Bibliographic record
Abstract
Inspired by the envelope approximation commonly applied to semiconductor heterostruc-tures, an analytical approach to study photonic crystal waveguides is presented. By treating the waveguide core as a slowly-varying perturbation in the cladding photonic crystal, mul-tiple scales analysis is used to derive an envelope equation which solves for the propagation constants and frequencies of the guided modes. The envelope approximation is completely general for sufficiently weak perturbations and applies to photonic crystal waveguides of any dimensionality. The multiple scales approach is verified through comparisons between the envelope ap-proximation and results from full numerical simulations. Heterostructure slab waveguides in three dimensional photonic crystal and a slab waveguide with a homogeneous dielectric core surrounded by photonic crystal cladding are studied. The mode shapes are in excel-lent agreement with simulations. The computed waveguide dispersion relations agree with simulated results to 1%. The implications and limitations of the envelope approximation are discussed and quan-
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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 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.003 | 0.001 |
| Scholarly communication | 0.003 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.494 | 0.155 |
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; the direct Gemma label and the distilled Codex classifier agree on what is shown here.
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".