What is the Brillouin zone of an anisotropic photonic crystal?
Bibliographic record
Abstract
The authors discuss the concept of the Brillouin zone, central to many fields of condensed matter physics. They challenge the universality of defining the Brillouin zone as a Wigner-Seitz cell of the reciprocal lattice. Experimental measurements of terahertz phonon-polariton dispersion in a photonic crystal fabricated in a thin slab of an anisotropic material (lithium niobate) demonstrate that the lowest band gap does not form at the boundary of the conventionally defined Brillouin zone, in contrast to a similar photonic crystal fabricated in a nearly isotropic lithium tantalate. The analysis motivated by this unexpected experimental result shows that in an anisotropic photonic crystal the Wigner-Seitz cell of the reciprocal lattice is no longer bounded by Bragg planes and, consequently, does not conform to the original definition of the Brillouin zone. The authors construct an alternative Brillouin zone bounded by the Bragg planes and show its utility in analyzing the dispersion bands of anisotropic photonic crystals.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), 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".