Hamiltonian formulation of coupled-mode theory in waveguiding structures
Bibliographic record
Abstract
We present a Hamiltonian formulation of coupled mode theory for scenarios in which the coupled modes are associated with different "parent structures," such as two nearby waveguides. The relativistic nature of the photon leads to the complication that not any set of orthonormal modes can be used as a basis if the associated amplitudes are to satisfy canonical commutation relations. This difficulty is circumvented by the introduction of "dressed parent modes," which are in fact seen to be the "coupled modes" of the system. While an exact solution of the linear problem within the restricted basis of interest formally must be found before these modes can be constructed, in practice they can be constructed directly from the modes of the parent structures. The approach can be applied to periodic parent structures, such as photonic crystal waveguiding structures, as well as to simpler waveguides. We illustrate the accuracy of the various approximations employed by studying two sample systems in detail. We derive the linear coupled mode equations, and show how the approach can be immediately generalized from the linear regime to treat problems in nonlinear quantum optics.
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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".