Confined modes in finite-size photonic crystals
Bibliographic record
Abstract
The real band structure of finite-size photonic crystals (PCs) is different from the band structure of infinite PCs derived using Bloch's theorem. There are isolated instead of a continuum of modes around a band edge. We use the envelope function approximation (EFA) method to derive simple formulas to describe the frequency and field pattern of the modes in finite-size PCs. The results are compared with those from finite-difference time-domain (FDTD) method. We observe that the agreement between the results from EFA with a vanishing boundary condition and FDTD is sensitive to the boundary orientation. In addition, although a simple group-velocity-based analysis explains the long lifetime of the confined modes, this explanation is inappropriate for certain structures. In particular, we find boundary orientations, for which the lifetime of the confined modes can be enhanced by orders of magnitude compared with that anticipated from group velocity analysis. We explain this by total internal reflection. Our results demonstrate the utility of the EFA approach in studying the modes in finite-size PCs and reveal the importance of boundary conditions to develop an EFA-based tool for cavity lasers and for studying nonlinear interactions.
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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 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| 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) | 0.001 | 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 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".