This manuscript was first drafted and then reviewed with AI assistance followed by editing by both authors to evaluate a narrow but practically relevant capability: producing a coherent tutorial/review on a technically nuanced topic while avoiding fabricated citations and internal inconsistencies. This should not be interpreted as evidence that AI replaces domain experts. Instead, it motivates a workflow in which AI accelerates early drafting while domain experts retain responsibility for technical correctness, scope control, and claim-to-citation alignment. In that sense, the contribution is methodological rather than experimental: the paper does not claim a new electromagnetic device or a new benchmark simulation, but instead documents how a review manuscript can be technically checked, delimited, and updated when AI is used in the drafting stage.

For technical review writing, the highest-risk failure modes remain (i) hallucinated or incorrect references, (ii) correct references but incorrect attribution of claims, and (iii) subtle technical inconsistencies (e.g., conflating periodic unit-cell results with finite-aperture behavior without qualification). Accordingly, this manuscript includes an explicit audit that (a) verifies each reference entry against external metadata, and (b) checks key equations, symbol definitions, and cross-section consistency. We recommend that AI-assisted reviews adopt a similar “trust but verify” protocol and that authors document what was verified and what remains interpretive.

Generative AI statement

The author(s) declared that generative AI was used in the creation of this manuscript. The authors acknowledge institutional access that supported the use of GPT-5.2 for initial drafting. The authors remain solely responsible for the scientific content, verification, and final editorial decisions.

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Footnotes

Edited by: Mohamed Latrach, École Supérieure d'Electronique de l'Ouest, France

Reviewed by: Anna Mikhailovskaya, Tel Aviv University, Israel

Juventino Lopez, TECNM Instituto Tecnologico de Queretaro, Mexico