Nonlinear optical interactions of wave packets in photonic crystals: Hamiltonian dynamics of effective fields
Bibliographic record
Abstract
We develop an effective-field formalism that is suitable for describing nonlinear interactions of multiple wave packets in photonic crystals of arbitrary dimensionality. The theory is valid for "high-contrast" variations of the refractive index in the photonic crystal, provided dispersion and absorption effects can be neglected; it is based on a Hamiltonian formulation of the underlying Maxwell equations. We show that the dynamical equations for the effective fields are similar to those commonly used in nonlinear optics of homogeneous media, but with coefficients determined from the photonic band structure. We can introduce an effective energy density and an effective Poynting vector, expressed in terms of the effective fields, that satisfy a continuity equation. We illustrate our approach with a solution of the problem of degenerate optical parametric amplification in the undepleted pump approximation, and by considering the linear electro-optic effect as a quadratic nonlinear optical process.
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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) | 0.000 | 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".