On the limitations of the first-order nonlinear Schrödinger equation in slow-light photonic crystal structures
Bibliographic record
Abstract
We investigate the limitations of the first-order nonlinear Schrödinger equation for describing slow-light enhanced optical nonlinearities in photonic crystal structures. We do this by introducing the concept of generalized Bloch modes to describe light propagation in nonlinear photonic crystal structures. By considering how the nonlinear effects perturb the eigenproblem that describes such generalized Bloch modes, we derive a formalism that allows us to determine the impact of nonlinearities up to an arbitrary order. Based on our formalism, we derive expressions for the first- and second-order nonlinear terms experienced by a single generalized Bloch mode. We then theoretically demonstrate that the second-order terms can in silicon-based slow-light photonic crystal waveguides already become significant at optical powers as small as 100 mW. Additionally, we show that the significance of the second-order term is closely related with the structural group index dispersion or second-order dispersion parameter of the structures considered.
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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 | 0.002 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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".