Approach to the analysis and synthesis of cylindrical metasurfaces with noncircular cross sections based on conformal transformations
Bibliographic record
Abstract
We present methods for analyzing and designing cylindrical electromagnetic metasurfaces with noncircular cross sections based on conformal transformations. It can be difficult to treat surfaces with noncanonical geometries since they generally do not admit straightforward solutions to the Helmholtz wave equation subject to the appropriate boundary conditions. This leads to the reliance on full wave numerical techniques which are only suitable for the analysis, but not the synthesis, of these surfaces. We address this issue by employing conformal transformations to map the physical space into a computational space in which the surface coincides with a circular cylinder. The electromagnetic boundary conditions on the surface remain intact under the transformations due to their angle-preserving nature. However, they are much more easily enforced. As a result, analytical modal solutions for the scattered fields are readily obtainable, which facilitates closed-form analysis and synthesis equations for general noncircular cylindrical metasurfaces. One important utility enabled by the proposed framework is the efficient identification of electromagnetic field distributions that satisfy local power conservation. This leads to passive and lossless surface designs, which are highly desirable in practice as they do not require active and/or lossy components.
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How this classification was reachedexpand
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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".