Variational Analysis of a Dually Polarized Waveguide Skew Loaded by Dielectric Slab
Bibliographic record
Abstract
An expression for the propagation constant, cutoff frequency, and associated fields of the first two modes in a waveguide filled with a tilted slab of the dielectric is derived using the variational analysis. The solution to such a problem is divided into two parts. First, the slab is assumed to be parallel with the walls of the waveguide with no tilt. In this part, the effective permittivities of the first two orthogonally polarized modes are derived from two different variational expressions for the transversal resonance frequencies. This results in a diagonal tensorial permittivity that represents an effective uniaxial anisotropic medium. Next, this tensorial permittivity is transformed into a tilted set of coordinates representing the required tilt angle. In the new set of coordinates, a variational expression for the propagation constant is solved using the Rayleigh-Ritz procedure. The resulting analytic expressions are verified using a full-wave analysis and a prototype measurement.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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) | 0.000 | 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".