Theoretical analysis of band gap formation in rotationally symmetric 2D photonic quasicrystal using rotational symmetry arguments
Bibliographic record
Abstract
The key feature that gives photonic crystals (PhCs) their ability to form a photonic band structure (PBS) is their translational symmetry. Structures that do not have translational symmetries also have a PBS. One explanation as to how these structures generate a PBS involves long-range interactions resulting in fractal dispersion relations (e.g. 1-D quasi-crystals, Fibonacci layers, etc.) However, long-range interactions do not fully explain why 2-D quasi-crystals structures also exhibit a PBS. This paper proposes an explanation for such results: by applying rotation operators from the SO(2) group to 1-D quasi-crystal dispersion relations. This process mimics the way electronic state amplitudes are calculated when such states have an angular dependence. Simulations results are presented in this paper.
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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) | 0.000 | 0.001 |
| 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".