Application of the Flexible Local Approximation Method to photonic crystal cavities
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Bibliographic record
Abstract
This thesis investigates the application of a recently developed numerical technique, the Flexible Local Approximation Method (FLAME) to compute the resonances of 2D photonic crystal (PC) cavities, formed by a defect in a regular array of dielectric rods. FLAME is a finite-difference-like method which is ideally suited to problems consisting of large numbers of identical structures. The anisotropic perfectly matched layer (PML) is used as an artificial absorbing layer to truncate the computational domain. The parameters of the PML are chosen carefully to provide adequate absorption without a large computational cost. FLAME method and PML boundaries are applied to cavities with 3x3, 5x5 and 7x7 arrays of rods. The resonant modes, field distribution, and quality factor are computed and compared with previously-published results. Good agreement is obtained. However, the matrix eigenproblem generated by FLAME is of a kind for which sparse-matrix algorithms are not available and dense-matrix software had to be used. This limitation will have to be overcome if FLAME is to be widely used for PC cavities.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 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 it