Modal Analysis and Wave Propagation in Finite 2D Transmission-Line Metamaterials
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Bibliographic record
Abstract
In this paper we examine the propagation of plane waves and Gaussian beams in 2D periodic grids constructed with lumped reactive immitances. We demonstrate the equivalence between the Bloch/Floquet modal description and the multiple coupled-line modal analysis of finite-sized periodic grids. This establishes that the Floquet analysis of 2D metamaterial negative-refractive-index grids and the associated exotic wave propagation/refraction/focusing phenomena, can be deduced from traditional analysis of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> coupled lines (and hence <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> eigenmodes), albeit with considerable algebraic complexity. We present simulation results of Gaussian beams through these grids to demonstrate that they can be analyzed using simple geometrical optics along with the index of refraction associated with Bloch/Floquet analysis.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
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 it