Statistics of Anderson-localized modes in disordered photonic crystal slab waveguides
Bibliographic record
Abstract
We present a fully three-dimensional Bloch mode expansion technique and a photon Green function formalism to compute the quality factors, mode volumes, and Purcell enhancement distributions of a disordered W1 photonic crystal slab waveguide in the slow-light Anderson-localization regime. By considering fabrication (intrinsic) and intentional (extrinsic) disorder we find that the Purcell enhancement statistics are well described by log-normal distributions without any fitting parameters. We also compare directly the effects of hole size fluctuations as well as fluctuations in the hole position. The functional dependence of the mean and standard deviation of the quality factor and Purcell enhancement distributions is found to decrease exponentially with the square root of the extrinsic disorder parameter. The strong coupling probability between a single quantum dot and an Anderson-localized mode is numerically computed and found to exponentially decrease with the squared extrinsic disorder parameter, where low disordered systems give rise to larger probabilities when state-of-the-art quantum dots are considered. The optimal spatial regions to position quantum dots in the W1 waveguide are also discussed. These theoretical results are fundamentally interesting for disordered photonics and connect to recent experimental works on photonic crystal slab waveguides in the slow-light regime. Our three-dimensional slab results also contradict some previous findings that use simpler two-dimensional models to understand these complex planar systems.
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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".