Complex Eigenmodes and Eigenfrequencies in Electromagnetics
Bibliographic record
Abstract
A comprehensive treatment on complex eigenmodes is presented for general lossy traveling-wave electromagnetic structures. The per unit length propagation phase shift ( β)-dependent complex eigenfrequencies Ω(β) are mapped to frequency-dependent complex propagation constant γ(ω0) for a variety of electromagnetic structures. Rigorous procedures are presented to compute the complex eigenmodes of both uniform and periodic electromagnetic structures, confirmed using full-wave simulations and known analytical results. We further present two mapping procedures for arbitrary uniform and periodic structures, where the known {Ω-β} relationship is expressed using rational polynomial expansions. Consequently, replacing {Ω, jβ} with {ω0, γ} in the known {Ω-β} relation, a characteristic equation is formed, which is then numerically solved for the propagation constant γ, representing the physical dispersion relation ω0(β) and the frequency-dependent attenuation relation α(ω0) of the structure. The mapping procedure is demonstrated for a variety of cases, including an unbounded uniform media, a rectangular waveguide, a Drude dispersive metamaterial, a biased ferrite medium, a periodic dielectric stack, and a periodic rectangular waveguide. The exact propagation characteristics have been successfully retrieved in all cases across both passbands and stopbands across frequency.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.007 | 0.003 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".